For an object that is under the pull of only the force of gravity, the motion is called free-fall. The equations that would allow us to calculate for the speed and distance is,
Speed = gt
Where g is the acceleration due to gravity and the t is the time.
For the distance, it is calculated through the equation,
Distance = vt + 1/2gt^2
Where v is the initial velocity and is equal to zero.
The graphs are attached.
In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.14 m. The mug slides off the counter and strikes the floor 0.60 m from the base of the counter.
The student's question pertains to the physics concept of projectile motion. The mug's trajectory is determined by its initial horizontal velocity, the counter's height, and gravity. One could compute the time it takes for the mug to hit the ground and its initial speed.
Explanation:
This question is about the physics concept of projectile motion. When the beer mug slides off the counter and falls to the ground, it follows a trajectory determined by the initial horizontal velocity at which it was pushed, the height of the counter, and the acceleration due to gravity.
To find out how long it takes for the mug to hit the ground, we can use the equation of motion: h = 0.5gt^2, where h is the height from which the object is dropped (1.14m in this case), g is acceleration due to gravity (approximately 9.8 m/s^2) and t is time. Solving for t gives us the time it takes for the mug to hit the floor.
Once we know the time, we can find the initial horizontal velocity using the formula v = d/t, where v is velocity, d is distance (0.60m) and t is time. This gives us the initial speed at which the mug was slid.
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The position of a 2.75×105n training helicopter under test is given by r⃗ =(0.020m/s3)t3i^+(2.2m/s)tj^−(0.060m/s2)t2k^. part a find the net force on the helicopter at t=5.0s.
The net force on the helicopter at t=5.0s = F = 1.65.10⁴i - 3.3.10³k
Further explanationNewton's 2nd law explains that the acceleration produced by the resultant force on an object is proportional and in line with the resultant force and inversely proportional to the mass of the object
[tex]\large{\boxed{\bold{a~=~\frac{F}{m} }}}[/tex]
∑F = m. a
F = force, N
m = mass = kg
a = acceleration due to gravity, m / s²
While the speed is the first derivative of distance
[tex]\large{\boxed{\bold{V~=~\frac{dr}{dt} }}}[/tex]
While acceleration is the first derivative of the velocity function for t
[tex]\large{\boxed{\bold{a~=~\frac{dv}{dt} }}}[/tex]
It is known that the distance function (r) = (0.020 t³i + 2.2 tj-0.06t²k
Then the speed (v)
[tex]v~=~\frac{dr}{dt}[/tex]
v = 0.06t²i + 2.2j - 0.12tk
Then acceleration (a)
[tex]a~=~\frac{dv}{dt}[/tex]
a = 0.12ti - 0.12k
While :
W = m . g
[tex]m~=~\frac{W}{g}[/tex]
m = 2.75.10⁵ : 10
m = 2.75.10⁴
so net force :
F = m . a
F = 2.75.10⁴ . ( 0.12ti - 0.12k)
for t = 5
F = 2.75.10⁴ . ( 0.12.5i - 0.12k)
F = 2.75.10⁴ (0.6i-0.12k)
F = 1.65.10⁴i - 3.3.10³k
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Keywords : Newton's Law, acceleration, net force
The net force on the helicopter at time [tex]t = 5.0\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].
Further Explanation:
The helicopter moves under the action of the force which changes the position of the helicopter with respect to time according to the following equation.
[tex]\vec{r}=(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}[/tex]
The force acting on the helicopter at a particular time is given by:
[tex]\fbox{\begin\\F= m\cdot{a}\end{minispace}}[/tex]
Here, [tex]m[/tex] is the mass of the helicopter and [tex]a[/tex] is the acceleration of helicopter.
The helicopter has a weight of [tex]2.75 \times {10^5}\,{\text{N}}[/tex]. This weight of the helicopter can be converted into the mass of the helicopter.
The weight of the helicopter can be represented as.
