Explanation:
Formula for centripetal acceleration of an object is as follows.
a = [tex]\frac{v^{2}}{r}[/tex]
When an object is travelling in a circular path then it is difficult to measure its velocity.
Hence, for a circular object the formula for acceleration is as follows.
a = [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex]
a = [tex]\frac{V^{2}}{r}[/tex], and V = [tex]\frac{d}{T} = \frac{2 \pi r}{T}[/tex]
a = [tex]\frac{(\frac{[2\pi r]}{T})^{2}}{r}[/tex]
= [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex]
Thus, we can conclude that the magnitude of the acceleration of the toy is [tex]\frac{4 \pi^{2} r}{T^{2}}[/tex].
A car accelerates uniformly from rest to 20 m/sec in 5.6 sec along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 9,000 N, and (b) the weight of the car is 14,000 N.
Answer:
(a) [tex]P=33000W[/tex]
(b) [tex]P=51000W[/tex]
Explanation:
The average power is defined as the amount of work done during a time interval:
[tex]P=\frac{W}{t}(1)[/tex]
According to work-energy theorem, the work done is equal to the change in kinetic energy. So, we have:
[tex]W=\Delta K\\W=K_f-K_0\\W=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}\\(2)[/tex]
Recall that the weight is given by:
[tex]w=mg\\m=\frac{w}{g}(3)[/tex]
The car accelerates uniformly from rest ([tex]v_0=0[/tex]). Replacing (3) in (2), we have:
[tex]W=\frac{wv_f^2}{2g}[/tex]
(a) Finally, we replace this in (1):
[tex]P=\frac{wv_f^2}{2gt}\\P=\frac{9000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=33000W[/tex]
(b)
[tex]P=\frac{14000N(20\frac{m}{s})^2}{2(9.8\frac{m}{s^2})(5.6s)}\\P=51000W[/tex]
(a) The average power required to accelerate the car of 9000 N is 32798.57 W.
(b) The average power required to accelerate the car of 14,000 N is 51020.40 W.
Given data:
The initial velocity of car is, u = 0 m/s. (Since car was initially at rest)
The final velocity of car is, v = 20 m/s.
The time interval is, t = 5.6 s.
The given problem is based on the concept of average power. The average power is defined as the amount of work done during a time interval. Then,
P = W/t
Here, W is the work done and its value is obtained from the work - energy theorem as,
[tex]W = \Delta KE\\\\W = \dfrac{1}{2}m(v^{2}-u^{2})[/tex]
Here, m is the mass.
(a)
For the weight of 9000 N, the mass of car is,
[tex]w = mg\\\\9000 = m \times 9.8\\\\m =918.36 \;\rm kg[/tex]
So, the Work is obtained as,
[tex]W =\dfrac{1}{2} \times 918.36 \times (20^{2}-0^{2})\\\\W =183672\;\rm J[/tex]
Then, the average power required to accelerate the car is,
P = W/t
P = 183672 / 5.6
P = 32798.57 W
Thus, we can conclude that the average power required to accelerate the car of 9000 N is 32798.57 W.
(b)
For the weight of 14,000 N, the mass of car is,
[tex]w = mg\\\\14,000 = m \times 9.8\\\\m =1428.57 \;\rm kg[/tex]
So, the Work is obtained as,
[tex]W =\dfrac{1}{2} \times 1428.57.36 \times (20^{2}-0^{2})\\\\W =285714.28\;\rm J[/tex]
Then, the average power required to accelerate the car is,
P = W/t
P = 285714.28 / 5.6
P = 51020.40 W
Thus, we can conclude that the average power required to accelerate the car of 14,000 N is 51020.40 W.
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A stretched rubber band has ___________ energy. a. elastic kinetic energy b. gravitational potential energy c. elastic potential energy d. gravitational potential energy
Answer: Option (c) is the correct answer.
Explanation:
An elastic object is defined as the object that is able to retain its shape when a force is applied on it.
For example, when we pull a rubber band then it stretches and when we withdraw the force applied on it then it retain its shape.
As we know that potential energy is the energy obtained by an object due to its position.
So, when we stretch a rubber band then it will have elastic potential energy as position of the rubber band is changing and since, it will retain it shape hence it has elastic potential energy.
Thus, we can conclude that a stretched rubber band has elastic potential energy.
A stretched rubber band has elastic potential energy. Option C
What is elastic potential energy?A rubber band that has been stretched holds elastic potential energy. The energy held in an object when it is stretched or distorted is known as elastic potential energy. The deformation of a rubber band's molecular structure causes it to gain potential energy when it is stretched.
Rubber bands are comprised of materials that are elastic and can be stretched before snapping back into place. Stretching the rubber band causes its structure to distort and its molecular structure to store potential energy. This potential energy is turned into kinetic energy when the rubber band is released, causing it to rebound and return to its original shape.
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A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 50 ft from the base of the pole?
To find the speed of the tip of the woman's shadow, we use related rates and the similarities of triangles. The rate at which the shadow tip moves is found by setting up a proportion based on similar triangles and differentiating with respect to time. The result is that the tip of the shadow moves at 10.67 ft/sec when the woman is 50 ft from the light pole.
The question is about a real-world application of related rates, which is a concept in calculus where one rate is determined based on another rate. In this scenario, we have a woman walking away from a light pole, and we need to find out how fast the tip of her shadow is moving. To solve it, we use the similarities of triangles created by the woman and the light pole with their respective shadows.
