Exercises on Potential Energy

Helena Dedic

Beware: Many of the solutions to these exercises use $g=10m/s^{2}$ !

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?

• SOLUTION EX 1
  
  

Exercise 2

Two blocks of masses $m_{1}=4$ kg and $m_{2}=8$ kg are released from rest. What is the change of the potential energy of the system after the blocks have moved 20 cm?

• SOLUTION EX 2
  
  

Exercise 3

A block of mass $m=3$ kg slides down when released. The spring (with spring constant $k=20$ N/m) is initially unstretched. Determine how far it moved down when the change in potential energy of the system was zero.

• SOLUTION EX 3
  
  

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 ($k=4$ N/m). Determine the compression of the spring when the change in potential energy of this system is zero.

• SOLUTION EX 4
  
  

Exercise 5

A satellite of mass 500 kg initially orbited the Earth in a circular orbit of radius $r=1.5R_{E}$. Over a period of time the radius decreased by 10%. What is the change in gravitational potential energy of the Earth-satellite system?

• SOLUTION EX 5
  
  

Exercise 6

Let us label the gravitational potential energy of a pair of interacting particles $m_{1}$ and $m_{2}$ as $U_{12}$ or in general the gravitational potential energy is labelled as $U_{ij}$ for a pair of interacting particles $m_{i}$ and $m_{j}$ where $i$ and $j$ 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 $n$ particles?

# Particles	System	# Pairs	Total Potential Energy
3
4
5
6

• SOLUTION EX 6
  
  

Exercise 7

Determine the change of the potential energy when a block $m_{1}$ slides down 30 cm. ($m_{1}=2$ kg; $m_{2}=3$ kg). The blocks were initially at rest.

• SOLUTION EX 7
  
  

Exercise 8

A 0.1-kg mass is placed on a compressed vertical spring $x_{i}=0.2$ m. The spring constant is $k=50$ 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.

• SOLUTION EX 8
  
  

Exercise 9

A satellite ($m_{S}=1000$ kg) is launched from the surface of the Earth to orbit the Earth at an altitude of $7\times 10^{5}$ m. Determine the change in gravitational potential energy of the Earth-satellite system.

• SOLUTION EX 9