# block 1 is at rest on a horizontal surface and is connected to a wall by an ideal spring. friction between block 1 and the surface is negligible. block 1 is held at rest at point a, to the left of point b which is the equilibrium position of the spring-block system, as shown in the figure. block 1 is then released and allowed to oscillate. some time later, block 1 is momentarily at rest at point c. consider the positive horizontal direction to be toward the right.

### James

Guys, does anyone know the answer?

get block 1 is at rest on a horizontal surface and is connected to a wall by an ideal spring. friction between block 1 and the surface is negligible. block 1 is held at rest at point a, to the left of point b which is the equilibrium position of the spring-block system, as shown in the figure. block 1 is then released and allowed to oscillate. some time later, block 1 is momentarily at rest at point c. consider the positive horizontal direction to be toward the right. from EN Bilgi.

## Question 3a: 2015 AP Physics 1 free response (video)

Graphing energy versus position for a block accelerated by a spring and stopped by friction.

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AP Physics 1 free response questions 2015

## Question 3a: 2015 AP Physics 1 free response

Graphing energy versus position for a block accelerated by a spring and stopped by friction.

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## AP Physics 1 free response questions 2015

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## Want to join the conversation?

Log in adiparekh101 5 years ago

Posted 5 years ago. Direct link to adiparekh101's post “why wouldn't potential en...”

why wouldn't potential energy increase after D=0? At 3D, isn't the spring stretched completely, and ,therefore, storing energy?

• samr0519 5 years ago

Posted 5 years ago. Direct link to samr0519's post “I had the same issue you'...”

I had the same issue you're having, but I realized that the spring and the block are not connected. Since the spring has negligible mass it can be assumed that it stops around the time it hits the equilibrium (x=0) and the block keeps going but decelerates because of friction.

alavrouk 6 years ago

Posted 6 years ago. Direct link to alavrouk's post “Wouldn't the kinetic ener...”

Wouldn't the kinetic energy from 0 to 3D be curved, because velocity is linear but kinetic energy is proportional to velocity squared, and squared linear is not linear?

• Vedaant Tambi 5 years ago

Posted 5 years ago. Direct link to Vedaant Tambi's post “Since the block will no l...”

Since the block will no longer be in contact with the spring at x=0, the only force acting on the block after this position is the force of friction which is CONSTANT throughout. After this it can be easily deduced why the Kinetic energy vs position graph will be linear:

From 3rd equation of motion,

'v^2-u^2=2as

Or -u^2/2a=s (since final velocity v will ultimately be 0 )

Or -u^2 is directly proportional to distance covered

Or (-m/2)*u^2 is proportional to distance covered', which means that kinetic energy is directly proportional to distance covered. One must remember that this is an energy vs position graph.

LUKE MATSUI a year ago

Posted a year ago. Direct link to LUKE MATSUI's post “Wouldn't the spring conti...”

Wouldn't the spring continue to oscillate after the object is released or is all of the energy transferred to the object?

• True 6 years ago

Posted 6 years ago. Direct link to True's post “What would the rest of th...”

What would the rest of the potential energy graph look like, from 0 to 3D? And I don't understand why from 0 to 3D the kinetic energy is decreasing as a linear function, 1/2mv^2, and the velocity is the factor changing due to the frictional force?

• akira01px2017 6 years ago

Posted 6 years ago. Direct link to akira01px2017's post “It's a linear function be...”

It's a linear function because it's essentially the floor doing work against the block, so W=d*F, where the friction force is the same since the the coefficient didn't change through out. This means the work done, amount of energy converted from kinetic in this case, is the same per unit distance. Therefore, it is linear. There is no more potential energy because it left the spring at point 0.