Let's let the height of the light pole be P (16 ft), the height of the woman be W (6 ft), the distance of the woman from the pole be w (50 ft), and the distance of the tip of her shadow from the pole be s. We will use the fact that the ratios P/s and W/(s-w) are equal because the triangles are similar. Setting up the proportions, after some algebra, we find that ds/dt (the rate at which the tip of the shadow moves) is a function of dw/dt (the rate at which the woman walks).
By differentiating both sides of the proportion with respect to time t, applying the chain rule, and plugging in the known values, we can solve for ds/dt as follows:
ds/dt = P/W * dw/dt * (s/w) = (16/6) * 4 * (50/50) = 64/6 = 10.67 ft/sec
The tip of her shadow is moving along the ground at a rate of [tex]\frac{1600}{61}\) ft/sec[/tex] when she is 50 ft from the base of the pole
To solve this problem, we can use similar triangles to relate the woman's height to the height of the street light and their respective shadows. Let [tex]\(x\)[/tex] be the distance from the woman to the pole, [tex]\(s\)[/tex] be the length of her shadow, and [tex]\(h = 16\)[/tex] ft be the height of the street light. The woman's height is [tex]\(w = 6\) ft.[/tex] At any given moment, the triangles formed by the woman and her shadow and the street light and the woman's shadow are similar. Therefore, we have the proportion:
[tex]\[\frac{h}{w} = \frac{h + s}{x}\][/tex]
We can solve for [tex]\(s\):[/tex]
[tex]\[h \cdot x = w \cdot (h + s)\][/tex]
[tex]\[h \cdot x = w \cdot h + w \cdot s\][/tex]
[tex]\[h \cdot x - w \cdot h = w \cdot s\][/tex]
[tex]\[s = \frac{h \cdot x - w \cdot h}{w}\][/tex]
Now, we want to find the rate at which [tex]\(s\)[/tex] is changing with respect to time, denoted as [tex]\(\frac{ds}{dt}\).[/tex] To do this, we differentiate the expression for [tex]\(s\)[/tex] with respect to time [tex]\(t\):[/tex]
[tex]\[\frac{ds}{dt} = \frac{d}{dt}\left(\frac{h \cdot x - w \cdot h}{w}\right)\][/tex]
[tex]\[\frac{ds}{dt} = \frac{h}{w} \cdot \frac{dx}{dt}\][/tex]
Given that [tex]\(h = 16\) ft, \(w = 6\) ft, and \(\frac{dx}{dt} = 4\) ft/sec,[/tex] we can substitute these values into the equation:
[tex]\[\frac{ds}{dt} = \frac{16}{6} \cdot 4\][/tex]
[tex]\[\frac{ds}{dt} = \frac{64}{6}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{160}{15}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{1600}{150}\][/tex]
[tex]\[\frac{ds}{dt} = \frac{1600}{61}\][/tex]
A loaded grocery cart is rolling across a parking lot in a strong wind. You apply a constant force \vec{F} =(33 N)\hat{i} - (41 N)\hat{j} to the cart as it undergoes a displacement \vec{s} = (-9.4 m)\hat{i} - (3.1 m)\hat{j}.
Part A
How much work does the force you apply do on the grocery cart?
Express your answer using two significant figures.
W =
{\rm J}
Answer:
[tex]W=-183.1\ J[/tex]
Explanation:
Given:
force applied, [tex]\vec{F} =(33 N)\hat{i} - (41 N)\hat{j}[/tex]
displacement caused, [tex]\vec{s} = (-9.4 m)\hat{i} - (3.1 m)\hat{j}[/tex]
Work done by the force on the cart:
[tex]W=\vec F.\vec s[/tex]
[tex]W=[(33 N)\hat{i} - (41 N)\hat{j}].[(-9.4 m)\hat{i} - (3.1 m)\hat{j}][/tex]
[tex]W=-310.2+127.1[/tex]
[tex]W=-183.1\ J[/tex]
Negative work means that the force and displacement have an obtuse angle between them.
Answer:
-180 J
Explanation:
We are given that
Constant force=[tex]F=(33 N)\hat{i}-(41 N)\hat{j}[/tex]
Displacement=[tex]\vec{s}=(-9.4m)\hat{i}-(3.1m)\hat{j}[/tex]
We have to find the work done .
We know that
Work done=[tex]F\cdot s[/tex]
Using the formula
Work done=[tex](33i-41j)\cdot (-9.4i-3.1j)[/tex]
Work done =[tex]33i\cdot (-9.4)i+41j\cdot 3.1 j[/tex]
By using rule [tex]i\cdot i=j\cdot j=k\cdot k=1,i\cdot j=j\cdot k=k\cdot i=i\cdot k=k\cdot j=j\cdot i=0[/tex]
Work done=[tex]-310.2+127.1[/tex]
Work done=-183.1 J
We have to write answer in two significant figures.
When units digit 3 is less than 5 then digits on left side of 3 remains same and digits on right side of 3 and 3 will be replace by zero
Work done=-180 J
Hence, the work done =-180 J
Match the following kinds of lights in order from the longest wavelength to the shortest wavelength on the EM spectrum:
Group of answer choices
1
2
3
4
5
6
7
Answers
radio
infrared
gamma ray
microwave
x-ray
ultraviolet
visible
Answer:
From longest to shortest wavelength:
1) Radio waves
2) Microwaves
3) Infrared
4) Visible light
5) Ultraviolet
6) X-rays
7) Gamma rays
Explanation:
Electromagnetic waves are periodic oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave itself.
