# Dropping two balls, one with twice the mass

## Homework Statement

Two masses are placed on top of a building. The mass of one is twice the mass of the other. Both are dropped at the same time. Neglecting air resistance, which statements are true?
1. Both objects have the same potential energy at the top
2. Both objects fall with the same acceleration
3. Both objects have the same kinetic energy before hitting the ground
4. Both objects have the same speed when they hit the ground

A. 1, 2
B. 1, 3
C. 2, 4
D. 1
E. 2

## The Attempt at a Solution

I know 1 and 2 are definitely true.
But I also thought 3 and 4 were true since for 4, I could use the kinematic equation
v2 = v02 + 2ay
And since a and y and v0 are the same for both, I thought they'd have the same final velocity and thus, the same kinetic energy.
But is that not true?

Nathanael
Homework Helper
I thought they'd have the same final velocity and thus, the same kinetic energy.
Are you saying kinetic energy only depends on speed?

I know 1 and 2 are definitely true.
Double check your thinking on this, too.

Are you saying kinetic energy only depends on speed?
Oh wait, never mind, the twice as heavy ball would have a greater kinetic energy since it has twice the mass.

I still think 1 and 2 are both right though.

2 and 4 are related, 1 and 3 are related. Can you think how?

Oh I see how they're related. So if I use 1 and 3 first, the potential energy should be equal to the kinetic energy at the bottom. So then, that means that they both have the same kinetic energy and since their masses differ, their velocities would have to differ.

But I don't see why using the kinematic equation tells me that the velocities at the bottom will be the same.

Nathanael
Homework Helper
Oh I see how they're related. So if I use 1 and 3 first, the potential energy should be equal to the kinetic energy at the bottom. So then, that means that they both have the same kinetic energy and since their masses differ, their velocities would have to differ.

But I don't see why using the kinematic equation tells me that the velocities at the bottom will be the same.
Okay then let's trust the kinematics and say the speed is the same at the bottom. Therefore the smaller ball has less kinetic energy at the bottom. What does this mean about the potential energy at the top?

Oh, wow, I was really stupid....
The potential energies at the top aren't the same..... because they have different masses.
Wow, thanks.

So the answer should be 2 and 4?

Nathanael
Homework Helper
So the answer should be 2 and 4?
Yep