# Clay falling onto a pan attached to a vertical spring

• ultimateman
In summary, the conversation discusses the use of conservation of momentum, conservation of mechanical energy, and the work-kinetic energy theorem to solve a physics problem involving a spring, a pan, and a lump of clay. The correct answer is found to be 0.233 meters, with the solution involving the inclusion of gravity and the spring potential energy in the equations.
ultimateman

## Homework Statement

"A spring is hung from the ceiling. A pan of mass 100.0 g is attached to the end, which causes it to stretch 5.00 cm. Find the maximum distance the pan moves downward when a lump of clay of mass 120.0 g is dropped from a height of 40.0 cm onto the pan."

The correct answer, according to my teacher is 0.233 meters.

## Homework Equations

Conservation of momentum, perfectly inelastic collision.

m1v1i + m2v2i = (m1 + m2)vf

Conservation of mechanical energy.

MEi = MEf

PEg = mgh
PEe = 1/2 kx^2
KE = 1/2 mv^2

Work kinetic energy theorem.

Fnet d cosθ = 1/2 m (vf^2 - vi^2)

## The Attempt at a Solution

I tried a perfectly inelastic conservation of momentum + work-KE theorem approach.

m(ball)v0 + 0 = M(combined)v(final)

Fnet d cos(θ) = 1/2 M(vf^2 - vi^2)

where Fnet was the average spring force minus gravity, F = [k(0.05) + k(x)] / 2 - M(combined)g

d was (x+0.05)

and vf = 0, vi = root(2gh)

UPDATE:

OK so I tried conservation of mechanical energy after the collision to no avail. I did:

1/2 (.22kg) (1.53 m/s)^2 + (.22 kg)(9.81) x = 1/2 (19.62 N/m) (x+0.05)^2

Solving for x I got x = 0.225 m.

I still can't get x = 0.233m. I'm sure it's not a rounding error of some sort. What am I missing?

Last edited:
ultimateman said:
I have tried using a conservation of energy approach. This equation looked like:

PEg(ball) + PEg(pan) + PEe(spring) = PEe(spring, (x+0.05))
Mechanical energy is not conserved during the collision, so that won't work.

I also tried a perfectly inelastic conservation of momentum + work-KE theorem approach.

m(ball)v0 + 0 = M(combined)v(final)
So far so good.

Fnet d cos(θ) = 1/2 M(vf^2 - vi^2)

where Fnet was the average spring force, F = [k(0.05) + k(x)] / 2

d was x

and vf = 0, vi = root(2gh)

Hint: After the collision, mechanical energy is conserved.

Actually I forgot to include gravity in my attempted solution post, but I did include it in my actual calculations already and I still got the wrong answer. : / But Fnet was the average spring force and gravity.

Thanks for pointing out that mechanical energy is not conserved during the collision. Obviously I should have seen that with it being perfectly inelastic.

Trying conservation of mechanical energy after the collision.

EDIT: OK so I tried conservation of mechanical energy after the collision to no avail. I did:

1/2 (.22kg) (1.53 m/s)^2 + (.22 kg)(9.81) x = 1/2 (19.62 N/m) (x+0.05)^2

Solving for x I got x = 0.225 m.

I still can't get x = 0.233m. I'm sure it's not a rounding error of some sort. What am I missing?

Last edited:
ultimateman said:
EDIT: OK so I tried conservation of mechanical energy after the collision to no avail. I did:

1/2 (.22kg) (1.53 m/s)^2 + (.22 kg)(9.81) x = 1/2 (19.62 N/m) (x+0.05)^2

Solving for x I got x = 0.225 m.

I still can't get x = 0.233m. I'm sure it's not a rounding error of some sort. What am I missing?
The left side of your equation is incomplete. You forgot the spring potential energy.

Doc Al said:
The left side of your equation is incomplete. You forgot the spring potential energy.

Derp...Ty!

## 1. What is the purpose of using a vertical spring in this experiment?

The vertical spring is used to simulate gravity and create a controlled environment for the clay to fall onto the pan. This allows for more accurate observations and measurements of the clay's behavior.

## 2. How does the height of the clay's fall affect its impact on the pan?

The higher the clay falls from, the greater the force of impact on the pan. This can result in a larger deformation of the pan and a higher rebound of the clay.

## 3. What factors can affect the behavior of the clay upon impact?

The density and shape of the clay, as well as the height of its fall and the stiffness of the spring, can all affect the behavior of the clay upon impact. Other factors such as temperature and humidity may also play a role.

## 4. How can this experiment help us understand the properties of different types of clay?

By observing the behavior of different types of clay upon impact, we can gather information about their elasticity, viscosity, and other physical properties. This can help in determining the best use for each type of clay in various applications.

## 5. Is this experiment only applicable to clay or can it be used for other materials?

While this experiment is specifically designed for studying the behavior of clay, the same principles can be applied to other materials such as putty or even certain liquids. However, the results may vary depending on the specific properties of each material.

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