Answer:
(A) 89.442 rad/sec
(B) 0.070 sec
(C) [tex]C=25\times 10^{-6}F[/tex]
Explanation:
We have given mass of the body m = 0.50 kg
It is given that spring is extended 2 mm from its equilibrium position
So x = 2 mm = 0.002 m
Resistive force is given F = 8 N
We know that force is equal to F = Kx, here K is spring constant and x is elongation in spring
So [tex]8=K\times 0.002[/tex]
K = 4000 N/m
(A) Angular frequency is equal to [tex]\omega =\sqrt{\frac{K}{m}}[/tex]
So angular frequency [tex]\omega =\sqrt{\frac{4000}{0.50}}=89.442rad/sec[/tex]
(b) Time period of oscillation is equal to [tex]T=\frac{2\pi }{\omega }=\frac{2\times 3.14}{89.442}=0.070sec[/tex]
So time period will be 0.070 sec
(c) Inductance is given L = 5 H
Angular frequency is equal to [tex]\omega =\frac{1}{\sqrt{LC}}[/tex]
[tex]89.442 =\frac{1}{\sqrt{5C}}[/tex]
Squaring both side
[tex]8000=\frac{1}{5C}[/tex]
[tex]C=25\times 10^{-6}F[/tex]
A child in danger of drowning in a river is being carried down-stream by a current that flows uniformly with a speed of 2.20 m/s . The child is 500 m from the shore and 1100 m upstream of the boat dock from which the rescue team sets out.
If their boat speed is 7.30 m/s with respect to the water, at what angle from the shore must the boat travel in order to reach the child?
Final answer:
To reach a child being carried by a river current, the rescue boat, with a speed of 7.30 m/s versus water, must aim at a specific angle upstream accounting for the current's speed of 2.20 m/s. The calculation involves vector addition and trigonometry to counteract the current and ensure a direct path to the child.
Explanation:
The question involves calculating the angle at which a rescue boat must travel to reach a child being carried away by a river current. The river flows at a speed of 2.20 m/s, while the boat's speed in still water is 7.30 m/s. Given the distances from the shore to the child (500 m) and from the boat dock upstream to the child (1100 m), we need to determine the angle relative to the shore for the boat to make a direct rescue.
To solve this, we need to use the concept of vector addition, where the boat's velocity vector and the river's current vector combine to create a resultant vector that points directly to the child's location. The angle can be calculated using trigonometry, particularly the tangent function. However, since the specific calculations and steps to obtain the angle are not provided in the question or the previous examples, it is crucial to understand the principles of vectors and relative motion to approach this problem.
Essentially, the rescue team needs to aim the boat at an angle upstream to counteract the river's flow. The effect of the river's current will adjust the boat's path towards the child. It's a classic application of relative motion in two dimensions, requiring careful consideration of both the magnitude and direction of the vectors involved.
An Olympic-class sprinter starts a race with an acceleration of 5.10 m/s2. What is her speed 2.40 s later?
Answer:
12.24 m/s
Explanation:
Speed: This can be defined as the rate of change of distance with time. The S.I unit of speed is m/s.
Using the formula,
a = v/t................ Equation 1
Where a = acceleration of the sprinter, v = speed of the sprinter, t = time.
making v the subject of the equation,
v = at ................. Equation 2
Given: a = 5.1 m/s², t = 2.4 s.
Substitute into equation 2
v = 5.1(2.4)
v = 12.24 m/s.
Hence, the speed of the sprinter = 12.24 m/s
You are operating a powerboat at night. You see green and white lights on another boat. What should you do?
Answer:
Just maintain the course you are on and your speed.
Explanation:
When you see a green and a white light, then from the port (left) side you will start coming across another craft. You are the stand-alone craft in this scenario and therefore should stay consistent with your pace and direction. The other craft must take important and early measures to keep the craft away from you.
On the Moon, gravitational field is around 1.6 N/kg. How does this affect gravitational potential and kinetic energy of objects dropped from a height on the Moon as compared with Earth?
Answer:An object with mass in a gravitational field experiences a force called weight. This weight on the moon is about 1/6 but the mass of that object remains the same due to the moon's gravitational field which is less than the earth.
Explanation:There are factors that affect the gravitational potential and kinetic energy . They are:
1. The height of the object in the moon
2.The mass of the object
3. The strength of the gravitational field
4. The change in position of the object.
The current through two identical light bulbs connected in a series is 0.25 amps. The voltage across both bulbs is 100 volts. Find the resistance of a single light bulb.
