Exercises on Potential Energy
Helena Dedic
Beware: Many of the solutions to these exercises use !
Exercise 1
A 2-kg block moves while increasing the gravitational potential energy by 40 J. How far and which way did the block move along the incline?
Exercise 2
Two blocks of masses kg and kg are released from rest. What is the change of the potential energy of the system after the blocks have moved 20 cm?
Exercise 3
A block of mass kg slides down when released. The spring (with spring constant N/m) is initially unstretched. Determine how far it moved down when the change in potential energy of the system was zero.
Exercise 4
A 0.1-kg block is placed on an incline 3 m above the spring. When released, the block will slide down and compress the spring ( N/m). Determine the compression of the spring when the change in potential energy of this system is zero.
Exercise 5
A satellite of mass 500 kg initially orbited the Earth in a circular orbit of radius . Over a period of time the radius decreased by 10%. What is the change in gravitational potential energy of the Earth-satellite system?
Exercise 6
Let us label the gravitational potential energy of a pair of interacting particles and as or in general the gravitational potential energy is labelled as for a pair of interacting particles and where and are integers.
(a) How many pairs of interacting particles are in the four systems shown in the table below?
(b) Write the total gravitational potential energy of the each system using the label for each interaction.
(c) Noting the pattern, can you tell how many terms are in the sum for the total gravitational potential energy of particles?
# Particles | System | # Pairs | Total Potential Energy |
---|---|---|---|
3 | |||
4 | |||
5 | |||
6 |
Exercise 7
Determine the change of the potential energy when a block slides down 30 cm. ( kg; kg). The blocks were initially at rest.
Exercise 8
A 0.1-kg mass is placed on a compressed vertical spring m. The spring constant is N/m. The mass moves up when released. Determine the change in potential energy of this system when the compression of the spring is 0.1 m.
Exercise 9
A satellite ( kg) is launched from the surface of the Earth to orbit the Earth at an altitude of m. Determine the change in gravitational potential energy of the Earth-satellite system.