3. Work and Energy

Potential Energy — Quiz

Test your understanding of potential energy with 5 practice questions.

Practice Questions

Question 1

A particle is subject to a conservative force described by the potential energy function $U(x) = ax^3 - bx$, where $a$ and $b$ are positive constants. What is the force $F(x)$ acting on the particle?

Question 2

A block of mass $m$ is attached to a spring with spring constant $k$. If the block is displaced by a distance $x$ from its equilibrium position, what is the elastic potential energy stored in the spring?

Question 3

A conservative force is defined as a force for which the work done in moving a particle between two points is independent of the path taken. Which of the following is a direct consequence of this definition?

Question 4

A particle moves in a region where its potential energy is given by $U(x,y) = Cxy^2$, where $C$ is a positive constant. What is the y-component of the force, $F_y$?

Question 5

An object of mass $m$ is initially at rest at a height $h$ above the ground. It is then released and falls freely. Ignoring air resistance, what is the relationship between its kinetic energy ($K$) and gravitational potential energy ($U_g$) as it falls?