Work, energy and power practice questions.

Which of the following is a renewable energy source?

• coal
• natural gas
• wind
• nuclear fission

Answer: wind

Wind is continuously replenished by solar heating of the atmosphere. Coal, natural gas and nuclear fission fuel (uranium) are all finite, non-renewable resources.

A sledge is pulled 10 m across horizontal ground by a rope under a tension of 50 N acting at 60° above the horizontal. Calculate the work done on the sledge by the tension.

• 500 J
• 250 J
• 433 J
• 25 J

Answer: 250 J

W = Fs cos θ = 50 × 10 × cos 60° = 250 J; only the component of the force along the displacement does work.

An object of mass m moving at speed v has kinetic energy E. What is the kinetic energy of an object of mass 2m moving at speed 2v?

• 2E
• 4E
• 16E
• 8E

Answer: 8E

E_k = ½mv², so doubling the mass multiplies it by 2 and doubling the speed multiplies it by 4, giving 8E in total.

A spring of spring constant 200 N m⁻¹ is compressed by 0.10 m. Calculate the elastic potential energy stored in the spring.

• 1.0 J
• 2.0 J
• 20 J
• 0.10 J

Answer: 1.0 J

E_p = ½kx² = ½ × 200 × (0.10)² = 1.0 J; forgetting the ½ gives 2.0 J, and forgetting both the ½ and the square gives 20 J.

A skydiver falls vertically at constant terminal speed. Which statement about the energy changes is correct?

• Kinetic energy increases as gravitational potential energy decreases
• Gravitational potential energy is conserved because the falling speed stays constant throughout
• Gravitational potential energy is transferred to thermal energy of the air and skydiver
• No energy transfers occur because the resultant force is zero

Answer: Gravitational potential energy is transferred to thermal energy of the air and skydiver

At terminal speed the kinetic energy is constant, so the gravitational potential energy lost is dissipated as thermal energy through work done against air resistance.

A variable force acts on an object moving in a straight line along the direction of the force. Which quantity is given by the area between a graph of that force against displacement and the displacement axis?

• The impulse delivered to the object by the force.
• The average power developed by the force.
• The work done on the object by the force.
• The change in momentum of the object.

Answer: The work done on the object by the force.

Force multiplied by displacement is work; force multiplied by time would be impulse, which is the area under a force–time graph instead. Power requires a division by time and can therefore never be an area on these axes.