## Video transcript

- [Voiceover] A block is initially at position x = zero, and in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position x = zero to x = -D, as shown above, compressing the spring by an amount delta x = D. So, the block starts here, and it's just in contact with the spring, so it's initially, the spring is uncompressed. And it's just touching the block. And then we start to compress the spring by pushing the block to the left, and we compress it by an amount, D. They tell us that, right there, delta x is = to D, so we compress, we move this block back over to the left by D, that compresses the spring by D. The block is then released at x = zero, the block enters a rough part of the track and eventually comes to rest at position x = 3D. So when we compress the spring, we're actually doing to work to compress the spring, so that work, that energy from the, or the work we're doing, gets stored as potential energy in the spring-block system. And then when we let go, that potential energy is going to be converted to kinetic energy, and that block is going to be accelerated all the way until we get back to x = zero, then the spring is back to uncompressed, so it's not gonna keep pushing on the block after that point. And then the block's going to have this kinetic energy and if there was no friction in this gray part here, it would just keep on going forever. And if there's no air resistance, and we're assuming no air resistance for this, for this problem, but since there is friction, it's just going to decelerate it at a constant rate. You're going to have a constant force of friction being applied to this block. So, let's see, they say, they tell us that it's going to come to rest at x = 3D, the coefficient of kinetic friction between the block and the rough track is mu. Alright, on the axes below, sketch and label graphs of the following two quantities as a function of the position of the block between x = negative D and x = 3D. You do not need to calculate values for the vertical axis but the same vertical scale should be used for both quantities. So they have the kinetic energy of the block and the potential energy of the block-spring system. So let's first focus on the potential energy, U, because when we start the first part of this, when we're compressing the spring, that's when we're starting to put potential energy into this spring-block system. So you have to think about what is the potential energy of a compressed spring? Well, the potential energy the potential energy is equal to one-half times the spring constant times how much you compress the spring squared. So if we wanna say delta x is how much you compress the spring, that squared. Now, if what I just wrote is completely unfamiliar to you, I encourage you to watch the videos on Khan Academy, the potential energy of a compressed spring or the work necessary to compress a spring, cause the work necessary to compress the spring that's going to be the potential energy that you're essentially putting into that system. And so, for this, as we compress the spring to D, you are, you're going to end up with a potential energy of one-half times the spring constant x our change in x is D, our change in x is D. x D, x D squared. So let's plot that on this right over here. So right, whoops, right when we are at x = zero there's no potential energy in our system, but then we start to compress it, and when we get to x = D, we're going to have a potential energy of one-half times the spring constant times D squared. So let's just say this, right over here, let's say that over there, actually let me do a, let's see that one is, actually I'll do it over here so it'll be useful for me later on. So, let's say that this, right over here, is one-half times our spring constant times D squared. So this is what our potential energy's going to be like once we've compressed the spring by D. And it's not going to be a linear relationship, remember the potential energy potential energy is equal to one-half times the spring constant, times the spring constant, times how much you've compressed the spring squared. So, the potential energy increases as a sqaure of how much we've compressed the spring. So when we've compressed the spring half as much, we're going to have one-fourth of the potential energy. So it's going to look like this, it's gonna be you can view it as the left side of a parabola. So it's going to, going to look something, something like this. So that's the potential energy. Now, when you're in this point, when the thing is fully compressed, and then you let go, what happens? Well that potential energy is turned into kinetic energy, so as the spring, as the spring accelerates the block, you're gonna go down this potential energy curve, as you go to the right, but then, it gets converted to kinetic energy. So the potential energy plus the kinetic energy needs to be constant, at least over this period from x = negative D to x = zero. So the kinetic energy starts off at zero, it's stationary, but then, it starts, the block starts getting accelerated. It starts getting accelerated. And the sum, the sum of these two things needs to be equal to one-half times our spring constant times D squared. And so you can see if you, if you were to add these two curves at any position, you are going, their sum is going to sum up to this value. And so right when you get back to x = zero, all of that potential energy has been converted into kinetic energy. And then that kinetic energy, we would stay at that high kinetic energy if there was no friction or no air resistance. But we know that the block comes to a rest at x is = to 3D. So all the kinetic energy is gone at that point, and you might say well, what's that getting converted into? Well, it's gonna get converted into, into heat, due to the friction. So that's where, ya know, energy cannot be cannot be created out of thin air or lost into thin air, it's converted from one form to another. And so the question is, what type of a curve is this? Do we just connect these with a line? Or is it some type of a curve? And the key realization is: is that you have a constant force of friction the entire time that the block is being slowed down, the coefficient of friction doesn't change, so the force of friction, and the mass of the block isn't changing, so the force of friction's going to be the same. And it's acting against the motion of the block. So you can, you can view the friction as essentially doing this negative work, and so it's sapping the energy away, if you think about it relative to distance, in a given amount of distance, it's sapping away the same amount of energy, it's doing that same amount of negative work. And so, this is going to decrease at a linear rate. So, let me draw that. So it's gonna be a linear decrease, just like that. And the key thing to remind yourself is: is this is a plot of energy versus position, not velocity versus position or velocity versus time, or energy versus time. This is energy versus position, and that's what gives us this linear relationship right over here. So, we have the kinetic energy, k, of the block. That's what I did in magenta, so this is the kinetic energy. Kinetic, kinetic energy, and in blue, just to make sure I label it right, this is the potential energy, potential, potential energy.