Answer: 200ohms
Explanation:
According to Ohm's law, the current (I) passing through a metallic conductor is directly proportional to the potential difference (v) between its ends at constant temperature and pressure. Mathematically, E=IRt
Where E is the voltage across both bulbs, I is the current, Rt is the total equivalent resistance
E = 100V, I = 0.25amps Rt = R+R(since they are 2 identical bulbs in series, we will add them together)
Rt = 2R
Substituting this values in the formula to get R, we have;
100 = 0.25(2R)
100 = 0.5R
R = 100/0.5
R = 200ohms
The resistance of a single light bulb will be 200ohms.
Note that the unit of resistance is ohms
If the L-shaped rod has a moment of inertia I=9kgm2, F1=12N, F2=27N, and again F3=0, how long a time t would it take for the object to move through 45∘ ( π/4 radians)? Assume that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. Express the time in seconds to two significant figures.
Answer:
Time, t = 2.80seconds
Explanation:
Calculating net Torque, T
Torque(net)= F2(0.08m) - F1(0.03)
Torque(net) = (27×0.08)-(12×0.03)
Torque(net)= 2.16 - 0.36 =1.8N/m
Pi/4= Torque(net)/ Inertia
3.142/4= 1.8/9 = 0.2rad/s^2=a
Pi/4= 1/2 at^2
3.142/4=1/2×0.2 ×t^2
0.7855= 0.1 t^2
t = sqrt(0.7856/0.1)
t= sqrt(7.855)
t=2.80 seconds
By Assuming that as the object starts to move, each force moves with the object so as to retain its initial angle relative to the object. then the time in seconds is 2.80seconds
What are the types of force ?Force can be denoted as the parameter obtained by pushing or pulling of any object which result in object’s interaction or movement, without force the objects can not move, it can be stopped or change the direction.
Force is a quantitative property and it is an interaction between two physical bodies, means an object and its environment, there are different types of forces in nature.
If an object is in its moving state then it will be either static or motion, if it is pushed or pulled the object will change its position and The external push or pull upon the object called as Force.
There are two types of forces such as contact force which are the force occurs when we apply some effort on the object such as Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force
Non-Contact forces can be defined as the force occur from a distance such as Electromagnetic Force, Gravitational Force, Nuclear Force
Calculating net Torque, T, Torque(net)= F2(0.08m) - F1(0.03)
Torque(net) = (27×0.08)-(12×0.03)
Torque(net)= 2.16 - 0.36 =1.8N/m
Pi/4= Torque(net)/ Inertia
3.142/4= 1.8/9 = 0.2rad/s^2=a
Pi/4= 1/2 at^2
3.142/4=1/2×0.2 ×t^2
0.7855= 0.1 t^2
t = sqrt(0.7856/0.1)
t= sqrt(7.855)
t=2.80 seconds
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An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 1510 kg. When that occupant drops a coin, its acceleration relative to the cab is 7.40 m/s2 downward. What is the tension in the cable?
Answer:
Explanation:
Given
Combined mass of cab and elevator is [tex]M=1510\ kg[/tex]
acceleration of coin with respect to elevator [tex]a_{ce}=-7.4\ m/s^2[/tex]
[tex]a_{ce}[/tex] can be written as
[tex]a_{ce}=a_{cg}-a_{eg}[/tex]
where
[tex]a_{cg}[/tex]=acceleration of coin with respect to ground
[tex]a_{eg}[/tex]=acceleration of elevator with respect to ground
[tex]a_{ce}=a_{cg}-a_{eg}[/tex]
[tex]-7.4=-9.8-a_{eg}[/tex]
[tex]a_{eg}=-9.8+7.4=-2.4\ m/s^2[/tex]
Forces on elevator
[tex]T-Mg=Ma_{eg}[/tex]
[tex]T=M(g+a_{eg})[/tex]
[tex]T=1510\times (9.8-2.4)[/tex]
[tex]T=11,174\ N[/tex]
Here we considered downward direction as negative and upward as positive
normal hearing elsewhere. How much more intense is a 6000 Hz tone than a 80 Hz tone if they are both barely audible to the child?
Explanation:
There is no any direct relationship between the frequency of a sound relative the intensity of the sound.
