Kinetic Energy,Work Energy therom, Maximum Height

1. Oct 21, 2012

Dejahboi

1. The problem statement, all variables and given/known data
A 0.145-kg baseball is struck by a bat 1.20 m above the ground, popping straight up at 21.8 m/s. (a) What's the ball's kinetic energy when it leaves the bat? (b) How much work is done by gravity once the ball reaches maximum height? (c) Use your answer in part (b) to find that maximum height. (d) Find the work gravity does on the ball from when it's batted until it hits the ground. (e) Ignoring air resistance, use your answer in part (d) to find the ball's speed at the ground.

2. Relevant equations
K= 1/2mv2

3. The attempt at a solution

a) I used K=1/2mv2

so,
(.5)(.145 kg)(21.8 m/s)2= 34.45 J

b) I'm not sure how I did it but I got = -34.45 J

c)According to the free body diagram I drew, my initial velocity is 21.8 m/s, and Vf is 0. I'm not sure what equation to use here, I used Wg= -mgΔy but my answer does not match the book's answer.

As for the rest of the problem, I have no clue how to do it.

2. Oct 21, 2012

PhanthomJay

yes
well you did something right or copied the book answer
I'm not sure why it doesn't match...show your work
Well for (d) you got (b) right somehow on the upward journey, so you should be able to find the work done by gravity on the downward trip, then add them up . For (e), use the work-energy theorem, and show your work.

3. Oct 21, 2012

Dejahboi

For (c)

I set -34.45 J = (-0.145 kg) (9.8 N/m) H

So,

-34.45/ -1.421 = 24.24 m

Book says 25.45 m but I can be doing something really wrong.

4. Oct 21, 2012

Simon Bridge

(b)When the ball has reached the top of it's trajectory, what is it's kinetic energy? How is work related to kinetic energy?

(d) is like (b) ... what is the KE it started with? Ended with? What is the relationship between KE and work?

(e) follows from (d) ... you have the final KE and the relationship between v and KE.

5. Oct 21, 2012

Dejahboi

W= (1/2)kx2?
K = 1/2mx2
Well I got 24.24 m and the book has 25.45 m

6. Oct 21, 2012

Simon Bridge

That would be energy stored in a spring ... what is the realtionship between work and kinetic energy? That would be the work-energy theorem PhantomJay was talking about.
??? Clearly you don't know - you can look it up: but here's a quickee refresher:

Kinetic energy: $K=\frac{1}{2}mv^2$

Work-Energy: $W=\Delta E$ ... work is change in energy.

The work done on something is the change in it's kinetic energy.

So, in terms of kinetic energy: $W=K_f-K_i$

So the book had a height 1.2m higher than yours ... hmmm... isn't that a familiar figure? Can you find that number in the question?

7. Oct 21, 2012

Dejahboi

Yeah, of course I wouldn't know, that's why I asked for help. Anyways, I have a list of equation I written down from class, but the professor had a tiny mistake categorizing the work of spring and the work energy, and yeah I have

ΔK = W

Now I lost track of what I'm trying to solve for :/..

8. Oct 21, 2012

Simon Bridge

No worries - sometimes people ask a question not realizing they know the relationships to use.
That won't be entirely a mistake - the idea is that the list of equations is to act to jog your memory ... you are expected to learn the physics and let that knowledge guide your choice. eg. you were expected to realize that the little "k" normally appears with an "x" if it is the spring constant. Just like it appears with a q or a Q if it is the coulomb constant and with a T if it is the Boltzman constant. You needed something with a W and a K or an E in it.

Don't worry - it is common to need to reread the question after thrashing out concepts ;)