All electromagnetic waves travel in a vacuum with the the same speed, which is know as the speed of light; it is one of the fundamental constants of nature, and its value is
[tex]c=3.0\cdot 10^8 m/s[/tex]
Electromagnetic waves are classified into 7 different types, depending on their wavelength/frequency. From longest to shortest wavelength (and so, from lowest to highest frequency, since frequency is inversely proportional to wavelength), we have (with their correspondant wavelength):
Radio waves (>1 m)
Microwaves (1 mm - 1 m)
Infrared (750 nm - 1 mm)
Visible light (380 nm - 750 nm)
Ultraviolet (10 nm - 380 nm)
X-rays (0.01 nm - 10 nm)
Gamma rays (<0.01 nm)
The electromagnetic spectrum spans from radio waves with the longest wavelength to gamma rays with the shortest. The order is: radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays.
Explanation:The question asks you to match the various types of light to their respective wavelengths on the EM spectrum. The Electromagnetic Spectrum (EM Spectrum) arranges different types of electromagnetic radiation in order of their wavelengths. Light types in order of longest to shortest wavelengths are as follows:
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When Raymond observes certain natural phenomena, he often forms ideas about their causes and effects. Suppose that Raymond surmises that leaves change color in autumn due to scarcity of sunlight. In order to test whether his idea is accurate, he must first construct a falsifiable that defines a clear relationship between two variables. Raymond's next step is to that would isolate and test the relationship between the two variables. This task can be pretty daunting because Raymond will need to identify and eliminate any variables that could confuse test results.
Answer:
The student needs to group variables into dimensionless quantities.
Explanation:
Large experiments take a lot of time to perform because the significant variables need to be separated from the non-significant variables. However, for large quantities of variables, it is necessary to focus on the key variables.
One technique to do that is to use the Buckingham Pi Theorem. The theorem states that the physical variables can be expressed in terms or independent fundamental physical quantities. In other words:
P = n- k
n = total number of quantities
k = independent physical quantities.
A place to start with will be to find dimensionless quantities involving the mass, length, time, and at times temperature. These units are given as M, L, T, and Θ
The grouping helps because it eliminates unwanted and unnecessary experiments.
Answer:
I just took the test, It's hypothesis then design an experiment, the last one i got wrong but its not dependent. hope that helped a little.
WILL MARK BRANLIEST
Two climates that are at the same latitude may be different because of ____.
A) bodies of water
B) distance from the poles
C) earth’s magnetic field
D) soil type
Answer: Bodies of water
Explanation:
Large bodies of water, such as oceans, seas and large lakes, can affect the climate of an area
What possible source of errors would be in this experiment besides human error and why?
Explanation:
Besides human error, other sources of error include friction on the cart (we assumed there is no friction, but in reality, that's never the case), and instrument errors (imprecision in the spring scale).
Besides human error, experiments can also encounter sampling errors, nonsampling errors, uncertainty factors, and spontaneous errors. These can be caused by an inaccurate sampling process, equipment malfunctions, variability in samples, and limitations in the measuring device.
Explanation:Possible sources of error in an experiment, besides human error, could include sampling errors and non-sampling errors. Sampling errors occur when the sample utilized may not be large enough or not accurately representative of the larger population.
This can lead to inaccurate assumptions and conclusions. Non-sampling errors, on the other hand, are unrelated to the sampling process and could be a result of equipment or instrument malfunction (like a faulty counting device). An example for this would be an uncertainty in measurement induced by the fact that smallest division on a measurement ruler is 0.1 inches.
Further, variability in samples can also lead to errors called spontaneous errors. These can be due to natural phenomena such as exposure to ultraviolet or gamma radiation, or to intercalating agents. Lastly, uncertainty factors can contribute to errors as well. These factors include limitations of the measuring device, inaccuracies caused by the instrument itself (e.g., a paper cutting machine that causes one side of the paper to be longer than the other).
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You are an evolutionary biologist studying a population of bats in the rain forest in Brazil. Most of the population possesses moderate length wings, although some individuals have long wings and some individuals have short wings. Over the course of time, you notice that the frequency of moderate-length wings increases. You conclude that the most likely cause of this development is:
a. diversifying natural selection
b. stabilizing natural selection.
c. directional natural selection.
d. co-evolution.
Answer:
Option (B)
Explanation:
In the stabilizing natural selection, the extreme traits from both the ends are eliminated by natural selection and natural selection favors the intermediate trait. So over time individuals having the intermediate traits are selected over the individuals having extreme traits.
So here the population of the bat which possesses moderate wing length is selected over the individual with extreme traits like individuals with short wings and long wings. As a result, the population of moderate length wing bats increased.
Therefore the correct answer is (B)- stabilizing natural selection.
What kind of line does Edward Hopper use in New York Movie to divide theatre space from lobby space?
Answer:
hard line, soft line
Explanation:
What sentence(s) is/are true when we talk about equipotential lines?
a. Electric potential is the same along an equipotential line
b. Work is necessary to move a charged particle along these lines.
c. They are always perpendicular to electric field lines
d. They are always parallel to electric field lines
Answer:
a. True
Explanation:
Equipotential lines are the imaginary lines in the space where actually the electric potential is same at each and every point.
Work is not required to move along such points of the equipotential line because the movement is always perpendicular to the electric field lines because these lines are always perpendicular to the electric field lines.
The electric potential for a point charge is given mathematically as:
[tex]V=\frac{1}{4\pi.\epsilon_0}\times \frac{Q}{r}[/tex]
where:
[tex]Q=[/tex] magnitude of the point charge
[tex]r=[/tex] radial distance form the charge
[tex]\epsilon_0=[/tex] permittivity of free space
Equipotential lines in physics are lines where the electric potential remains constant, perpendicular to electric field lines, and require no work to move a charge along them.