Frequency is a perception of pitch of the sound whereas intensity determines the loudness of the sound. Intensity is proportional to amplitude of the sound.
[tex]\beta= log_{10}\frac{I}{I_o}[/tex]
So, it would be hard to determine how much more intense is a 6000 Hz tone than a 80 Hz tone.
The distance between two successive crests of a certain transverse wave is 1.40 m. 25 crests pass a given point along the direction of travel every 12.4 s. Calculate the wave speed. Answer in units of m/s.
Answer: 2.82m/s
Explanation:
Wave speed(v) is the product of the frequency (f) of a wave and its wavelength (¶)
V = f¶
Since wavelength is the distance between two successive crests or trough, the wavelength given is 1.40m i.e ¶ = 1.40m
If the total crest is 25, this means that 25 oscillations occurs in 12.4s.
Since the number of oscillation made in one second is the frequency, frequency = 25/12.4 = 2.01cycle/seconds
Speed of the wave v = 2.01×1.4
V =
Wave speed is 2.82m/s
A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40 m/s and observes that it takes 1.50 s to reach the water.
A. How high above the water was the preserver released?
B. List the knowns in this problem.
Answer:
13.125 m
Explanation:
b) The quantity which are known as
Initial velocity of life preserver, u = 1.40 m/s
time to reach, t = 1.50 s
final velocity of the life preserver, v = 0 m/s
acceleration due to gravity = 9.8 m/s²
a) height of the preserver above water
using equation of motion
[tex]h = u t + \dfrac{1}{2}gt^2[/tex]
[tex]h = 1.4\times 1.50 + \dfrac{1}{2}\times 9.8\times 1.5^2[/tex]
h = 13.125 m
Hence, the height from where preserver is thrown is equal to 13.125 m
Final answer:
The life preserver was released from approximately 8.925 meters above the water. This calculation was based on the initial velocity, time it took to reach the water, and the acceleration due to gravity, making use of kinematic equations.
Explanation:
To find out how high above the water the life preserver was released, we can use the kinematic equations for uniformly accelerated motion. Since there is an initial velocity and the acceleration due to gravity is applicable, the following kinematic equation can be used:
h = vot + ½at²
Where:
h is the height from which the preserver is released (unknown)vo is the initial velocity = 1.40 m/s (given)t is the time the preserver takes to hit the water = 1.50 s (given)a is the acceleration due to gravity = -9.8 m/s²Plugging in the known values into the kinematic equation, we get:
h = (1.40 m/s)(1.50 s) + ½(-9.8 m/s2)(1.50 s)²
Calculating this gives us:
h = 2.10 m - 11.025 m = -8.925 m
Since height can't be negative, we take the absolute value which is 8.925 m. Hence, the life preserver was released approximately 8.925 m above the water.
Knowns
Initial velocity (vo) = 1.40 m/sTime (t) = 1.50 sAcceleration due to gravity (a) = -9.8 m/s²An automobile moves at a constant speed over the crest of a hill traveling at a speed of 88.5 km/h. At the top of the hill, a package on a seat in the rear of the car barely remains in contact with the seat. What is the radius of curvature (m) of the hill?
Answer:
[tex]r=61.65m[/tex]
Explanation:
Since the package remains in contact with the car's seat, the package's speed is equal to the car's speed. At the top on the mountain the package's centripetal force must be equal to its weight:
[tex]mg=F_c[/tex]
The centripetal force is defined as:
[tex]F_c=ma_c=\frac{mv^2}{r}[/tex]
Here v is the linear speed of the object and r is the radius of curvature. We need to convert the linear speed to [tex]\frac{m}{s}[/tex]:
[tex]88.5\frac{km}{h}*\frac{1000m}{1km}*\frac{1h}{3600s}=24.58\frac{m}{s}[/tex]
Now, we calculate r:
[tex]mg=\frac{mv^2}{r}\\r=\frac{v^2}{g}\\r=\frac{(24.58\frac{m}{s})^2}{9.8\frac{m}{s^2}}\\\\r=61.65m[/tex]
Which one of the following statements is true?
1. Burning coal contributes to sulfur aerosols in the stratosphere; these sulfur aerosols have moderated global warming.
2. Sulfur compounds released into the atmosphere have relatively short lifetimes of only an hour or two.
3. Volcanoes are an anthropogenic source of sulfur compounds.
4. The widespread use of nuclear energy has released significant amounts of sulfur dioxides that have made their way into the stratosphere.
