Answer:
Every object has a total energy which is the sum of its kinetic and potential energy:
E = Ek + Ep
Kinetic energy is, as the name suggests, the energy of moving. It is given through the equation:
Ek = m • v^2 / 2
From here, we can see that Ek depends on the object's velocity; if v=0, then Ek will also be zero.
Potential energy is the energy an object has on a certain height:
Ep = m • g • h
Obviously, if the height is zero, then the Ep=0 too.
Another important thing to note is that E is always constant; if Ek increases (or decreases), Ep will decrease (or increase) so that their sum will always be a constant value.
If the bowling ball sits at the top of the 40 meters tall building, it has no velocity, it doesn't move, but it is located on a certain height.
That means that, at the top of the building, the bowling ball has no kinetic energy:
E = Ep + Ek
- no velocity ---> Ek =0
E = Ep = mgh
Ep = 2 kg • 9.81 m/s^2 • 40 m
E = Ep = approximately 785 J
To conclude, at the top of the building Ep > Ek.
Now, the ball is falling, and it's halfway down and it's travelling 19.8 m/s. Now, its kinetic energy is:
Ek = m • v^2 / 2
Ek = 2 • 19.8^2 / 2
Ek = approximately 392 J
Now, since the ball is halfway down, that means that its height is 20 meters. So, its Ep is:
Ep = mgh
Ep = 2•9.81•20
We already stated that total energy is constant and that is the sum of Ep and Ek and that it is around 785 J. We could also find Ep:
Ep = E - Ek
Ep = 785 - 392
Whichever way we use to calculate, we'll get the value of approximately 392 J.
That means that, halfway down, Ep=Ek.
Since the ball is halfway down, that means that its Ep is half the value it was while at the top of the building. The other half is used on the ball's velocity producing kinetic energy. That's why these two are equal at the halfway down.
Just before it hits the ground, the bowling ball has no height, meaning it has no potential energy. That also means that its total energy is equal to its kinetic energy:
E = Ep + Ek
Ep = 0
E = Ek
We already said that the ball's total energy was around 785J, so its kinetic energy just before it hits the ground will be that exact value.