Equipotential lines are lines along which the electric potential remains constant. These lines are perpendicular to the electric field lines. It requires no work to move a charge along an equipotential line, but work is needed to move a charge from one equipotential line to another.
Calculate the efficiency of an engine with an input temperature of 755 K and exhaust temperature of 453 K.
Answer:
40%
Explanation:
The other person got it right up until making it opposite because its a percentage. The equation is correct but you'd just need to take the 60% answer and subtract it from 100% because 60% is equal to how much effiency the exhaust is taking away, thus making your answer 40%
A car starts from rest and uniformly accelerated to a speed of 40 km/h in 5 s . The car moves south the entire time. Which option correctly lists a vector quantity from the scenario?
Explanation:
Speed= distance / time
Making distance the subject of the formula.
Distance = speed × time
Convert km/hr to m/ s
(40× 1000)/3600= 11.1m/s
Distance = 11.1m/s × 5s
Distance= 55.6m
So it is vector ,although the question is not complete.
Answer:
speed: 40 km/h
distance: 40 km
acceleration 8 km/h/s south
velocity: 5 km/h north
A 72.9 kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.21 m/s in 0.80 s. It travels with this constant speed for 4.97 s, undergoes a uniform downward acceleration for 1.52 s, and comes to rest. What does the spring scale register (a) before the elevator starts to move?
Answer:
(a) 72.9 kg
Explanation:
Before the elevator starts to move, only gravitational force exerts on the man, this force is generated by the man mass and the gravitational acceleration, which in turn register in the scale. So the scale would probably indicate the man mass, which is 72.9 kg.
Two large parallel conducting plates are separated by a distance d, placed in a vacuum, and connected to a source of potential difference V. An oxygen ion, with charge 2e, starts from rest on the surface of one plate and accelerates to the other. If e denotes the magnitude of the electron charge, the final kinetic energy of this ion is:
Answer:
2eVI
Explanation:
The final kinetic energy of an oxygen ion, with a charge of 2e, accelerated from one plate to another separated by a potential difference V, equals twice the product of the electron charge and the potential difference, or 2eV.
Explanation:The question involves an oxygen ion with a charge of 2e that is accelerated between two conducting plates separated by a distance d and connected to a potential difference V. This physical scenario falls under the domain of physics, specifically electromagnetism. The energy an ion gains when accelerated through a potential difference is called its kinetic energy. From conservation of energy, we understand that the kinetic energy of the accelerated ion should equal the work done on it by the electrical force, which is itself equal to the charge of the ion times the potential difference of the plates.
Therefore, the kinetic energy (KE) of the ion can be expressed as follows: KE = qV, where q is the charge of the particle and V is the potential difference. In this case, the charge is 2e (twice the electron charge), and the potential difference is V. Thus, the final kinetic energy of the ion is 2eV. It's important to note that this equation is derived from the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.
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A jetliner, traveling northward, is landing with a speed of 70.9 m/s. Once the jet touches down, it has 727 m of runway in which to reduce its speed to 14.0 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive).
Answer:
Magnitude the of the acceleration is 3.32[tex]m/s^2[/tex] and direction is south
Explanation:
[tex]v_{0} =70.9 m/s\\v=14 m/s\\S=727 m[/tex]
we know that
[tex]v^2 = v_{0}^2 +2aS[/tex]
by substituting the values we can get the required acceleration
[tex]v^2 = v_{0}^2 +2aS\\14^2 = 70.9^2 +2\times a\times 727\\a=3.32 m/s^2[/tex]
Magnitude the of the acceleration is 3.32[tex]m/s^2[/tex] and direction is south
LPG is a useful fuel in rural locations without natural gas pipelines. A leak during the filling of a tank can be extremely dangerous because the vapor is denser than air and drifts to low elevations before dispersing, creating an explosion hazard. a.) What volume of vapor is created by a leak of 40 L of LPG? Model the liquidbefore leaking as propane with density pL=0.24g/cm^3. b) what is the mass density of pure propane vapor after depressurization to 293K and 1 bar? compare to the mass density of air at the same conditions.
Answer:
The aanswers to the question are
(a) 5.33 m³
(b) 1.83 kg/m³
Explanation:
Volume of leak = 40 L, density of propane = 0.24g/cm³
Mass of leak = Volume × Density = 40000 cm³×0.24 g/cm³ = 9600 gram
Molar mass of propane = 44.1 g/mol Number of moles = 9600/44.1 = 217.69 moles
at 1 atmosphare and 298.15 K we have
PV = nRT therefore V = nRT/P = (217.69×8.3145×298.15)/101325 = 5.33 m³
The volume of the vapour = 5.33 m³
(b) Density = mass/volume
Recalculating the above for T = 293 K we have V = 5.33×293÷298.15 = 5.23 m³
Therefore density of propane vapor = 9600/5.23 = 1834.22 g/m³ or 1.83 kg/m³
A horse pulls on an object with a force of 300 newtons and does 12,000 joules of work. How far was the object moved?
1. 40
2. 0.03
3. 5 ×10↑5
4. 10 ×10↑4
Answer:
1.
Explanation:
because 12,000 divided by 300 is 40 so its 40m
Air in human lungs has a temperature of 37.0°C and a saturation vapor density of 44.0 g/m³.
(a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person?
(b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of 6.31 × 10³ N/m².
