Question

A 2 kg ball is released from rest at the top of a track and

reaches a speed of 10 mls at the bottom.
a. How much kinetic energy does the ball have?
b. How much potential energy did it have at the top of
t
hill (assuming no energy was lost?
c. What was the height of the hill?

Answer 1

The ball has a kinetic energy of 100 Joules and a potential energy of 100 Joules. The height of the hill is 5 meters.

Step-by-step explanation:

a. The kinetic energy of the ball can be found using the formula:

KE = 1/2 * m * v^2

where KE is the kinetic energy, m is the mass, and v is the velocity.

Plugging in the given values, we have:

KE = 1/2 * 2 kg * (10 m/s)^2 = 100 J

So, the ball has a kinetic energy of 100 Joules.

b. The potential energy of the ball can be found using the formula:

PE = m * g * h

where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

Since the ball starts from rest and falls to the bottom, its potential energy at the top of the hill is equal to its kinetic energy at the bottom.

So, the potential energy at the top of the hill is also 100 Joules.

c. To find the height of the hill, we can rearrange the formula for potential energy:

h = PE / (m * g)

Plugging in the values, we have:

h = 100 J / (2 kg * 10 m/s^2) = 5 meters

Therefore, the height of the hill is 5 meters.

Answer 2

a) The formula for kinetic energy is E = 1/2 mv^2, so the energy of the ball is 1/2 * 2 * 10^2 = 100J. b) Energy is always conserved, and so if no energy is lost to resistive forces then all 100J of kinetic energy came from its potential energy at the top of the track. c) The formula for potential energy is E = mgh, which we can rearrange for h = E/mg. We know the energy, the mass and the strength of gravity, so we can find h = 100 / (2*9.81) = 5.10m.