Potential Energy and Kinetic Energy Problem?

Question

Hi to all!

Hope someone could help me on this.I just want to check if my answers are correct; or if its the same with yours.

The problem is:

A 40Kg stone is dropped from a height of 150m.What is the PE and KE?

a) at t= 1 second

b) at a distance of 20m

Many Thanks!

Answer 1

The potential energy at t=0 sec. is simply
Ep = mgh where m is mass, g is gravitational acceleration, and h is height. The trick is to remember that the total energy (potential plus kinetic) of the system will remain constant. So you start out with
Ep = 40 * 9.8 * 150 = 58800 J and the Ke = 0 (since it's not moving).

After 1 second, it's fallen (1/2)at² = 4.9 meters so its Ep is now
Ep = 40 * 9.8 * 145.1 = 56879.2 J so it's Ke must be
Ke = 58800-56879.2 = 1920.8 J (As a check, calculate its Ke.
V=at = 9.8 m/s and Ke = (1/2)mv² = (1/2) * 40 * 9.8² = 1902.8 !!!!!)
You can work it out for a distance (I'm guessing that's distance above the ground) of 20 m.

What's really instructive to do is to work out the equation(s) for Ep and Ke as a function of time, but I'll let you play with that ☺

Doug