The maximum loss of water vapor per breath is 0.088 g. The partial pressure of water vapor is 6286.41 N/m², which closely matches the given vapor pressure of 6.31 × 10³ N/m², confirming the saturation condition.
To solve the given problem, we need to perform the following calculations:
(a) Maximum Loss of Water Vapor
The saturation vapor density of water vapor at 37.0°C is 44.0 g/m³. Given that 2.00 L of air is exhaled, we first convert the volume to cubic meters (since the density is in g/m³):
[tex]2.00 L = 2.00 * 10^{-3} m^3[/tex]
Now, using the density to find the mass of water vapor exhaled:
[tex]mass = density * volume = 44.0 g/m^3 *2.00 * 10^{-3} m^3 = 0.088 g[/tex]
Thus, the maximum loss of water vapor per breath is 0.088 g.
(b) Partial Pressure of Water Vapor
To find the partial pressure of water vapor, we use the Ideal Gas Law: PV = nRT. First, we convert the given water vapor density into moles per unit volume:
Density (44.0 g/m³) divided by the molar mass of water (18.015 g/mol) gives us:
44.0 g/m³ ÷ 18.015 g/mol = 2.44 mol/m³
So the number of moles, n, per unit volume is 2.44 mol/m³. Now using the Ideal Gas Law:
P = nRT, where R is the universal gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin (310.15 K)
[tex]P = 2.44 mol/m^3 * 8.314 J/(mol.K) * 310.15 K = 6286.41 N/m^2[/tex]
Thus, the partial pressure of water vapor is 6286.41 N/m². Comparing this with the vapor pressure of 6.31 × 10³ N/m², we see they are very close, confirming the saturation condition.
In the vertical jump, an Kobe Bryant starts from a crouch and jumps upward to reach as high as possible. Even the best athletes spend little more than 1.00 s in the air (their "hang time"). Treat Kobe as a particle and let ymax be his maximum height above the floor. Note: this isn't the entire story since Kobe can twist and curl up in the air, but then we can no longer treat him as a particle.
To explain why he seems to hang in the air, calculate the ratio of the time he is above ymax/2 moving up to the time it takes him to go from the floor to that height. You may ignore air resistance.
Answer:
the athlete spends 2.4 times more time at the upper part of his way than in the lower one.
Explanation:
Let’s find the velocity V1 of an athlete to reach half of the maximum height equation
V1 = v20 -2gh = v20 -2g(ymax)/2
Here, Vo is the initial velocity of athlete, v1 is the velocity of athlete at half the maximum height, g is the acceleration due to gravity, h=ymax /2 is half of the maximum height.
We can fund the maximum height that athlete can reach from the law of conservation of energy
KE = PE
1/2M v20 = mg ymax
ymax = v20 /2g
Then, substituting ymax into the first equation we get
V21 = v20 – v20/2 = v20/2
V1 = V0/∫2, we can find the time that the athlete needs to reach the maximum height (ymax) from the kinematic equation
V = V0 – gt
Here, V is the final velocity of an athlete at the maximum height; V0 is the initial velocity of an athlete
Since, V=0ms-1, we get t=V0/g
Similarly, we can find the time t1 that an athlete needs to reach maximum height from the Ymax/2:
T1 = V1/g =V0/g∫2
So, it is obvious that the time to reach Ymax from Ymax/2 is nothing more than the difference between t and t1:
t-t1 =V0/g(1-1/∫2)
finally, we can calculate the ratio of the time he is above Ymax/2 to the time it takes him to go from floor to that height.
T1/t-t1 =V0/g∫2V0 ×g∫2/∫2-1 =2.4
Answer; the athlete spends 2.4 times more time at the upper part of his way than in the lower one.
One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at a frequency 129 Hz. The other end passes over a pulley and supports a mass of 1.50 kg. The linear mass density of the rope is 0.0590 kg/m. What is the speed of a transverse wave on the rope? What is the wavelength? How would your answers to parts (a) and (b) be changed if the mass were increased to 2.80 kg?
Answer:
(a). The speed of transverse wave on the rope is 15.78 m/s.
(b). The wavelength is 0.122 m.
(c). The changed speed of transverse wave on the rope is 21.56 m/s.
The changed wavelength is 0.167 m.
Explanation:
Given that,
Frequency = 129 Hz
mass = 1.50 kg
Linear mass density of the rope = 0.0590 kg/m
(a). We need to calculate the speed of a transverse wave on the rope
Using formula of speed
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{1.50\times9.8}{0.0590}}[/tex]
[tex]v=15.78\ m/s[/tex]
(b). We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda =\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{15.78}{129}[/tex]
[tex]\lambda=0.122\ m[/tex]
(c). If the mass were increased to 2.80 kg.
We need to calculate the speed of a transverse wave on the rope
Using formula of speed
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]
Put the value into the formula
[tex]v=\sqrt{\dfrac{2.80\times9.8}{0.0590}}[/tex]
[tex]v=21.56\ m/s[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda =\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{21.56}{129}[/tex]
[tex]\lambda=0.167\ m[/tex]
Hence, (a). The speed of transverse wave on the rope is 15.78 m/s.
(b). The wavelength is 0.122 m.
(c). The changed speed of transverse wave on the rope is 21.56 m/s.
The changed wavelength is 0.167 m.
The speed of the transverse wave on the rope is 2.48 m/s and the wavelength is 0.019 m. If the mass were increased to 2.80 kg, the speed of the wave would stay the same but the wavelength would be different.
