# Conservation of Energy: Kinetic to Elastic Potential

• awelex
In summary, the problem involves a 0.150-kg frame suspended from a coil spring, which stretches the spring by 0.050m. A 0.200-kg lump of putty is dropped from a height of 30.0m onto the frame. Using the equations for conservation of energy and momentum, the final answer for the displacement of the frame is either 0.2m or 0.25m, depending on whether the initial displacement of 0.05m is included. However, this answer is incorrect due to the assumption that both the frame and putty are initially moving with the same speed. To find the correct answer, the speed of the putty-frame combination immediately after the collision must
awelex

## Homework Statement

A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.050m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0m.

mass of frame: mf
mass of putty: mp
height: h

## The Attempt at a Solution

I tried the following, which was wrong:

0.150 * 9.8 = k * 0.050 --> k = 29.4

velocity of putty when it touches frame:
0.200*g*0.3=(1/2)*0.200*v^2 --> v^2 = 2hg

(1/2)(mp+mf)*v^2 = (1/2)*k*x^2
--> x = 0.2m

So the final answer is either 0.2m or 0.25m (depending on whether one adds the initial 0.05m). Both answers are wrong, though. What am I doing wrong?

Thanks.

awelex said:

## Homework Statement

A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.050m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0m.

mass of frame: mf
mass of putty: mp
height: h

## The Attempt at a Solution

I tried the following, which was wrong:

0.150 * 9.8 = k * 0.050 --> k = 29.4

velocity of putty when it touches frame:
0.200*g*0.3=(1/2)*0.200*v^2 --> v^2 = 2hg
You're fine up to here. I take it that h=30 cm, not 30 m like you wrote above.
(1/2)(mp+mf)*v^2 = (1/2)*k*x^2
--> x = 0.2m

So the final answer is either 0.2m or 0.25m (depending on whether one adds the initial 0.05m). Both answers are wrong, though. What am I doing wrong?

Thanks.
You're assuming that both the frame and the putty are initially moving with the speed the putty had just before hitting the frame. So right before the collision, the putty has a certain amount of kinetic energy, and immediately after the collision, it still has that amount of kinetic energy because it still has speed v. But now the frame is moving too, so there's even more kinetic energy. Does that make sense?

You need to find the speed of the putty-frame combination immediately after the collision. If you use that speed in your calculations instead, you should get the right answer.

## What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another.

## What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## What is elastic potential energy?

Elastic potential energy is the energy stored in an object when it is compressed or stretched. It is calculated by the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement from equilibrium.

## How does kinetic energy transform into elastic potential energy?

When an object with kinetic energy collides with a spring, the kinetic energy is transferred to the spring and is stored as elastic potential energy as the spring is compressed. This transformation occurs due to the conservation of energy.

## What are some real-life examples of the conservation of energy from kinetic to elastic potential?

A few examples include bouncing balls, pogo sticks, and trampolines. In all of these situations, the object initially has kinetic energy and then transfers it to the spring, which stores it as elastic potential energy.

Replies
2
Views
424
Replies
12
Views
3K
Replies
3
Views
2K
Replies
2
Views
325
Replies
5
Views
1K
Replies
55
Views
3K
Replies
6
Views
689
Replies
4
Views
872
Replies
12
Views
2K
Replies
21
Views
2K