Bob throws a 0.50 kg baseball straight up. At a height of 30.0 m it is moving at 12m/s
a) what is the ball's kinetic energy?
b) What is the gravitational potential energy of the ball?
c) How much work was done by Bob to get the ball up into the air?

- korosh23

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- anonymous

m=0.50 kg
h=30 m
v=12m/s
a. apply the kinetic energy formula \(\sf KE= \frac{1}{2}mv^2\)
b. apply the potential energy formula \(\sf PE= mgh \), where g is the acceleration due to gravity.
c. apply work energy theorem: \(\sf W=\Delta E\)

- korosh23

Thank you for mentioning the formulas. I already know how to use them, I did part a and b, but not c. Could you please explain me how to do it?

- korosh23

@Michele_Laino

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## More answers

- korosh23

I do not know how to do C.

- Michele_Laino

I'm pondering...

- korosh23

Ok. My teacher gave me the answer. He did not show the work. Do you want the answer? Maybe it can help you to find how?

- Michele_Laino

ok!

- korosh23

46) a) 36J
b) 150J
c) 180J

- Michele_Laino

part a)
\[KE = \frac{1}{2}m{v^2} = \frac{1}{2} \times \frac{1}{2} \times 144 = 36Joules\]

- korosh23

Yes

- Michele_Laino

part b)
\[PE = mgh = \frac{1}{2} \times 10 \times 30 = 150Joules\]
here g=10 m/sec^2

- korosh23

Yes

- korosh23

It is challengic! :D

- Michele_Laino

yes! Lol!
for part c) we can write this equation:
\[\Large \frac{1}{2}mv_{INITIAL}^2 - \frac{1}{2}mv_{FINAL}^2 = mgh\]

- korosh23

No,

- Michele_Laino

where v_FINAL= 12 m/sec

- korosh23

ok go on

- Michele_Laino

and v_INITIAL is the starting speed of your ball

- korosh23

Starting speed is o m/s

- korosh23

I think

- Michele_Laino

it is impossible, since v_INITIAL =0 then the ball can not go away

- korosh23

Then how the answer is 180J? You are tight it is impossible.

- korosh23

One more question? it is important for me to know.

- korosh23

easy for you

- Michele_Laino

I think that it is an approximated value, since the work done by Bob has to be equal to the initial kinetic energy

- Michele_Laino

namely:
\[W = \frac{1}{2}mv_{FINAL}^2 + mgh = 36 + 150\]

- korosh23

W is change in kinetic energy, but not mechanical energy. It is fine, we can move to another question.

- korosh23

May I ask you my another question?

- Michele_Laino

W is the work done by Bob.
more explanation:
if the ball is thrown by a compressed spring, then we can say that the potential energy of the spring is equal to the kinetic energy of the ball, so the work done by the spring on the ball is equal to the initial kinetic energy of our ball

- Michele_Laino

the same reasoning goes if we replace the spring with Bob

- korosh23

Ok. Makes sense.

- korosh23

Can I ask you one more question. It is important for me to know for my exam

- Michele_Laino

ok!

- korosh23

I open a new question

- Michele_Laino

ok!

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