Explanation:To find the speed of a transverse wave on the rope, we can use the equation:
v = √(T/μ)
where v is the speed of the wave, T is the tension in the rope, and μ is the linear mass density of the rope. Plugging in the values given in the question, we get:
v = √(1.50 kg * 9.8 m/s^2 / 0.0590 kg/m) = 2.48 m/s
To find the wavelength of the wave, we can use the equation:
λ = v/f
where λ is the wavelength, v is the speed of the wave, and f is the frequency of the tuning fork. Plugging in the values given in the question, we get:
λ = 2.48 m/s / 129 Hz = 0.019 m
If the mass were increased to 2.80 kg, the speed of the wave on the rope would remain the same. However, the wavelength would be different because it is determined by the frequency of the tuning fork and the speed of the wave, not the mass of the hanging weight.
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A closed Gaussian surface in the shape of a cube of edge length 1.9 m with one corner at x = 1 4.8 m, y = 1 3.9 m.
The cube lies in a region where the electric field vector is given by [tex]E = 3.4 \hat{i} + 4.4 y^2 \hat{j} + 3.0 \hat{k}[/tex] NC with y in meters.
What is the net charge contained by the cube?
Answer:
Net charge = 2.59nC
Explanation:
Gauss' Law states that the net electric flux is given by:
∮→E⋅→d/A = q enc/ϵ0
At this point, we have to solve the net electric flux through each side.
One corner is at (4.8, 3.9, 0).
The other corners are each 1.9m apart, so the other corners are at
(4.8, 5.8, 0), (6.7, 3.9, 0) and (6.7, 5.8, 0).
The other four corners are 1.9m away in the z-axis:
(4.8, 5.8, 2), (6.7, 3.9, 2) and (6.7, 5.8, 2).
Therefore, there are two planes (parallel to the x-z plane), one at
y = 3.9
and the other at
y = 5.8 which have a constant y-coordinate and are facing in the −^j and +^j respectively.
Area = 1.9m * 1.9m = 3.61m²
The flux through the first plane (area of 3.61m²) is given by:
E.A = (3.4i + 4.4 * 3.9²j + 3.0k) * (-3.61m²j) = -241.59564
The flux through the other plane is
E.A = (3.4i + 4.4 * 5.8²j + 3.0k)* (3.61m²j) = 534.33776
Now, for the other planes. There are no ^j components for the unit vectors for the area.
Therefore, even though they change in y-coordinate, those terms cancel out.
Therefore, for the planes with unit vector in the x-direction, we get:
E.A = (3.4i + 4.4y²j + 3.0k) * (1.9m * 1.9m) = ±12.274
And in the z-direction:
E.A = (3.4i + 4.4y²j + 3.0k) * (1.9m * 1.9m) = ±10.83
Now, when we sum all these fluxes together, the contribution from the x- and z-directions cancel out. Therefore, our net flux is:
-241.59564 + 534.33776 = 292.74212
Therefore, the enclosed charge is given by
q enc = ϵ0* (292.74212)
= 2.5856871136363E−9C
= 2.59E-9 nC--_- Approximated
= 2.59nC
Answer:
Q_enclosed = 1.576 nC
Explanation:
Given:
- The edge length of the cube L = 1.9 m
- One corner of the cube P_1 = ( 4.8 , 13.9 ) m
- The Electric Field vector is given by:
E = 3.4 i + 4.4*y^2 j + 3.0 k N/C
Find:
What is the net charge contained by the cube?
Solution:
- The flux net Ф through faces parallel to y-z plane is:
net Ф_yz = E_x . A . cos (θ)
Where, E_x is the component of E with unit vector i.
θ is the angle between normal vector dA and E.
Hence,
net Ф_yz = 3.4 . 1.9^2 . cos (0) + 3.4 . 1.9^2 . cos (180)
net Ф_yz = 3.4 . 1.9^2 - 3.4 . 1.9^2 . cos (180)
net Ф_yz = 0.
- Similarly, The flux net Ф through faces parallel to x-y plane is:
net Ф_xy = E_z . A . cos (θ)
Where, E_z is the component of E with unit vector k.
net Ф_xy = 3 . 1.9^2 . cos (0) + 3 . 1.9^2 . cos (180)
net Ф_xy = 3 . 1.9^2 - 3 . 1.9^2 . cos (180)
net Ф_xy = 0
-The flux net Ф through faces parallel to x-z plane is:
net Ф_xz = E_y . A . cos (θ)
Where, E_y is the component of E with unit vector j.
net Ф_xz = 4.4y_1^2 * 1.9^2 . cos (0) + 4.4y_2^2. 1.9^2 . cos (180)
Where, The y coordinate for face 1 y_1 = 3.9 - 1.9 = 2, & face 2 y_2 = 3.9
net Ф_xz = - 4.4*2^2*1.9^2 . cos (0) - 4.4*3.9^2. 1.9^2 . cos (180)
net Ф_xz = -63.536 + 241.59564 = 178.0596 Nm^2/C
- From gauss Law we have:
Total net Ф_x,y,z = Q_enclosed / ∈_o
Where,
Q_enclosed is the charge contained in the cube
∈_o is the permittivity of free space = 8.85*10^-12
Hence,
Total net Ф_x,y,z = net Ф_xz + net Ф_yz + net Ф_xy
Total net Ф_x,y,z = 178.0596 + 0 + 0 = 178.0596 Nm^2/C
We have,
Q_enclosed = Total net Ф_x,y,z * ∈_o
Q_enclosed = 178.0596 * 8.85*10^-12
Q_enclosed = 1.576 nC
In which of these models is heat being added to the molecules? 2 points Molecules are moving fast. As they run into slower molecules, they slow down. Molecules are moving slow. As they run into faster molecules, they speed up. The molecules are moving at different speeds. As they run into each other, some molecules slow down while others speed up. The molecules bounce around. Every time they collide with another molecule, they slow down.