[tex]\fbox{\begin\\W=m \cdot g\end{minispace}}[/tex]
Rearrange and simplify the expression for the mass of helicopter.
[tex]\begin{aligned}m&=\frac{W}{g}\\&=\frac{{2.75\times{{10}^5}}}{{9.8}}\,{\text{kg}}\\&=2.{\text{80}}\times{\text{1}}{{\text{0}}^4}\,{\text{kg}}\\\end{aligned}[/tex]
The velocity of the helicopter can be determined by the differentiation of the position vector of the helicopter with respect to time.
[tex]\begin{aligned}\vec{v}&=\dfrac{{d\vec{r}}}{{dt}}\\&=\dfrac{d}{{dt}}\ [(0.020\text{ m}/\text{s}^3)\text{ t}^3\hat{i}+(2.2\text{ m}/\text{s})\text{ t}^3\hat{j}-(0.060\text{ m}/\text{s}^2)\text{ t}^2\hat{k}]\\&=0.060{t^2}\hat{i}+2.2\hat{j}-0.12t\hat{k}\end{aligned}[/tex]
The acceleration of the helicopter is the derivative of the velocity with respect to the time.
[tex]\begin{aligned}\vec a&=\frac{{d\vec v}}{{dt}}\\&=\frac{d}{{dt}}\left({0.060{t^2}\hat i+2.2\hat j-0.12t\hat k}\right)\\&=0.12t\hat i-0.12\hat k\\\end{aligned}[/tex]
Substitute the value of [tex]t = 5.0\,{\text{s}}[/tex] in equation of the acceleration.
[tex]\begin{aligned}a&=0.12\left({5.0}\right)\hat i-0.12\hat k\\&=0.6\hat i-0.12\hat k\\\end{aligned}[/tex]
Substitute the values of the acceleration and the mass of the helicopter in the equation of force.
[tex]\begin{aligned}F&=\left( {2.80\times{{10}^4}\,{\text{kg}}}\right)\left({0.6\hat i-0.12\hat k}\right) \\&=\left({1.68\times{{10}^4}\,\hat i-3.36\times{{10}^3}\,\hat j}\right)\,{\text{N}}\\\end{aligned}[/tex]
Thus, the net force acting on the helicopter at time [tex]t = 5\,{\text{s}}[/tex] is [tex]\fbox{\begin\\\left( {1.68 \times {{10}^4}\,\hat i - 3.36 \times {{10}^3}\,\hat j} \right)\,{\text{N}}\end{minispace}}[/tex].
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Answer Details:
Grade: College
Subject: Physics
Chapter: Force and acceleration
Keywords:
Helicopter, force, time, 5s, position, velocity, derivative, acceleration, weight, net force, t=5s, 0.020t3 m/s3, 2.75x10^5 N, helicopter under test, gravity, mass of helicopter.
The branch of mechanics dealing with the mathematical methods of describing motion is calle
In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. the stone moves approximately 40 m before coming to rest. the final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. judicious sweeping can lengthen the travel of the stone by 3 m.
From Newton’s law of motion, the relation for velocity, acceleration and displacement is given by v^2 = vo^2 + 2as. Where v and vo are final and initial velocity respectively, and a, s are the acceleration and displacement respectively. From Newton’s second law, F = ma. Where m is the mass.
The magnitude of the frictional fore can be calculated only before estimating the ston’s acceleration. The initial speed of stone is mentioned in the problem as 3 m/s. Also, after 40m, the stone will stop. This means that its final speed is 0 m/s and the displacement is 40m.The acceleration of rock is calculated as:
(0 m/s)^2 = (3 m/s)^2 + 2a (40m).
9 m^2/s^2 = -2a(40m)
a= -9m^2/s^2/80m = 0.1 m/s^2.
This means that deceleration will occur and this will stop the stone. Substituting to Newton’s second law of motion,
-F = 20kg * -0.1 m/s^2. Further solve,
F = 20kg * 0.1 m/s^2 = 2N. Hence, the magnitude frictional force is 2N.
