Work, Energy, and Power — Practice Quiz

A Physics cheat sheet for Work, Energy, and Power — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Work Done by a Constant Force: The work \(W\) done by a force \(F\) over a displacement \(d\) at an angle \(\theta\).

$$W = Fd\cos(\theta)$$

Work-Energy Theorem: The net work \(W_{net}\) done on an object equals its change in kinetic energy \(\Delta KE\).

$$W_{net} = \Delta KE$$

Kinetic Energy: The energy \(KE\) of an object due to its motion, where \(m\) is mass and \(v\) is velocity.

$$KE = \frac{1}{2}mv^2$$

Gravitational Potential Energy: Energy \(PE_g\) stored based on vertical position \(h\) in a gravitational field.

$$PE_g = mgh$$

Where: \(g\) = acceleration due to gravity (approx. \(9.8 m/s^2\) on Earth)

Elastic Potential Energy: Energy \(PE_s\) stored in a spring stretched/compressed by distance \(x\).

$$PE_s = \frac{1}{2}kx^2$$

Where: \(k\) = spring constant

Total Mechanical Energy: Sum of kinetic and potential energies.

$$E_{total} = KE + PE_g + PE_s$$

Power: The rate at which work \(W\) is done or energy is transferred over time \(t\).

$$P = \frac{W}{t}$$

Work Done by Gravity: The work done by the gravitational force as an object moves from initial height \(h_0\) to final height \(h_f\).

$$W_{gravity} = mg(h_0 - h_f)$$

Work by Non-conservative Forces: The net work \(W_{nc}\) done by non-conservative forces equals the change in total mechanical energy.

$$W_{nc} = E_f - E_0$$

Where: \(E\) = total mechanical energy (KE + PE)

Power (Energy Change): Power is also defined as the rate at which energy changes.

$$P = \frac{\Delta E}{t}$$

Work Done by a Variable Force: The work done is equal to the area under the graph of the force component \(F\cos\theta\) versus displacement \(s\).

$$W = \text{Area under } F\cos\theta \text{ vs } s$$

Instantaneous Power: The product of force \(F\) and velocity \(v\) in the direction of the force.

$$P = Fv\cos(\theta)$$

Practice quiz

  1. A $10 \text{ kg}$ box is pulled $5 \text{ m}$ across a horizontal floor by a constant force of $30 \text{ N}$ acting at an angle of $30^\circ$ above the horizontal. How much work is done by this force?

    • $150 \text{ J}$
    • $129.9 \text{ J}$
    • $75 \text{ J}$
    • $0 \text{ J}$

    Answer: $129.9 \text{ J}$

  2. A $2 \text{ kg}$ object initially moving at $4 \text{ m/s}$ is acted upon by a net force that does $16 \text{ J}$ of work on it. What is the final speed of the object?

    • $4 \text{ m/s}$
    • $5.66 \text{ m/s}$
    • $8 \text{ m/s}$
    • $16 \text{ m/s}$

    Answer: $5.66 \text{ m/s}$

  3. A $0.5 \text{ kg}$ ball is thrown vertically upwards. If its gravitational potential energy increases by $19.6 \text{ J}$, what is the maximum height it reaches from its initial position? (Assume $g = 9.8 \text{ m/s}^2$)

    • $2 \text{ m}$
    • $4 \text{ m}$
    • $8 \text{ m}$
    • $19.6 \text{ m}$

    Answer: $4 \text{ m}$

  4. A spring with a spring constant $k = 200 \text{ N/m}$ is compressed by $10 \text{ cm}$. How much elastic potential energy is stored in the spring?

    • $0.1 \text{ J}$
    • $1 \text{ J}$
    • $10 \text{ J}$
    • $20 \text{ J}$

    Answer: $1 \text{ J}$

  5. A crane lifts a $500 \text{ kg}$ load to a height of $10 \text{ m}$ in $5 \text{ seconds}$. What is the average power exerted by the crane? (Assume $g = 9.8 \text{ m/s}^2$)

    • $980 \text{ W}$
    • $4900 \text{ W}$
    • $9800 \text{ W}$
    • $49000 \text{ W}$

    Answer: $9800 \text{ W}$

  6. A $0.2 \text{ kg}$ apple falls from a tree branch $3 \text{ m}$ above the ground. What is its speed just before it hits the ground, assuming it starts from rest? (Neglect air resistance, $g = 9.8 \text{ m/s}^2$)

    • $5.42 \text{ m/s}$
    • $7.67 \text{ m/s}$
    • $9.8 \text{ m/s}$
    • $12.12 \text{ m/s}$

    Answer: $7.67 \text{ m/s}$

  7. A $1 \text{ kg}$ block slides down a rough incline. Its initial speed is $2 \text{ m/s}$ at a height of $5 \text{ m}$. At the bottom, its speed is $8 \text{ m/s}$. How much work was done by friction (a non-conservative force)? (Assume $g = 9.8 \text{ m/s}^2$)

    • $19 \text{ J}$
    • $-19 \text{ J}$
    • $32 \text{ J}$
    • $-32 \text{ J}$

    Answer: $-19 \text{ J}$

  8. A car engine exerts a constant force of $1500 \text{ N}$ on the car while it is moving at a constant velocity of $20 \text{ m/s}$. What is the instantaneous power delivered by the engine?

    • $1500 \text{ W}$
    • $20000 \text{ W}$
    • $30000 \text{ W}$
    • $60000 \text{ W}$

    Answer: $30000 \text{ W}$

  9. A person lifts a $5 \text{ kg}$ object from the ground to a height of $2 \text{ m}$. What is the work done by gravity during this process?

    • $98 \text{ J}$
    • $-98 \text{ J}$
    • $0 \text{ J}$
    • $19.6 \text{ J}$

    Answer: $-98 \text{ J}$

  10. A light bulb consumes $60 \text{ J}$ of electrical energy every second. What is the power of the light bulb?

    • $1 \text{ W}$
    • $60 \text{ W}$
    • $120 \text{ W}$
    • $3600 \text{ W}$

    Answer: $60 \text{ W}$

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