Molecules are moving slow, as they run into faster molecules, they speed up.
Explanation:
The model that best depicts heat being added to the molecules is that slow moving molecules run into faster ones and they speed up.
When heat is added to a body, the kinetic energy of the system increases.
Slow moving particles have low kinetic energy among them. Heat causes gain in kinetic energy. The slow moving particles first begins to vibrate and as time proceeds starts colliding with other ones. The overall entropy of the system increases as they run into faster molecules.learn more;
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The net external force acting on an object is zero. Is it possible for the object to be traveling with a velocity that is not zero if the answer is yes state whether any conditions must be placed on the magnitude and direction of velocity?
Answer:
Yes, this is according to the Newton's first law of motion.
Neither its direction nor its velocity changes during this course of motion.
Explanation:
Yes, it is very well in accordance with Newton's first law of motion for a body with no force acting on it and it travels with a non-zero velocity.
During such a condition the object will have a constant velocity in a certain direction throughout its motion. Neither its direction nor its velocity changes during this course of motion.
An object can maintain a nonzero velocity in the absence of a net external force due to Newton's first law of motion. The object will continue to move with the velocity it has until a net force acts upon it. This state of motion with constant velocity is known as dynamic equilibrium.
Explanation:Yes, it is possible for an object to be traveling with a velocity that is not zero even if the net external force acting on it is zero. According to Newton's first law of motion, also known as the law of inertia, an object will maintain its state of motion unless acted upon by a net external force. This means that if there is no net external force on the object, its acceleration is zero, and it will continue moving at its current velocity, which can be nonzero. This constant velocity can be in any direction and of any magnitude, and it remains constant until acted upon by a net force.
For example, when your car is moving at a constant velocity down the street, even though it is moving, the net external force on it can be zero. The forces such as friction and air resistance are balancing out the driving force, leading to no net force on the car, which is a state of dynamic equilibrium.
John performs an experiment on an electric circuit. He increases the voltage from 25 volts to 50 volts while keeping the resistance constant. What will be the effect of John's changes on the current?
The current will double
Explanation:
The relationship between voltage and current in an electric circuit is given by the following equation (Ohm's law):
[tex]V=IR[/tex]
where
V is the voltage
I is the current
R is the resistance
making R the subject,
[tex]R=\frac{V}{I}[/tex]
Since in this experiment the resistance is kept constant, we can write:
[tex]\frac{V_1}{I_1}=\frac{V_2}{I_2}[/tex]
where
[tex]V_1=25 V[/tex] is the voltage in the 1st experiment
[tex]V_2=50 V[/tex] is the voltage in the 2nd experiment
[tex]I_1,I_2[/tex] are the currents in the 1st and 2nd experiment
We can re-arrange the equation as
[tex]\frac{I_2}{I_1}=\frac{V_2}{V_1}=\frac{50}{25}=2[/tex]
This means that the current will double in the 2nd experiment.
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A shoreline runs north-south, and a boat is due east of the shoreline. The bearings of the boat from two points on the shore are 110° and 100°. Assume the two points are 550 ft apart. How far is the boat from the shore?
Answer:
2930.90 ft
Explanation:
*Attached are two rough sketches I made to represent the problem.
In diagram 2, the bearings are represented relative to the boat's position.
To find x, the distance between the boat and point having bearing 110° to the boat, we can use sine rule:
(sin 10°) / 550 = (sin 100) / x
=> x = (550 * sin 100°) / sin 10°
x = 3119 ft
Having found this, we can now find the distance between the host and the shore, as represented in diagram 1.
Using trigonometric function of SOHCAHTOA, we have that:
cos 20° = y / 3119
=> y = 3119 * cos 20°
y = 2930.90 ft
Hence, the distance between the boat and the shore is 2930.90 ft
The child then walks towards the center of the merry-go-round and stops at a distance 0.455 m from the center. Now what is the angular velocity of the merry-go-round? Answer in units of rad/s.
Final answer:
The new angular velocity of the merry-go-round can be calculated using the conservation of angular momentum. By considering the initial angular momentum of the merry-go-round and the child after they grab the outer edge, we can determine the final angular velocity. The new angular velocity is approximately 0.414 rad/s.
Explanation:
To calculate the new angular velocity of the merry-go-round, we can use the conservation of angular momentum. The initial angular momentum of the merry-go-round is equal to the sum of the angular momentum of the original system and the child after they grab the outer edge. The initial angular momentum of the merry-go-round is given by Li = Imerry-go-round ● ωi, where Imerry-go-round is the moment of inertia of the merry-go-round and ωi is the initial angular velocity. The angular momentum of the original system is zero since the children are initially at rest. The angular momentum of the child after they grab the outer edge is equal to child ● child ● ω, where child is the mass of the child, the child is the distance of the child from the axis of rotation, and ω is the angular velocity.