In curling, the final position of the stone depends on its initial speed and the force of friction. Team members can use brooms to adjust the stone's speed and trajectory. The force of friction opposes the stone's motion.
Explanation:In the winter sport of curling, the final position of the stone depends on the initial speed at which it is launched and the force of friction between the ice and the stone. Team members can use brooms to sweep the ice, which can adjust the stone's speed and trajectory. By judicious sweeping, they can lengthen the travel of the stone by a few meters. The force of friction between the ice and the stone will oppose the motion of the stone and slow it down.
The initial speed at which the stone is launched will determine how far it travels before coming to rest. If the stone is launched with a higher initial speed, it will travel a farther distance. The force of friction between the ice and the stone will also influence the distance the stone travels. A higher frictional force will cause the stone to slow down more quickly, resulting in a shorter travel distance.
What kind of materials can become electrically charged when they are rubbed together?
Answer:
When insulating materials rub against each other, they may become electrically charged . Electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. The material that gains electrons becomes negatively charged.
Explanation:
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A satellite revolves around a planet at an altitude equal to the radius of the planet. the force of gravitational interaction between the satellite and the planet is f0. then the satellite is brought back to the surface of the planet. find the new force of gravitational interaction f4. express your answer in terms of f0.
A 20000 kg rocket has a rocket motor that generates 3.0×105 n of thrust. part a what is the rocket's initial upward acceleration?
Answer:
a=5.20 m/s²
Explanation:
Given Data
Thrust = T (N)=3.0×10⁵N
Mass=m=20000kg
To find
acceleration=a=?
Solution
Newton Second law states that
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
(resultant force F)=ma
a=(resultant force F)/m
where
(resultant force F) is (Thrust-weight)
Weight = mg = 2.0^4 kg*9.8 N/kg = 1.96^5 N
a = (resultant force F) / mass
a = (T - mg)/m = (3.0^5 N - 1.96^5 N)/ 2.0^4 kg
a=5.20 m/s²
The rocket's initial upward acceleration is 5.2m/s²
According to Newton's second law of motion
[tex]\sum F = ma[/tex]
The sum of forces is the difference between the weight and the thrust
[tex]\sum F = T -W[/tex]
[tex]T - W = ma\\a=\frac{T-W}{a}[/tex]
Given the following parameters:
T = [tex]3.0 \times 10^5 N[/tex]
W = [tex]20,000 \times 9.8 = 1.96 \times 10^5 N[/tex]
m = [tex]20,000kg[/tex]
Substitute the given parameters into the formula to have:
[tex]a=\frac{(3.0-1.96)\times 10^5}{2\times 10^4} \\a=\frac{1.04\times 10^5}{2\times 10^4} \\a = 0.52 \tmes 10\\a = 5.2m/s^2[/tex]
Hence the rocket's initial upward acceleration is 5.2m/s²
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Why is the primary mirror in a telescope curved?
to magnify the image
to direct light rays to a focal point to intensify them
to change the direction of the rays
to bend the rays
to absorb extra light
Answer: to direct light rays to a focal point
Explanation:
A reflecting telescope uses curved mirror as primary and a plane mirror placed at an angle as secondary. A curved mirror is used as primary because this mirror collects the light from distant celestial object and converges its light at focus where the plane mirror is kept at an angle so that the reflected light is received by the eyepiece.
It is used as a curved primary mirror in a telescope because to direct light rays to a focal point.
What lenses are used in the telescope?For the construction of a telescope, the physicist Galileo used a lens of the converging type and a lens of the diverging type. In his telescope, the first lens, called the objective, formed a real image of the object in question.
A reflecting telescope uses curved mirror as primary because this mirror collects the light from distant celestial object and converges its light at focus where the plane mirror is kept at an angle so that the reflected light is received by the eyepiece.
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which measurement gives the most accurate number for a population in an area?
