help with change in energy i so do not get it.?

Question

A child of 15-kg is in a swing that has two-meter long chains attached to the supporting rod. If the child swings with a speed of 5.5 m/s at the bottom of the arc and is 1.5 meters higher at the top of her swing, determine the change in total energy between the top and bottom of one swing.
A 226 J
B 452 J
C 150 J
D 0 J

Answer 1

Are you assuming that the system is closed and isolated? If so, then use the conservation of energy theorem (total energy is conserved). Therefore, the answer is automatically 0 joules since there is no gain or loss of energy in a closed and isolated system.

But if you wanted to crunch numbers, here's how you'd do it:

1) Use formula for total energy
energy = kinetic energy + potential energy (due to gravity)

2) Calculate the initial total energy
You're setting the reference point at the bottom of the swing. Therefore, the height at this point is 0 m. Since the formula for potential energy is mass*gravity*height, there is no potential energy in this system.
Then find the potential energy. The formula for potential energy is (1/2)*mass*(velocity)^2. Just plug in your numbers, and you'll come up with (1/2)*(15 kg)*(5.5 m/s)^2 = 226.875 joules.
When you add the potential energy (0) and kinetic energy (226.875) at the start, you get a total energy of 226.875 joules.

3) Calculate the final total energy
Same formulas. Start with potential energy. This time, the child is now 1.5 meters above the starting point. Plug the two into the potential energy equation, and you get (15 kg)*(10 m/s^2... earth's gravity)*(1.5 m) = 225 J.
Then calculate the kinetic energy. Since she stops at the top of the swing, you know her velocity is now zero. Therefore, this gives you 0 J of kinetic energy.

4) Compare the two total energies
initial... 226.875 J
final... 225 J
difference... -1.875 J

Well... it's not quite zero, and this is probably due to the fact that the writer of the problem rounded off a number for simplicity's sake (probably the initial speed or the final height). Also, it doesn't even come close to any of the other answers. Answer... D) 0 joules.

I hope this helps. Good luck understanding the energy method! :-)

Answer 2

The 15 kg child has a force by virtue of gravity of about 149 newtons. At the bottom of the swing, the child has, by relative height, a zero potential datum but maximum velocity. So the energy is mv2/2 = A.
At the top of the swing, he has no velocity but maximum height potential. Here mgh=A. So there is no change in total energy.