Freefall motion: velocity, acceleration, momentum, kinetic energy

In summary, the three ball bearings must be dropped from the same height in order for all of their momentum, kinetic energy and velocity to be the same.
  • #1
SA32
32
0

Homework Statement


Consider three ball bearings, one with a mass of 8 g, one with a mass of 16 g and one with a mass of 32 g.
a.) What heights should the three ball bearings be dropped from so that at impact all three ball bearings will have the same velocity?
b.) What heights should the three ball bearings be dropped from so that at impact all three ball bearings will have the same acceleration?
c.) What heights should the three ball bearings be dropped from so that at impact all three ball bearings will have the same momentum?
d.) What heights should the three ball bearings be dropped from so that at impact all three ball bearings will have the same kinetic energy?

Homework Equations


F=ma
v2f=v2i+2ad
p=mv
KE=(1/2)mv2


The Attempt at a Solution


a.) I know that in free fall motion, neglecting air resistance, objects have the same and constant acceleration, 9.81 m/s2 downward. If I release all three objects from the same height at the same time, they will all hit the ground at the same time. Doesn't this mean that in order for the velocity of the three objects to be the same at impact, the height all three are dropped from must be the same? If not, I'm confused... I don't know how to relate mass and velocity in this case.
b.) Since it is free fall motion and we can neglect air resistence, does the height really matter? Aren't the balls all going to have an acceleration of 9.81 m/s2 at every point in their motion?
c.) p=mv, so obviously, since the masses are different, the velocities must also be different in order for all balls to have the same momentum. Building on what I said in a.), if the velocities are different it means they were dropped from different heights.

I said m1 = 8 g, m2 = 16 g, and m3 = 32 g

Then p=m1v1=m2v2=m3v3

We know "m" and that "p" is constant for all balls, so I tried to condense all the velocity variables into one "v" like so...

v1=v

p=8v=16(1/2)v=32(1/4)v

But that doesn't make sense because, solving for v, I get 1 m/s... and also because, using this, I could also say that v3 = v, then p=8(4v)=16(2v)=32v and end up with a different momentum.
d.) Since kinetic energy involves a similar relationship to momentum I think I can try this again with some tips on how to approach c.)

Thank you!
 
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  • #2
SA32 said:
a.) I know that in free fall motion, neglecting air resistance, objects have the same and constant acceleration, 9.81 m/s2 downward. If I release all three objects from the same height at the same time, they will all hit the ground at the same time. Doesn't this mean that in order for the velocity of the three objects to be the same at impact, the height all three are dropped from must be the same?

Correct.

b.) Since it is free fall motion and we can neglect air resistence, does the height really matter? Aren't the balls all going to have an acceleration of 9.81 m/s2 at every point in their motion?

Correct.

c.) ...We know "m" and that "p" is constant for all balls, so I tried to condense all the velocity variables into one "v" like so...

v1=v

p=8v=16(1/2)v=32(1/4)v

But that doesn't make sense...

It doesn't make sense because the velocities are not the same!

What you mean is p = 8v1 = 16v2

Therefore v2 = 1/2 v1.

NB you are not given the actual value of the momentum, so you can only find the relative heights (i.e find h2 and h3 in terms of h1)
 
  • #3
Thanks so much! Now I think I can use the kinematics equation to find the relations between the heights, and do likewise for the kinetic energy question. Cool.
 

1. What is freefall motion?

Freefall motion is the movement of an object under the sole influence of gravity. This means that the object is not being affected by any other forces, such as air resistance or friction.

2. How is velocity related to freefall motion?

In freefall motion, an object's velocity increases as it falls due to the acceleration of gravity. This means that the object's speed and direction of motion are constantly changing.

3. What is acceleration in freefall motion?

Acceleration in freefall motion is the rate at which an object's velocity changes. In this case, the acceleration is always equal to the acceleration of gravity, which is approximately 9.8 meters per second squared.

4. How does momentum play a role in freefall motion?

Momentum is a measure of an object's mass and velocity, and it is conserved in freefall motion. This means that as an object falls, its momentum remains constant, but its velocity increases due to the acceleration of gravity.

5. What is kinetic energy in freefall motion?

Kinetic energy is the energy an object possesses due to its motion. In freefall motion, an object's kinetic energy increases as it falls due to its increasing speed. This energy can be calculated using the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.

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