A) add the biodiversity of an area to the carrying capacity.
B) add the individuals who come into an area because of reproduction or immigration.
C) add the individuals living or born in an area and subtract those who die.
D) subtract the animals that die from the total carrying capacity.
The most accurate number for a population in an area is measured by adding the individuals living or born in an area and subtract those who die. So, option C.
The amount of people living in a particular area is called population density.
The majority of the time, it applies to people, but occasionally it also does to other living things. It is a significant geographic term. Population density is the total number of people residing in a certain area per square kilometer, or other units of land area.
Demography is the statistical study of populations and how they change through time.
Population size, or the total number of people, and population density, or the number of people per unit of space or volume, are the two most important measurements of a population.
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Final answer:
The most accurate way to measure population size is by adding the number of births and individuals present, while subtracting the number of deaths (which corresponds to option C). Sampling techniques like quadrats and mark-recapture are often used due to the impracticality of counting all individuals.
Explanation:
In the context of estimating population size, the most accurate measurement for a population in an area would be to add the individuals living or born in an area and subtract those who die (Option C). This method accounts for natural population changes such as births and deaths.
Although counting all individuals would provide the most precise number, this is often not feasible. Instead, scientists often use sampling techniques to estimate population size. For stationary or slow-moving organisms, a quadrat can be used, while for mobile organisms, methods like mark and recapture might be employed.
Carrying capacity is a separate concept indicating how many individuals an area can sustain based on resources. Adjustments to population estimates may be necessary when populations near their carrying capacity, as density-dependent factors might affect population growth.
Magnetic field lines curve out from one pole and return to the same pole.
t/f
Answer:
the answer is false
Explanation:
your welcome
Describe what would happen if you rubbed a mineral with a Mohs hardness value of 7 against a mineral with a value of 5?
If a mineral with a Moh's hardness value of 7 is rubbed against the mineral with a value of 5, the mineral with value 5 get scratched with the mineral with hardness value 7.
• A scale of relative mineral hardness invented by German scientist Mohs is known as the Mohs scale of hardness or Mohs scale.
• It is a 10 point scale, with 10 given to mineral diamond as the most hardest mineral, which can scratch the minerals below it, that is, coming below it in the hardness scale.
• The minerals coming in the 7 scale are Quartz, Citrine, Agate, and Amethyst, and the mineral coming in the 5 scale is apatite.
• Thus, when one rubs the mineral with 7 hardness with a mineral with 5 hardness, than the mineral with 5 hardness will easily get scratched as it is less harder to the mineral in the 7 scale.
Thus, the mineral with value 5 get scratched with the mineral with hardness value 7.
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A race car is moving with a velocity of 144 kilometers/hour. The driver applies the brakes, and the car comes to a halt in 12.0 seconds. What is the average acceleration of the car during those 12.0 seconds? –12.0 meters/second2
\a stone is dropped from the top of a cliff. it hits the ground below after 3.80s. how high is the cliff in meters?
The carpal bones in the hands are an example of __________.
Answer:
A gliding joint means a freely moving joint in which the articulations allow only gliding motions
Explanation:
In order to climb a steep hill on a bicycle, a rider shifts to the lowest gear. The lowest gear has the greatest mechanical advantage because it
The lowest gear on a bicycle provides the greatest mechanical advantage by amplifying the force exerted on the pedals, requiring the rider to pedal more but with less effort per stroke, due to the conservation of energy.
In order to climb a steep hill on a bicycle, a rider shifts to the lowest gear. The lowest gear has the greatest mechanical advantage because it allows the rider to apply a force over a greater distance. When a gear with many teeth drives a gear with fewer teeth, the driven gear spins more times but with a smaller turning force, amplifying the force the rider exerts on the pedals.
However, this means the rider will have to spin the pedals more times to cover the same distance, which is a trade-off.
This concept of mechanical advantage applies to all machines and is governed by the conservation of energy, which states that work input is equal to work output, minus any losses due to inefficiency like friction.
