# How Does Spring Compression Affect Block Motion on an Inclined Plane?

• uchicago2012
In summary: It will have no potential energy, and it will move back up the ramp at the same speed it came down. For c), when the box is heading back up the ramp, it will have potential energy in the form of kinetic energy and potential energy in the form of potential energy of the spring.
uchicago2012

## Homework Statement

In the figure the block starts from rest at A, slides down the ramp, compresses the spring 0.75 meters, and goes back. The spring constant is 520 N/m, the block's mass is 12 kg, and the ramp is inclined at 30°. The horizontal part of the sliding is frictionless. If point A is 2 meters above the floor, (a) what is the block's speed at the bottom of the ramp? (b) How much work does friction do while the block descends the ramp? (c) After rebounding, the block starts back up the ramp. What is its speed at the bottom, heading up? (d) How far does it move back up the ramp? (Give a vertical distance.)
See Figure 1

## Homework Equations

Wnonconservative forces = Change in KE + Change in PE

## The Attempt at a Solution

for a.
in the equation Wnon = KE2 - KE1 + PE2 - PE1
where the initial is at the top of the ramp and the final is the point at which the spring is at its maximum compression
is PE2 = 1/2kx2? I think that should be the only component of PE2, I just wasn't sure. It gave a reasonable answer once I solved for everything, it just made me a bit nervous to have the only final potential energy of the box be that of the spring.

for c.
now Wnon = 0 so
Ui + Ki = Uf + Kf
where the initial is the point at which the spring is at its maximum compression and the final is the point at which the box begins heading up the ramp.
I was confused as to what Uf should be. It's mgy, but I'm not sure what to use for y. The box is beginning to head up the ramp but I'm unclear on whether it actually has an elevation at that point.

#### Attachments

• Figure 1.jpg
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For the part while the block is sliding down/up the ramp, you need to take friction into account.

Are you given a coefficient of friction?

No, but I solved for it. I did in part a and b, but in part c it said the horizontal bit was frictionless.

In that case, when the box is just about to head up the ramp, its energy will be entirely in the form of kinetic energy.

I would like to clarify a few things about the given scenario. First, it is important to define the reference point for potential energy calculations. In this case, since the block is initially at rest at point A, it would be appropriate to take point A as the reference point for potential energy calculations. This means that the potential energy at point A would be zero.

Now, for part (a), the block's speed at the bottom of the ramp can be calculated using the conservation of energy principle. The initial kinetic energy is zero, since the block starts from rest. The final kinetic energy can be calculated using the equation KE = 1/2mv^2, where m is the mass of the block and v is its speed. The final potential energy can be calculated using the equation PE = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block at the bottom of the ramp (which can be calculated using trigonometry and the given angle of the ramp). The work done by the non-conservative forces (friction) can be calculated using the equation W = Fd, where F is the force of friction and d is the distance traveled by the block on the horizontal part of the ramp. This work done by friction will be equal to the change in kinetic energy of the block. Using these equations, the speed of the block at the bottom of the ramp can be calculated.

For part (b), the work done by friction can be calculated using the equation W = Fd, where F is the force of friction and d is the distance traveled by the block on the horizontal part of the ramp. This work done by friction will be equal to the change in kinetic energy of the block, which was calculated in part (a).

For part (c), the final potential energy can be calculated using the equation PE = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the block at the bottom of the ramp (which can be calculated using trigonometry and the given angle of the ramp). The initial potential energy can be calculated using the equation PE = 1/2kx^2, where k is the spring constant and x is the maximum compression of the spring. The initial kinetic energy will be zero, since the block starts from rest. Using the conservation of energy principle,

## 1. What is a Spring Force Ramp and Block?

A Spring Force Ramp and Block is a physics experiment used to demonstrate the concepts of potential energy, kinetic energy, and spring force. It involves a ramp, a block, and a spring attached to the block.

## 2. How does the Spring Force Ramp and Block work?

The block is placed at the top of the ramp and released, causing it to roll down the ramp. As it rolls, the spring attached to the block compresses due to the block's kinetic energy. The spring then releases its potential energy, pushing the block back up the ramp.

## 3. What factors affect the behavior of the Spring Force Ramp and Block?

The behavior of the Spring Force Ramp and Block is affected by the mass of the block, the stiffness of the spring, the angle of the ramp, and the surface of the ramp. These factors can affect the speed and height of the block as it rolls down and up the ramp.

## 4. What is the significance of the Spring Force Ramp and Block in science?

The Spring Force Ramp and Block experiment helps to illustrate the principles of potential and kinetic energy, as well as spring force, in a hands-on and visual way. It is also used to demonstrate the conservation of energy and the relationship between force, mass, and acceleration.

## 5. How is the data collected and analyzed in a Spring Force Ramp and Block experiment?

Data is collected by measuring the height of the ramp, the distance the block travels, and the time it takes for the block to complete one full cycle. This data is then used to calculate the potential and kinetic energy of the block, as well as the spring force. Graphs can also be created to show the relationship between these variables.

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