AP Physics 1 work, energy and power
Energy is often the fastest way to solve an AP Physics 1 problem. Here are the ideas from Unit 3 and how to use them.
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Work
Work is energy transferred by a force: W = Fd cosθ. A force does positive work when it acts in the direction of motion and negative work when it opposes it. A force perpendicular to the motion does no work.
Forms of energy
- Kinetic energy K = ½mv².
- Gravitational potential energy ΔUg = mgΔh near Earth's surface.
- Spring potential energy Us = ½kx².
Conservation of energy
For a system with no external work and no friction, total mechanical energy stays constant. When friction acts, mechanical energy is converted to internal energy. External forces doing work on the system change its total energy.
The work-energy theorem
The net work done on an object equals its change in kinetic energy. It is a quick way to find speed after a force acts over a distance.
Energy bar charts
AP questions often ask you to draw bar charts of energy before and after. Choose the system carefully: whether the Earth or a spring is inside the system changes which energies appear.
Power
Power is the rate of energy transfer: P = ΔE/Δt, or P = Fv for a constant force along the motion.
When to use energy
- The question asks about speed or height, not time.
- The path is curved or complicated, such as a roller coaster.
- Springs are involved.
Worked examples
Example 1: a roller coaster
A cart starts from rest at a height of 20 m. Ignoring friction, find its speed at a point 5 m high.
- Energy: mg(20) = mg(5) + ½mv², so v = √(2 × 9.8 × 15) ≈ 17.1 m/s. The mass cancels.
Example 2: friction and energy
A 2 kg block slides across a rough floor at 6 m/s and stops after 4.5 m. Find the friction force.
- All kinetic energy (½ × 2 × 36 = 36 J) is removed by friction: F × 4.5 = 36, so F = 8 N.
Example 3: a spring launcher
A spring with k = 500 N/m is compressed 0.2 m and launches a 0.5 kg ball straight up. How high does it rise?
- ½kx² = ½ × 500 × 0.04 = 10 J = mgh, so h = 10/(0.5 × 9.8) ≈ 2.0 m.
Example 4: power
A motor lifts a 50 kg load 12 m in 10 s at constant speed. Find its power output.
- Work = mgh = 50 × 9.8 × 12 = 5880 J. Power = 5880/10 = 588 W.
Choosing the system
The same situation can be described in different ways depending on the system:
- Block only: gravity does work on it from outside. Use the work-energy theorem.
- Block and Earth: gravity is internal, so you use gravitational potential energy instead.
Never count gravity twice, as both work done and potential energy. Pick one system and stick to it.
Practice questions
Try each one before opening the answer.
Q1. A 1500 kg car speeds up from 10 m/s to 20 m/s. How much work is done on it?
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Q2. A pendulum bob is released from 0.45 m above its lowest point. Find its speed at the bottom.
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Q3. A 40 N force pushes a box 3 m at 60° to the direction of motion. Find the work done by the force.
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Q4. Is work done by the centripetal force on an object in uniform circular motion?
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Common mistakes
- Using conservation of mechanical energy when friction acts.
- Forgetting that work can be negative.
- Mixing up power (watts) and energy (joules).
The key ideas in more depth
Energy is a bookkeeping tool
Energy is a number that a system keeps track of. It can move between forms (kinetic, gravitational, spring) and between objects, but in a closed system the total stays constant. Most energy questions are really accounting questions: what was there at the start, what is there at the end, and where did the difference go?
When energy is the best method
Energy ignores the path. A ball rolling down a twisting track arrives at the bottom with the same speed as one dropped straight down from the same height, if there is no friction. That makes energy the fastest method for curved paths, loops, ramps and springs, where forces change direction constantly.
Friction and internal energy
Friction does not destroy energy; it converts mechanical energy into internal energy, which warms the surfaces. In bar charts, show this as an increase in internal energy (or as negative work done by friction, depending on the system you choose).
Exam tips
- State the system before writing any energy equation.
- Draw before-and-after energy bar charts for every free-response energy question.
- If time is asked for, energy alone will not answer it; combine it with kinematics or momentum.
More practice
Try each one before opening the answer.
Q1. A 2 kg block is pushed 3 m up a frictionless 30° incline at constant speed. How much work does the pushing force do?
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Q2. Two identical balls are thrown from a cliff at the same speed, one up and one down. Which hits the ground faster?
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Frequently asked questions
Is energy a vector?
No. Energy is a scalar, so you add energies as plain numbers with no directions.
Can potential energy be negative?
Yes. Only changes in potential energy matter, so where you set zero is your choice. Pick a convenient level, such as the ground.
Why does a pendulum eventually stop?
Air resistance and friction at the pivot convert mechanical energy into internal energy a little on every swing.
Extra practice
Try each one before opening the answer.
Q1. A 0.5 kg ball is thrown up at 12 m/s. Find its maximum height using energy.
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Key takeaways
- Work is energy transferred by a force: W = Fd cosθ.
- Kinetic, gravitational and spring energy can convert into each other.
- Mechanical energy is conserved only when no friction or outside work acts.
- Choose your system before writing an energy equation.
- Power is the rate of energy transfer, measured in watts.
Quick check
A 70 kg climber gains 500 m of height in one hour. Find the average useful power.