A golf ball is hit with an initial speed of 33 m/s at an angle less than 45∘ above the horizontal.
The region around a magnet where the magnetic force is exerted is known as
If f = 136 lb , determine the resultant couple moment.
A car goes from 40n/s to 60 m/s in 8s the acceleration of the car is
The normal boiling point of cyclohexane is 81.0 ℃. what is the vapor pressure of cyclohexane at 81.0 ℃?
Final answer:
The vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃ is 101.3 kPa.
Explanation:
The question is asking for the vapor pressure of cyclohexane at its normal boiling point of 81.0 ℃. By definition, the normal boiling point of a liquid is the temperature at which its vapor pressure is equal to the external atmospheric pressure at sea level, which is 101.3 kPa (or 1 atmosphere). Therefore, the vapor pressure of cyclohexane at 81.0 ℃ is 101.3 kPa.
What determines the amount of chemical energy asubstance has
The amount of chemical energy a substance has is determined by its molecular structure and the type of chemical bonds it contains.
1. Molecular Structure:
- The arrangement of atoms within a molecule determines its potential energy content.
- Different substances have varying numbers and arrangements of atoms, leading to differences in chemical energy.
2. Type of Chemical Bonds:
- Chemical energy is stored in the bonds between atoms within molecules.
- The strength and type of chemical bonds, such as covalent bonds, ionic bonds, and hydrogen bonds, dictate the amount of energy stored in the substance.
- Stronger bonds require more energy to break and thus store more chemical energy.
3. Potential Energy:
- Chemical energy represents the potential energy stored within a substance's chemical bonds.
- When chemical bonds are broken during a chemical reaction, the stored energy is released as heat or used to perform work.
4. Examples:
- Substances with complex molecular structures and strong chemical bonds, such as hydrocarbons in fossil fuels, tend to have high chemical energy content.
- Conversely, simpler molecules with weaker bonds, such as gases like hydrogen and oxygen, have lower chemical energy content.
Therefore, the amount of chemical energy a substance possesses is determined by its molecular structure and the type of chemical bonds it contains, with stronger bonds and more complex structures generally correlating with higher chemical energy content.
The complete Question is given below:
What determines the amount of chemical energy a substance has?
12 points. Change of state:
Identify the process that causes each change of sate describe below, Write the appropriate answer on the space provided.
_______a. an ice cube left in a freezer for a month becomes smaller.
_______b. drops of water appear on the side of a glass of ice water.
_______c. a rainy morning turns sunny, and puddles disappear from a sidewalk.
What is the boiling point of oxygen
The boiling point of oxygen is 90.2 K or -183.15 °C.
At standard atmospheric pressure, the boiling point of oxygen is 90.2 K, which is equivalent to -183.15 °C or -297.67 °F.This allows oxygen to be separated from nitrogen and other components in liquid air through fractional distillation due to their different boiling points.what energy is the flow of electrons that creates a charge, one of the main forms of energy
Answer:
electricity
Explanation:
just got the question and it was right
______ interference occurs when two waves overlap and the resulting wave has a larger amplitude.
Answer: The correct answer is constructive interference.
Explanation:
Interference is the phenomenon in which there is superposition of the two waves. Interference are of two types: Constructive interference and Destructive interference.
Constructive interference occurs when the there is a superposition of the two waves. The resulting wave has a large amplitude.
Destructive interference occurs when the there is a superposition of the two waves. The resulting wave has a low amplitude.
Therefore, Constructive interference occurs when two waves overlap and the resulting wave has a larger amplitude.
Answer:
B. Constructive
Newton's first law of motion states that an object remains at rest unless a(n) ____ force acts on it. a. balanced c. gravitational b. frictional d. unbalanced Please select the best answer from the choice
The right ventricle transports oxygenated blood to the lungs.
Please select the best answer from the choices provided.