Answer:
1. Burning coal contributes to sulfur aerosols in the stratosphere; these sulfur aerosols have moderated global warming.
Explanation:
Sulfur aerosols both absorb as well as scatter solar radiation coming from the sun , thus saving the earth from getting wormed up . In this way it has moderating effect on the global warming . This is also called global dimming effect. Less of the solar radiation is able to reach earth surface due to these aerosol.
One of the many steps in the production of toothpaste is to screw the caps on the tubes, which is still a manual process, performed by on man, Mr. Bucket. Which statement about this situation is BEST?
A) This is most appropriate for an output measure of capacity.
B) In this case, the capacity of this step is not the maximum rate of output.
C) This is most appropriate for an input measure of capacity.
D) Utilization of the worker at this process step cannot be measures as it is a manual process.
Answer:A) This is most appropriate for an output measure of capacity.
Explanation: Toothpaste is a paste used to promote oral health and hygiene, Most toothpaste contain an active agent(floride) and it acts as an abrasive agent which helps to remove dental plaques or unwanted attachments to the teeth.
Among the options the Option(A) which says that THIS IS MOST APPROPRIATE FOR THE MEASURE OF CAPACITY is the statement that best Describes the situation. Toothpastes have a long history as it can be traced to about 4000years ago.
If you put two 60 W bulbs in series across a 120 V outlet, how much power would each consume if its resistance were constant?
Answer:15 watts
Explanation:
To get the current
Power P=iV
(Where P is power of bulb 60watts, i is current, and V is the voltage 120V
i=P/V
i = 60/120
i = 1/2A
But
V=iR where R is the resiance
Therefore R=V/i
=120÷1/2
=120×2
=240ohms
For series connection, each bulb draws the same current since,
Since the two bulbs are 60-watt bulbs, they will have the same resistance, therefore the voltage across each bulb is the same and equals halve of the applied voltage, 120/2 = 60 volts.
Taken the resistance 240 ohm is constant across the series, we can roughly estimate the current flow and calculate power dissipation in the series connection.
We have 120 V/(240 + 240 ) ohms = 1/4 A.
The power dissipated in each bulb is (1/4) × 60 = 15 watts.
When two 60 W bulbs are connected in series across a 120 V outlet, each bulb consumes 30 W of power because they share the same current, and the voltage is divided equally among them due to their series connection.
When two 60 W bulbs are connected in series across a 120 V outlet, they share the same current because they are in a series circuit. In a series circuit, the current is constant throughout, and the voltage is divided among the components. Since power is related to both voltage and current, we can use the formula P = VI to find out how much power each bulb consumes.
Total Resistance (R_total): In a series circuit, the total resistance is the sum of the individual resistances. Let's assume the resistance of each bulb is R.
Since P = VI, we can rearrange the formula to find current (I):
I = P / V
The power of each bulb is 60 W, and the voltage is 120 V, so the current passing through the circuit is:
I = 60 W / 120 V = 0.5 A
Voltage Across Each Bulb: In a series circuit, the voltage is divided among the components. Each bulb receives a portion of the total voltage. So, the voltage across each bulb is 60 V.
Power Consumed by Each Bulb: Now, we can use the formula P = VI to find the power consumed by each bulb. We know the voltage (60 V) and the current (0.5 A) passing through each bulb:
P = (0.5 A) * (60 V) = 30 W
Each bulb consumes 30 W of power when connected in series across the 120 V outlet.
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A bicyclist is moving toward a sheer wall while holding a tuning fork rated at 488 Hz. 1) If the bicyclist detects a beat frequency of 8 Hz (between the waves coming directly from the tuning fork and the echo waves coming from the sheer wall), calculate the speed of the bicycle. Assume the speed of sound is 343 m/s.
Answer:
speed of the bicycle = 2.81 m/s
Explanation:
given data
tuning fork rated f = 488 Hz
beat frequency fb = 8 Hz
speed of sound vs = 343 m/s
solution
we get here frequency that rider is listening that is
rider hearing frequency = 488 Hz + 8 Hz
rider hearing frequency = 496 Hz
and when it bouncing from sheer wall at frequency of related to stationary object
frequency = 488 Hz + 4 Hz
frequency = 492 Hz
so now we get speed of the bicycle that is
speed of the bicycle = ( [tex]\frac{492}{488}[/tex] × 343 ) - 343 Hz
speed of the bicycle = 2.81 m/s
The speed of the bicycle is 2.81 m/s.
