Finding Velocity for Work and Energy Problem

[petern]

[SOLVED] Finding Velocity for Work and Energy Problem

A 2 kg physics textbook is dropped form rest out a window 10 meters above the ground. What is the textbook's speed when it's kinetic and potential energies are equal?

The answer is v = 9.90 m/s.

You would use the equation U = (1/2)kx^2 and K = (1/2)mv^2, right?

I really don't know what to do especially since the k is in the equation of U. How do I solve this?

 

[Tedjn]

You would only use U = (1/2)kx^2 when you have a force that is proportional to some quantity x. For example, spring force is -kx by Hooke's Law, so you would use U = (1/2)kx^2, which is what you are probably thinking about. A book dropping from a window is subject to a constant force, so you need to use a different equation for potential energy.

You have your kinetic energy equation right. Because that equation has a v in it, you can use it to find velocity if you know the total mechanical energy. How can you find that?

 

[petern]

So you would use U = mgh then. I would set the 2 equations equal to each other and then solve for v. I get v = sq. root of (2gh), but that is the right answer.

 

[Tedjn]

When U = mgh, where h is the original height above the ground (i.e. 10 meters), there is no kinetic energy because you have not dropped the book yet. You need to find an expression for the potential energy when it is equal to the kinetic energy. Use the conservation of mechanical energy.

 

[petern]

Oooh, the point where they are equal is at the midpoint, which is 5 m. so I use v = sq. root of (gh). Thanks!