Which of the following contains the most mechanical energy?

A 10 kg ball at the top of a hill 10 meters high
A 5 kg ball rolling with a velocity of 12 m/s
A 10 kg ball rolling with a velocity of 5 m/s
A 5 kg ball at the top of a hill 10 meters high

I think it is A

PE = mgh = 10 * 9.8 * 10 = 980J.

KE = 0.5mV^2 = 0.5 * 5 * (12)^2 = 360J.

KE = 0.5 * 10 * 5^2 = 125J.

PE = 5 * 9.8 * 10 = 490J.

You are correct!

To determine which object contains the most mechanical energy, we need to consider both its potential energy and kinetic energy.

Potential energy is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. Kinetic energy is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Let's calculate the energy for each object:

A) 10 kg ball at the top of a hill 10 meters high:
Potential energy = 10 kg * 9.8 m/s^2 * 10 m = 980 J (joules)
Kinetic energy = 0 J (since the ball is not moving)

B) 5 kg ball rolling with a velocity of 12 m/s:
Potential energy = 0 J (since the ball is not at a height)
Kinetic energy = (1/2) * 5 kg * (12 m/s)^2 = 360 J

C) 10 kg ball rolling with a velocity of 5 m/s:
Potential energy = 0 J (since the ball is not at a height)
Kinetic energy = (1/2) * 10 kg * (5 m/s)^2 = 125 J

D) 5 kg ball at the top of a hill 10 meters high:
Potential energy = 5 kg * 9.8 m/s^2 * 10 m = 490 J
Kinetic energy = 0 J (since the ball is not moving)

Comparing the results, we can see that object B, the 5 kg ball rolling with a velocity of 12 m/s, has the most mechanical energy. It has a kinetic energy of 360 J, whereas all the other objects have either zero kinetic energy or smaller values. Therefore, the correct answer is B.