T
F
Answer: False
Explanation: The circulatory system of the body consists of the heart, blood vessels and blood. The deoxygenated blood from the body is carried to the heart.
Here, the deoxygentaed blood is converted into oxygenated by removing carbon dioxide from them and making it oxygenated.
The impure blood from the body is collected by the right ventricle and transported to the lungs for purification and then transported to the body.
The correct answer is F (False)
Explanation:
In anatomy, the heart which is the organ in charge of pumping blood to all the body is divided into different sections that include the aorta, the superior vena cava, the right/left atrium, the pulmonary valve, and the right/left ventricles. In the case of the right ventricle, this is a chamber located on the right side of the hearth and the main function of this is to pump blood that is low in oxygen or de-oxygenated blood to the lungs through the pulmonary artery. On the other hand, the left ventricle pumps oxygenated blood to all the body. This implies, it is false the right ventricle transports oxygenated blood to the lungs because it pumps de-oxygenated rather than oxygenated blood.
A second order chemical reaction involves the interaction (collision) of one molecule of a substance p with one molecule of a substance q to produce one molecule of a new substance x; this is denoted by p + q → x. suppose that p and q, where p = q, are the initial concentrations of p and q, respectively, and let x(t) be the concentration of x at time t. then p − x(t) and q − x(t) are the concentrations of p and q at time t, and the rate at which the reaction occurs is given by the equation dx/dt = α(p − x)(q − x), (i) where α is a positive constant. (a) if x(0) = 0, determine the limiting value of x(t) as t → ∞ without solving the differential equation. then solve the initial value problem and find x(t) for any t.
if you push a block across the floor with constant force the block will
A favorable entropy change occurs when δs is positive. what can be said about the order of the system when δs is positive?
A positive entropy change (delta S) indicates that the system has become less ordered, as there is an increase in the number of possible microstates. This is aligned with the Second Law of Thermodynamics, which states that entropy increases in spontaneous processes, leading to greater disorder.
Explanation:When a system undergoes a change and the entropy change (δS) is positive, this implies that the order of the system has decreased. This is because positive entropy reflects an increase in the number of microstates or possible configurations that the system can adopt, leading to a less ordered, more random state. A common example is the melting of a solid into a liquid where the rigid structure of the solid is lost, providing the particles more freedom to move in the liquid state, which translates into an increased entropy.
As per the Second Law of Thermodynamics, for all spontaneous processes in the real world, the change in entropy is positive (dδS > 0), which is consistent with the natural tendency for systems to move towards greater disorder and randomness. This concept is fundamental in predicting the spontaneous direction of chemical and physical processes. For instance, when a liquid freezes into a solid, the process is accompanied by a negative entropy change, signifying increased order in the system.
Final answer:
A positive entropy change (δS > 0) means that the order of the system has decreased, leading to a more disordered and randomized state with more microstates. This is in line with the Second Law of Thermodynamics, which predicts that the entropy of an isolated system tends to increase in spontaneous processes.
Explanation:
When the entropy change (δS) is positive, it indicates that the order of the system has decreased. This is because a positive δS suggests that the number of microstates and, therefore, the randomness of the system has increased. For example, when a solid changes into a liquid, there is an increase in entropy because the liquid state allows the particles more freedom of movement and positioning, leading to a higher number of microstates compared to the solid state. If the process were reversed and the liquid turned into a solid, δS would be negative, signifying a decrease in entropy as the system becomes more ordered.
Furthermore, the Second Law of Thermodynamics asserts that for any spontaneous process, the entropy of an isolated system will increase. This means the system will move towards a state with more microstates or higher disorder. It aligns with the observation that in irreversible processes, entropy tends to increase, indicating a spontaneous change in an isolated system.
In conclusion, a positive entropy change (δS > 0) aligns with the expectation that there are more microstates available in the final state compared to the initial one, resulting in a decrease in the orderliness of the system. The increase in entropy reflects the fundamental tendency for systems to evolve towards states of higher disorder and randomness.