## AP Physics 1 Unit 4 Progress Check A Flashcards

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## AP Physics 1 Unit 4 Progress Check A

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A block of mass M on an inclined surface is attached to a spring of negligible mass, as shown. The other end of the spring is attached to a wall, and there is negligible friction between the block and the incline. The block is pulled to a position such that the spring is stretched from its equilibrium position. The block is then released from rest. Which of the following systems can be classified as a closed system?

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A system consisting of the block, spring, and Earth

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The total mechanical energy of a system as a function of time is shown in the graph. Which of the following statements is true regarding the system?

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The system should be classified as an open system because mechanical energy can be added and removed from the system.

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### Terms in this set (16)

A block of mass M on an inclined surface is attached to a spring of negligible mass, as shown. The other end of the spring is attached to a wall, and there is negligible friction between the block and the incline. The block is pulled to a position such that the spring is stretched from its equilibrium position. The block is then released from rest. Which of the following systems can be classified as a closed system?

A system consisting of the block, spring, and Earth

The total mechanical energy of a system as a function of time is shown in the graph. Which of the following statements is true regarding the system?

The system should be classified as an open system because mechanical energy can be added and removed from the system.

A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following systems does the total mechanical energy of the system remain constant?

The closed system containing the planet and the star

A 5 kg object near Earth's surface is released from rest such that it falls a distance of 10 m. After the object falls 10 m, it has a speed of 12 m/s. Which of the following correctly identifies whether the object-Earth system is open or closed and describes the net external force?

The system is open, and the net external force is nonzero.

A toy car has an initial acceleration of 2m/s2 across a horizontal surface after it is released from rest. After the car travels for a time t=5 seconds, the speed of the car is 25m/s. Is the system consisting of only the car an open system or a closed system, and why?

Open system, because an external force is applied to the car that causes it to accelerate.

A student performs an experiment in which a ball travels in a perfect circle. The ball is attached to a string and travels in the horizontal, circular path, as shown in Figure 1. At time t0, the ball has a speed ν0. During the time interval of 0s to 2s, the force of tension in the string is recorded and graphed, as shown in Figure 2. Is the system consisting of the ball, string, and student an open system or closed system, and why?

Open system, because the force due to gravity from Earth is an external force that is exerted on the ball-string-student system

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table.

How should the student use the data collected and the known quantities from the experiment to determine the total mechanical energy of the block-ramp-Earth system for all trials in the experiment?

Use K=1/2 mv2K=1/2mv2 with the block's initial speed for one trial because the initial speed is the same in all trials.

A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table.

Consider the trial with the 45° ramp. Suppose the block is launched up the ramp such that it comes to rest at point B and then travels down the ramp. Which of the following best describes the block's kinetic energy KA when it reaches point A at the bottom of the ramp in comparison to the initial kinetic energy K0 before it travels up the ramp?

## (AP P1) Quiz 4.2

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## (AP P1) Quiz 4.2

(AP P1) Quiz 4.2 43%

294 11th 11th Physics Dr. Stawiery 2 years

## 15 Qs

1. Multiple-choice 15 minutes

Q.