Based on the given information,
• The tuning fork rated at frequency (f) 488 Hz.
• The beat frequency (fb) given is 8Hz.
• The speed of the sound is 343 m/s.
Now with the help of the given information, the rider is hearing a frequency of,
[tex]=(f+fb)\\=(488+8)\\=496 Hz[/tex]
However, it is bounding from sheer wall at the frequency of,
[tex]=(488+\frac{8}{2})\\= 492 Hz[/tex]
Now the speed of the bicycle will be,
[tex]=(\frac{492}{488} * 343)-343\\=2.811 m/s\\= 2.81 m/s[/tex]
Thus, the speed of the bicycle is 2.81 m/s.
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wooden floor at a constant speed of 1.0 m/s. The coefficient of kinetic friction is 0.15. Now you double the force on the box. How long would it take for the velocity of the crate to double to 2.0 m/s?
Answer:
Time = 1.36s
Explanation:
coefficient of kinetic friction = μk
μk = F/N = F / mg
where m = mass of the body
g = acceleration due to gravity.
Doubling the force on the box we have,
μk = 2ma/mg
hence μk = 0.15/2 = 0.075
To determine the time it takes to reach a velocity of 2m/s from 1m/s .
From Newton law of motion,
v = u + a*t
for a deceleration of a = μk x g
2m/s = 1m/s + 0.075 x 9.8m/s² x t
t = (2m/s - 1m/s)/0.735m/s²
t = 1.36 seconds..
it will take the 1.36s for the crate to double to 2.0m/s
__________ refers to the spreading of the signal that different parts of the signal arrive at different times at the destination. a. turnaround time b. propagation delay c. dispersion d. insulation e. attenuation
Final answer:
Dispersion refers to the spreading of a signal where different parts of the signal reach the recipient at varying times, affecting the wave by causing signal broadening due to the speed differential of its frequency components.
Explanation:
The term that refers to the spreading of a signal where different parts arrive at the receiver at different times is known as dispersion. Dispersion affects waves by causing a broadening of the signal, as different frequency components of the wave travel at different speeds. This is especially important in optical fibers, where dispersion can cause pulse broadening, potentially limiting the bandwidth and impairing the integrity of the data being transmitted. Option C is correct .
Factors such as scattering and refraction directly relate to the phenomenon of dispersion. For instance, scattering causes the redirection of light within a medium and refraction is the bending of a wave when it enters a medium where its speed is different. In the context of signal transmission, residence time is the average time a molecule spends in its reservoir, though this concept is less directly related to the question at hand.
The partial pressure of ethanol in the air above a sample of liquid ethanol in a closed container is 19.5 torr, at a given experimental Temperature. Assuming the pressure inside the container is 758.6 torr at the experimental T, what is the molar percent of ethanol in the air?
Answer:
The molar percent of ethanol in the air is 2.6%
Explanation:
Molar percent of ethanol in the air = partial pressure of ethanol/total pressure × 100 = 19.5 torr/758.6 torr × 100 = 2.6%
As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 39.0 m/s.
How fast is the watermelon going when it passes Superman?
Answer:
The velocity of watermelon when it passes Superman is 78 m/s.
Explanation:
Height of the building, d = 320 m
Speed of the superman, v = 39 m/s
We need to find the speed of watermelon when it passes Superman. Let t is the time taken by the watermelon. So,
[tex]d=ut+\dfrac{1}{2}gt^2[/tex]
Here u = 0
[tex]d=\dfrac{1}{2}gt^2[/tex]
[tex]39t=\dfrac{1}{2}\times 9.8\times t^2[/tex]
t = 7.95 seconds
Let v is the speed of the watermelon. It is given by :
[tex]v=gt[/tex]
[tex]v=9.8\times 7.95[/tex]
v = 77.91 m/s
or
v = 78 m/s
So, the velocity of watermelon when it passes Superman is 78 m/s.
Oxygen initially is at 40 F and 16.8 Ibf/in?. It fills a closed, rigid 5 ft³ tank filled with a paddle wheel. During the process, paddle wheel provides 4 Btu of energy transfer by work to the gas. During the process, Gas temperature increases up to 90 F. Assuming ideal gas behavior and ignoring K.E and P.E effects, determine the Heat transfer in Btu and the mass of oxygen.
