Calculate Retarding Force of 50kg & 6kg Objects

[Taidhg]

1. An object with a mass of 50kg is raised vertically 4 meters above an object of 6kg and then is allowed to fall freely onto the object into the ground. Both objects travel into the ground to a depth of 24cm without rebounding.
Calculate the retarding force causing both objects to come to rest.

KE/GPE = mgh = 0.5m v²

 

[Chandra Prayaga]

What have you done so far? The relevant equation that you wrote is wrong.

 

[Taidhg]

What have you done so far? The relevant equation that you wrote is wrong.

I've calculated the velocity upon the objects impact which is 1.476 m/s²
I also have calculated the GPE before it falls which is 1962J and the kinetic energy upon impact which is 1961.33J
I just don't see how I am meant to calculate this last question.

 

[Chandra Prayaga]

In all such problems, you should draw a diagram, labeling the different positions. Similarly, label the two balls as A and B. For example, the initial position , with ball A at the top of its path and ball B on the ground can be called position 1. The position just before impact is called 2, and the final position after the two balls sink and come to rest together is called 3.

Your unit for velocity is wrong.
Do you think the kinetic energy in position 2 should be different from the potential energy in position 1?
What information do you need to calculate the last part? How can you get that information?

 

[gneill]

Please show your calculations in detail.

 

[Taidhg]

In all such problems, you should draw a diagram, labeling the different positions. Similarly, label the two balls as A and B. For example, the initial position , with ball A at the top of its path and ball B on the ground can be called position 1. The position just before impact is called 2, and the final position after the two balls sink and come to rest together is called 3.

Your unit for velocity is wrong.
Do you think the kinetic energy in position 2 should be different from the potential energy in position 1?
What information do you need to calculate the last part? How can you get that information?

I really don't know what information I need for the last part that's the issue. I know that the energy used in response to stop the objects will obviously be equal but I've never worked with retarding forces before.

 

[gneill]

I've never worked with retarding forces before

How about friction?

 

[Taidhg]

How about friction?

I stated in the original post that the object is in free fall. The question is about a pile driver falling onto a pile but I usually ignore those details.

 

[gneill]

I stated in the original post that the object is in free fall. The question is about a pile driver falling onto a pile but I usually ignore those details.

After the collision occurs, the objects are not in free-fall. The ground is impeding their progress. Friction.

 

[gneill]

I've calculated the velocity upon the objects impact which is 1.476 m/s2

Please show your calculation.

I also have calculated the GPE before it falls which is 1962J and the kinetic energy upon impact which is 1961.33J

Why are they different?

 

[haruspex]

the energy used in response to stop the objects will obviously be equal

The energy taken by the retarding force in bringing them to rest will not be equal to the initial GPE. There is energy lost in the impact itself. Have you worked with impacts before?