Need quick help - Ball swings down, hits block - Speed of the block?

[nukeman]

Homework Statement

Ok I can't seem to figure this out. Maybe I am tired, or strung out on coffee :), but I need some help!

The image shows the question with diagram:

Homework Equations

The Attempt at a Solution

Iv done this a few different ways, but all WRONG. The CORRECT answer is V = 0.767 m/s

First I found the speed of the ball by going mgh (.300)(9.8)(.500) which gave me 1.47 m/s

Then I found the speed as it left the block after hitting it by the same method. Which would be 0.588 m/s

So then I simply used: m1v1i + m2v2i = m1v1f + m2v2f

(.300)(1.47) + (.200)(0) = (.300)(.588) + (.200)(x) and solve for x gave me: 1.32 m/s

WHAT am I doing WRONG?

Very appreciate any help on this one guys. Thanks!

 

[sandy.bridge]

Personally, I would determine the potential energy that the object has at hi, and then determine the potential energy at hf. The difference between these values will equal the gain in kinetic energy of the box.

 

[nukeman]

Can you possibly elaborate on that for me? :)

 

[sandy.bridge]

Have you explored any energy theorems in Physics yet, pertaining to potential energy and kinetic energy?

 

[nukeman]

Have you explored any energy theorems in Physics yet, pertaining to potential energy and kinetic energy?

Yes I have.

So, you are saying determine the potential energy at Hi and Potential energy at Hf

Once I have those to peices of data, what do I do with them?

 

[sandy.bridge]

You will notice that at h2 the object has a smaller potential energy than it did when it was at hi; that is, energy was transferred from the ball to the block, which can be seen as kinetic energy.

 

[nukeman]

so is it like...

So to calculate the potential energy at Height initial: its (m)(g)(h) ?

same with height final? (m)(g)(h) ?

 

[sandy.bridge]

Yes, assuming constant mass, we have,
$$m_{ball}g(h_1-h_2)=\frac{1}{2}mv_{block}^2$$

 

[nukeman]

Is that expression saying that the difference in potential energy = the same amount in Kinetic energy?

 

[sandy.bridge]

In words, the loss of energy depicted by the swinging ball can be accounted for by the gain in kinetic energy of the box. The potential energy of the ball changed did it not? Law of of conservation of mass implies the energy of the system remains constant, and hence is merely a transfer from the ball to the box.

 

[nukeman]

So I have then kinetic energy of .882 applied to the block.

How do I use that to find the blocks speed?

 

[sandy.bridge]

What is the formula for kinetic energy? I already provided it to you.

 

[gneill]

First I found the speed of the ball by going mgh (.300)(9.8)(.500) which gave me 1.47 m/s

mgh yields potential energy in Joules, not speed. You need to use the kinetic energy equation relating velocity to KE in order to find the speed that comes from converting this PE to KE.

 

[nukeman]

What is the formula for kinetic energy? I already provided it to you.

KE = 1/2mv^2

 

[nukeman]

mgh yields potential energy in Joules, not speed. You need to use the kinetic energy equation relating velocity to KE in order to find the speed that comes from converting this PE to KE.

How do you do this? :( Relating Velocity to KE?

 

[gneill]

How do you do this? :( Relating Velocity to KE?

See your post immediately above! KE = (1/2) MV².

If some potential energy PE = Mgh is converted to kinetic energy KE = (1/2) MV², then that means KE = PE.

Mgh = (1/2) MV². Solve for V.