Explanation:
The given data is as follows.
Initial temperature ([tex]T_{1}[/tex]) = [tex]40^{o}F[/tex] = 499.67R
Initial pressure ([tex]P_{1}[/tex]) = 16.8 Psi
Volume (V) = 5 [tex]ft^{3}[/tex]
Work done = 4 Btu
Final temperature ([tex]T_{2}[/tex]) = 90 F
So, R of [tex]O_{2}[/tex] = 0.3353 Psi ft^{3}/lbm R
Therefore, we will calculate the mass of oxygen as follows.
M = [tex]\frac{PV}{RT}[/tex]
= [tex]\frac{16.8 \times 5}{0.3353 \times 499.67}[/tex]
= 0.50137 lbm
Therefore, mass of oxygen is 0.50137 lbm.
Now, we will calculate the change in internal energy as follows.
[tex]\Delta U = mC_{v} [T_{2} - T_{1}][/tex]
= [tex]0.50137 \times 0.157 \times (90 - 40)[/tex]
= 3.936 BTU
Relation between heat energy and internal energy is as follows.
[tex]\Delta Q = \Delta u + W.d[/tex]
= [tex]3.936 + (-4)[/tex]
= -0.0642 BTU
Therefore, amount of heat transfer in BTU is 0.0642 BTU.
A hanging titanium wire with diameter 2.0 mm (2.0 × 10-3 m) is initially 2.5 m long. When a 9 kg mass is hung from it, the wire stretches an amount 0.605 mm. A mole of titanium has a mass of 48 grams, and its density is 4.51 g/cm3. Find the approximate value of the effective spring stiffness of the interatomic bond.
To find the approximate value of the effective spring stiffness of the interatomic bond, calculate the stiffness constant of the titanium wire using Young's modulus.
Explanation:To find the approximate value of the effective spring stiffness of the interatomic bond, we need to calculate the stiffness constant of the titanium wire. The stiffness constant, or Young's modulus (Y), is given by the formula Y = F/A/L, where F is the force applied, A is the cross-sectional area of the wire, and L is the original length of the wire.
First, we need to find the force applied. The force can be calculated using the equation F = mg, where m is the mass and g is the acceleration due to gravity.
Next, we need to calculate the cross-sectional area of the wire. The cross-sectional area can be calculated using the formula A = π(r^2), where r is the radius of the wire.
Finally, we can substitute the values into the formula Y = F/A/L to find the Young's modulus of the titanium wire.
A beam of light is traveling through a medium at 200,000 km/s. It enters a different medium and speeds up to almost 250,000 km/s. Finally, it enters a third medium and halts. What were the media the light traveled through, in order? Hurry!!!!!!!!!!!
Answer
From the question we can see that the in medium 1 speed of light is 200,000 Km/s where as in Medium 2 speed of light is 250,000 km/s.
We can conclude that medium 1 is denser than Medium 2.
In third medium Light speed halts so, the third medium is opaque.
We can say that
Medium 1 can be either water, glass.
Medium 2 will be gas
Medium 3 will be an opaque material.
Answer:
D
Explanation:
A nonlinear spring is used to launch a toy car. The car is pushed against the spring, compressing the spring 2.5 cm. The force the spring exerts on the car is given by the equation F=−Kx2, where K=5000 Nm2. The potential energy stored in the spring when the car is pushed against it is most nearly:________________
The potential energy stored in the spring when the car is pushed against it is most nearly is 0.026 J.
The calculation is as follows:Non linear spring is
[tex]F = -kx^2 \rightarrow force[/tex]
The potential energy
[tex]\frac{dU}{dX} = -F\\\\U = \int\limits {-Fdx}\\\\U = + \int\limits^x_0 {kx^2dx}\\\\U = \frac{kx^3}{3} \\\\U = 5000 \div 3 (\frac{2.5}{100}^)2\\\\U = \frac{5000 \times 2.5\times 2.5\times 2.5}{3\times 100\times 100\times 100}[/tex]
= 0.026 J
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We divide the electromagnetic spectrum into six major categories of light, listed below. Rank these forms of light from left to right in order of increasing wavelength. To rank items as equivalent, overlap them.a.gamma raysb.X raysc.ultravioletd.visible lighte.infraredf.radio waves
Answer:
(1.) gamma rays. (2.) X-rays. (3.) ultraviolet. (4.) visible light. (5.) infrared.
