help how do i solve for the total energy of the system ? also how do i find maxi
ID: 1330715 • Letter: H
Question
help how do i solve for the total energy of the system ? also how do i find maximum or minimul values of KE?
A 300-g ball is thrown straight up into the air. It is exactly 2 m above the ground when it is released. It reaches a height 12 m above the height from which it was released, and then falls straight back down.
a) Assume that y = 0 is located at the point of release of the ball. Find the maximum and minimum values of y and PEg. What is the total energy of the system? Find the maximum and minimum values of KE.
b) Repeat part (a), with y = 0 located at the ground.
Explanation / Answer
The ball will reach 12m above the release point and y=0 for the release point. This means that from the release point, the ball will reach a max of y=12. Then, when it falls back down to Earth, it will hit the ground 2m below the release point (since the ball was released at 2m above the ground, but now we are setting y=0 to that release point). So the ball can reach a minimum value of y=(-2).
Since PE=mgh. (Potential Energy is equal to the mass times gravity, times height). So the max y value for the ball, we have max PE...
PE(max)=(.3kg)(9.8m/s^2)(12m)
PE(max)=35.28J
The same for the minimum value of Y for the ball.
PE(min)=(.3kg)(9.8m/s^2)(-2m)
PE(min)= -5.88J
For KE we know that at the minimum value of Y will have a velocity of zero since it is at it's maximum height. So...
KE(min)=0
For the maximum value of KE, we will add the total magnitudes of the PE(max) and PE(min) and set it to the KE at y= -2.
KE(max)=PE(max)+PE(min)
KE(max)= 35.28J+5.88J
KE(max)= 41.16J
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