A block of mass 0.10 kg is attached and secured to one end of a spring with spring constant 50 N/m. The other end of the spring is secured to a wall. The block is pushed against the spring, which compresses the spring to a position of x=-0.04x=−0.04 m. When uncompressed, the end of the spring that is attached to the block is at a position of x=0.00x=0.00 m. The block-spring system is then released from rest, and the block travels along a horizontal, rough track. A motion sensor is placed so that it measures the velocity of the object as it slides along the track. A graph of total mechanical energy of the block-spring system as a function of position is shown. Which of the following statements about the block-spring system are true? **Select two answers**

answer choices

The force exerted on the block by the spring at x=-0.02x=−0.02 m is 1 N.

The block has maximum speed at x=0.00x=0.00 m.

The block has half the initial spring potential energy at x=-0.025x=−0.025 m.

The work done by friction as the block travels from x=-0.04x=−0.04 m to x=-0.02x=−0.02 m is 0.01 J

2. Multiple-choice 15 minutes Q.

A ball is dropped from rest and falls to the floor. The initial gravitational potential energy of the ball-Earth-floor system is 10 J. The ball then bounces back up to a height where the gravitational potential energy is 7 J. What was the mechanical energy of the ball-Earth-floor system the instant the ball left the floor?

answer choices 0 J 3 J 7 J 10 J 3. Multiple-choice 15 minutes Q.

A block on a horizontal surface of negligible friction is placed in contact with an ideal spring, as shown above. The block is moved to the left so that the spring is compressed a distance xx from equilibrium and then released from rest. The block has kinetic energy K_1K1 when it separates from the spring. When the spring is compressed a distance 2x2x and the block is released from rest, the kinetic energy of the block when it separates from the spring is

answer choices K_1K1 \sqrt{2}K_12K1 2K_12K1 4K_14K1 4. Multiple-choice 15 minutes Q.

A nonrotating spherical planet with no atmosphere has mass MM and radius RR . A projectile of mass mm is launched radially from the surface of the planet with initial speed v=\sqrt{\frac{GM}{2R}}v=2RGM . The potential energy of the projectile-planet system, as a function of the projectile's distance rr from the center of the planet, is given by U=-G\frac{Mm}{r}U=−GrMm . The greatest distance from the center of the planet that the projectile reaches is

answer choices infinity RR \frac{7}{5}R57R \frac{4}{3}R34R 5. Multiple-choice 15 minutes Q.

A person holds a book at rest a few feet above a table. The person then lowers the book at a slow constant speed and places it on the table. Which of the following accurately describes the change in the total mechanical energy of the Earth-book system?

answer choices

The total mechanical energy is unchanged, because there is no change in the book’s kinetic energy as it is lowered to the table.

The total mechanical energy is unchanged, because no work is done on the Earth-book system while the book is lowered.

The total mechanical energy decreases, because the person does positive work on the book by exerting a force that opposes the gravitational force.

The total mechanical energy decreases, because the person does negative work on the book by exerting a force on the book in the direction opposite to its displacement.

6. Multiple-choice 15 minutes Q.

A rubber ball with mass 0.20 kg is dropped vertically from a height of 1.5 m above a floor. The ball bounces off of the floor, and during the bounce 0.60 J of energy is dissipated. What is the maximum height of the ball after the bounce?

answer choices 0.30 m 0.90 m 1.2 m 1.5 m 7. Multiple-choice 15 minutes Q.

A sled slides down a hill with friction between the sled and hill but negligible air resistance. Which of the following must be correct about the resulting change in energy of the sled-Earth system?

answer choices

The sum of the kinetic energy and the gravitational potential energy changes by an amount equal to the energy dissipated by friction.

The gravitational potential energy decreases and the kinetic energy is constant.

The decrease in the gravitational potential energy is equal to the increase in kinetic energy.

The gravitational potential energy and the kinetic energy must both decrease.

8. Multiple-choice 15 minutes Q.

An inclined track is secured to a table. The height of the highest point of the track above the tabletop is h_1h1 . The height from the tabletop to the floor is h_2h2 . A block of mass MM is released from rest and slides down the track such that all frictional forces are considered to be negligible. The block leaves the track horizontally and strikes the ground at a distance DD from the edge of the track as shown. Which of the following statements are correct about the scenario? **Select two answers**

Guys, does anyone know the answer?