(6.) radio waves
Explanation:
Notice that these wavelengths span an enormous range. The wavelengths of gamma rays can be smaller than the size of an atomic nucleus, while the wavelengths of radio waves can be many meters (or even milometers) long. Visible light spans only a very narrow range of wavelengths, from about 400 nano meters at the blue (violet) end to about 700 nano meters at the red end.
The types of light in the electromagnetic spectrum, ranked from shortest to longest wavelength, are gamma rays, X-rays, ultraviolet, visible light, infrared, and radio waves.
Explanation:The electromagnetic spectrum is made up of different types of waves, each characterized by specific wavelengths. The categories of light in the electromagnetic spectrum from shortest to longest wavelength are:
Gamma raysX-raysUltravioletVisible lightInfraredRadio wavesAs we move from gamma rays to radio waves, the wavelength increases. Gamma rays have the shortest wavelength, while radio waves have the longest.
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Henrietta is going off to her physics class, jogging down the sidewalk at a speed of 2.95 m/s . Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of bagels, so he runs to the window of their apartment, which is a height 39.6 m above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time 7.50 s after Henrietta has passed below the window, and she catches them on the run. You can ignore air resistance. With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground?
Answer:
Explanation:
Given
Speed of Henrietta is [tex]v=2.95\ m/s[/tex]
Height of tower [tex]h=39.6\ m[/tex]
Bruce throws the bangle after 7.5 s
During 7.5 s Henrietta travels
[tex]x=2.95\times 7.5=22.125\ m[/tex]
Suppose bangle hit the ground after t sec so bangle will has to cover a distance of x and distance traveled by Henrietta during this time t
Range of bangle when thrown with speed u
[tex]R=u\times t[/tex]
[tex]R=x+2.95\times t-----1[/tex]
bangle will also cover a vertical distance of 39.6 m
so using equation of motion
[tex]h=u_yt+\frac{1}{2}gt^2[/tex]
here initial vertical velocity is zero
[tex]39.6=0+\frac{1}{2}\cdot 9.81\cdot t^2[/tex]
[tex]t=\sqrt{8.0816}[/tex]
[tex]t=2.84\ s[/tex]
Substitute the value of t in
[tex]u\times 2.84=22.125+2.95\times 2.84[/tex]
[tex]u=10.743\ m/s[/tex]
On the earth, when an astronaut throws a 0.250-kg stone vertically upward, it returns to his hand a time T later. On planet X he finds that, under the same circumstances, the stone returns to his hand in 2T. In both cases, he throws the stone with the same initial velocity and it feels negligible air resistance. The acceleration due to gravity on planet X (in terms of g) is:_______
a) g/.
b) g/4.
c) 2g.
d) g/2.
e) g.
Answer:
d) g/2
Explanation:
We need to use one of Newton's equations of motion to find the position of the stone at any time t.
x(t) = x₀(t) + ut - ¹/₂at²
Where
x₀(t) = initial position of the stone.
x(t) - x₀(t) = distance traveled by the stone at any time.
u = initial velocity of the stone
a = acceleration of the stone
t = time taken
On both planets, before the stone was thrown by the astronaut, x = 0 and t = 0.
=> 0 = x₀(t)
=> x₀(t) = 0
On earth, when the stone returns into the hand of the astronaut at time T on earth, x = 0.
=> 0 = 0 + uT - ¹/₂gT² (a = g)
=> uT = ¹/₂gT²
=> g = 2u/T
On planet X, when the stone returns into the hand of the astronaut, time = 2T , x = 0.
=> 0 = 0 + u(2T) - ¹/₂a(2T)²
=> 2uT = 2aT²
=> a = u/T
By comparing we see that a = g/2.
Final answer:
The acceleration due to gravity on planet X is determined by comparing the time it takes for a stone thrown vertically upward to return to the thrower's hand. Using kinematic equations and given that it takes twice the time to return on planet X as it does on Earth, we deduce the acceleration on planet X is half that of Earth's gravity (g/2).
Explanation:
The question concerns finding the acceleration due to gravity on an unknown planet, which is an essential concept in physics. To determine the gravitational acceleration (g) on planet X, given that a stone thrown with the same initial upward velocity as on Earth returns in 2T instead of T, we can use the kinematic equations for motion under constant acceleration.
