Question

3. Create energy bar graphs for a cart rolling down a ramp. The cart and the Earth is the system. Assume the

system has a total of 4 units of energy. On the picture below, label h=0. Assume there is no friction or air
resistance.

Answer 1

The picture correctly represents the behaviour of gravitational energy and kinetic energy.

Step-by-step explanation:

The mechanical energy of a system is defined as the sum of the gravitational potential energy and the kinetic energy:

E = U + K

where:

- The gravitational potential energy (U) is the energy due to the position of the object in the gravitational field, and it is proportional to the height of the object, h

- The kinetic energy (K) is the energy due to motion, and it is proportional to the square of the speed of the object

In absence of friction or air resistance, the mechanical energy is constant. Therefore, as the cart rolls down, the gravitational potential energy decreases (since h decreases) while the kinetic energy increases. Since the total energy of the system is 4 units, the sum of U and K must remain 4 units.

At t = 0, we have U = 4, so K = E - U = 4 - 4 = 0

At t = 1, we have U = 3, so K = E - U = 4 - 3 = 1

At t = 2, we have U = 2, so K = E - U = 4 - 2 = 2