Applying the principle of conservation of angular momentum, we have:
Li = (Imerry-go-round + child ● child) ● ωf
Solving for ωf, we get:
ωf = Li / (Imerry-go-round + child ● child)
Substituting the given values, we have:
ωf = (1000.0 kg.m² ● 6.0 rev/min) / (1000.0 kg.m² + 22.0 kg ● 0.455 m)
Converting rev/min to rad/s, we get:
ωf = (1000.0 kg.m² ● (6.0 rev/min ● 2π rad/rev) / (60 s/min)) / (1000.0 kg.m² + 22.0 kg ● 0.455 m)
Simplifying the expression, we find that the new angular velocity of the merry-go-round is approximately 0.414 rad/s.
A friend of yours is loudly singing a single note at 412 Hz while racing toward you at 25.8 m/s on a day when the speed of sound is 347 m/s . What frequency do you hear?
Answer:
5541Hz
Explanation:
If the frequency of a wave is directly proportional to the velocity we have;
F = kV where;
F is the frequency
K is the constant of proportionality
V is the velocity
Since f = kV
K = f/v
K = F1/V1 = F2/V2
Given f1 = 412Hz v1 = 25.8m/s f2 = ? V2 = 347m/s
Substituting in the formula we have;
412/25.8=f2/347
Cross multiplying
25.8f2 = 412×347
F2 = 412×347/25.8
F2 = 5541Hz
The frequency heard will be 5541Hz
550 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 11.0, starting from its initial volume?
Final answer:
To calculate the work done to compress the gas by a factor of 11.0, we can use the relationship between work and volume changes. The work required to compress the gas by a factor of 11.0 is -11,000 J.
Explanation:
To calculate the work done to compress the gas by a factor of 11.0, we can use the relationship between work and volume changes. The work done on a gas during compression is given by the equation:
Work = Pressure ×Change in Volume
In this case, we know that the work required to compress the gas to half its initial volume is 550 J. Let's assume the initial volume of the gas is V. So the work done to compress the gas by a factor of 11.0 can be calculated as:
Work = Pressure × Change in Volume
550 J = Pressure ×(V/2 - V)
550 J = Pressure ×(-V/2)
Solving for Pressure, we get:
Pressure = -1100 J/V
Therefore, the work required to compress the gas by a factor of 11.0 is -1100 J/V× (11V - V) = -11,000 J (negative sign indicates work is done on the gas).
Two manned satellites approaching one another at a relative speed of 0.150 m/s intend to dock. The first has a mass of 4.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest. Incorrect: Your answer is incorrect. m/s (b) What is the loss of kinetic energy in this inelastic collision? Incorrect: Your answer is incorrect. J (c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity Incorrect: Your answer is incorrect. Check the sign of your answer for velocity in part (c). m/s loss of kinetic energy Correct: Your answer is correct. J
a) Final velocity after docking: +0.094 m/s
b) Kinetic energy loss: 31.6 J
c) Final velocity after docking: -0.056 m/s
d) Kinetic energy loss: 31.6 J
Explanation:
a)
Since the system of two satellites is an isolated system, the total momentum is conserved. So we can write:
[tex]p_i = p_f[/tex]
Or
[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]
where, in the reference frame in which the first satellite was originally at rest, we have:
[tex]m_1 = 4.50\cdot 10^3 kg[/tex] is the mass of the 1st satellite
[tex]m_2 = 7.50\cdot 10^3 kg[/tex] is the mass of the 2nd satellite
[tex]u_1 = 0[/tex] is the initial velocity of the 1st satellite
[tex]u_2 = +0.150 m/s[/tex] is the initial velocity of the 2nd satellite
v is their final velocity after docking
Solving for v,
[tex]v=\frac{m_2 u_2}{m_1 +m_2}=\frac{(7.50\cdot 10^3)(0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=0.0938 m/s[/tex]
b)
The initial kinetic energy of the system is just the kinetic energy of the 2nd satellite:
[tex]K_i = \frac{1}{2}m_2 u_2^2 = \frac{1}{2}(7.50\cdot 10^3)(0.150)^2=84.4 J[/tex]
The final kinetic energy of the two combined satellites is:
[tex]K_f = \frac{1}{2}(m_1 +m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+7.50\cdot 10^3)(0.0938)^2=52.8 J[/tex]
Threfore, the loss in kinetic energy during the collision is:
[tex]\Delta K = K_f - K_i = 52.8 - 84.4=-31.6 J[/tex]
c)
In this case, we are in the reference frame in which the second satellite is at rest. So, we have
[tex]u_2 = 0[/tex] (initial velocity of satellite 2 is zero)
[tex]u_1 = -0.150 m/s[/tex] (initial velocity of a satellite 1)
Therefore, by applying the equation of conservation of momentum,
[tex]m_1 u_1 + m_2 u_2 = (m_1 + m_2)v[/tex]
And solving for v,
[tex]v=\frac{m_1 u_1}{m_1 +m_2}=\frac{(4.50\cdot 10^3)(-0.150)}{4.50\cdot 10^3 + 7.50\cdot 10^3}=-0.0563 m/s[/tex]
d)
The initial kinetic energy of the system is just the kinetic energy of satellite 1, since satellite 2 is at rest:
[tex]K_i = \frac{1}{2}m_1 u_1^2 = \frac{1}{2}(4.50\cdot 10^3)(-0.150)^2=50.6 J[/tex]
The final kinetic energy of the system is the kinetic energy of the two combined satellites after docking:
[tex]K_f = \frac{1}{2}(m_1 + m_2)v^2=\frac{1}{2}(4.50\cdot 10^3+ 7.50\cdot 10^3)(-0.0563)^2=19.0 J[/tex]
Therefore, the kinetic energy lost in the collision is
[tex]\Delta K = K_f - K_i = 19.0 -50.6 = -31.6 J[/tex]
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