On Earth, the total time for the stone to return to the thrower's hand is T, which implies that the time to reach the maximum height is T/2. Applying the equation v = u + at, where v is the final velocity (0 m/s at maximum height), u is the initial upward velocity, a is the acceleration due to gravity (which is -g on Earth), and t is the time (T/2), we have 0 = u - g(T/2). Solving for u gives us u = g(T/2).
On Planet X, the total time for the stone to return to the thrower's hand is 2T, so the time to reach maximum height is T. Using the same equation with the acceleration on Planet X as aX, we get 0 = u - aX(T). Since u = g(T/2), we have g(T/2) = aX(T), leading to aX = g/2.
Therefore, the correct answer is (d) g/2.
in circuit A, two resistors R1 and R2 are connected in series. In circuit B, two identical resistors are connected in parallel. Both circuits are powered by identical energy sources and include no other resistors. In which circuit, if any, is the current greater across R1?
A. Circuit A
B. Neither circuit
C. Circuit B
The current across R1 in circuit A is the same as the current across the resistors in circuit B.
Explanation:In circuit A, two resistors R1 and R2 are connected in series. In circuit B, two identical resistors are connected in parallel. In a series circuit, the current is the same in each resistor. Therefore, the current across R1 in circuit A is the same as the current across the resistors in circuit B, since they are connected in parallel.
A library of e-books contains metadata for each book. The metadata is intended to help a search feature find
books that users are interested in. Which of the following is LEAST likely to be contained in the metadata of each e-book?
a. An archive containing previous versions of the e-book
b. The author and title of the e-book
c. The date the e-book was first published
d. The genre of the e-book (e.g., comedy, fantasy, romance, etc.)
The metadata is intended to help a search feature the least likely feature contained in the metadata is An archive containing previous versions of the e-book so, option A is correct.
What are e-books?The term "e-book" refers to a digital file with a body of text and graphics that is suited for electronic distribution and displays on-screen similarly to a printed book.
E-books can be made by converting a printer's source files into forms that are simple to download and read on a screen, or they can be taken from a database or a collection of text files that weren't made just for printing.
When businesses like Peanut Press started offering book content for reading on personal digital assistants (PDAs), handheld devices that were the forerunners of today's smartphones and tablet computers, the market for buying and selling e-books first became a mainstream industry in the late 1990s.
Thus, metadata does not contain a feature to find an archive containing previous versions of the e-book.
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If a word problem gives the separation distance between two charges in centimeters (cm), you should ____. Question 4 options:
1) enter that value directly since cm is the standard unit
2) convert that distance to inches, the standard unit
3) convert that distance to meters, the standard unit
4) convert that distance to whatever units are given in the second distance
5) look to see whether the charges are like or opposite to know what to do
Answer:3
Explanation:
Convert the distance to meters,the standard units.
Final answer:
When a word problem provides the separation distance between two charges in centimeters, you should (3) convert that distance to meters, the standard SI unit for measurements in physics. Hence, (3) is the correct option.
Explanation:
If a word problem gives the separation distance between two charges in centimeters (cm), you should convert that distance to meters, the standard unit. Physicists use the International System of Units (SI units) for calculations to ensure consistency and comparison of data.
Since the SI unit for displacement is the meter (m), converting from centimeters to meters is necessary for performing electrostatic calculations involving Coulomb's law or any other physics formula.
For instance, when using Coulomb's law to find the force between two charges, the formula is F = k * (q₁ * q₂ / r²), where k is Coulomb's constant (8.987 x 10⁹ N m²/C²), q₁ and q₂ are the charges, and r is the separation distance in meters. If the problem states the distance in centimeters, you would convert the distance to meters by dividing by 100, since there are 100 centimeters in a meter.
A stack of bricks weighs 170 KN (Kilo-newtons). The stack exerts 180 KPa (Kilo-pascals) of pressure on the ground. What is the area upon which this pressure is exerted (in square ft)?
Answer:
10.12square feet
Explanation:
Pressure exerted on the object is defined as the ratio of the force exerted on it to its unit area. Mathematically, Pressure = Force/Area
Given the force = 170kN
Pressure = 180KPa
Area = Force /Pressure
Area = 170kN/180KPa
Area = 0.94N/Pa
Note that 1Newton/Pascal = 10.764square feet
Therefore 0.94N/Pa = x
x = 0.94× 10.764
x = 10.12square feet
Therefore the area upon which this pressure is exerted is 10.12sqft.