AP Physics 1 · Exam guide
AP Physics 1 Energy and Momentum Question: Collisions and Work by Friction
Many free-response questions chain two ideas: momentum is conserved in a collision, and energy tells you what happens afterward. The skill is to name which principle applies at each stage. This guide works one chain, with \(g = 10\ \mathrm{m/s^2}\).
Which principle for which stage
| Stage | Principle | Why |
|---|---|---|
| During a collision | Momentum is conserved. | The forces between the objects are internal and brief. |
| Before and after a collision | Kinetic energy may change. | Inelastic collisions lose kinetic energy to other forms. |
| Sliding on a rough surface | Work by friction equals the energy lost. | Friction converts kinetic energy into thermal energy. |
A worked example
A 2.0 kg cart moving at 6.0 m/s collides with a 4.0 kg cart at rest, and the two stick together. They then slide on a rough level surface with coefficient of kinetic friction 0.25 until they stop. (a) Find their speed just after the collision. (b) How much kinetic energy is lost in the collision? (c) How far do they slide?
(a) Momentum is conserved: \((2.0)(6.0) = (6.0)v\), so \(v = 2.0\) m/s.
(b) Before: \(\dfrac{1}{2}(2.0)(6.0)^2 = 36\) J. After: \(\dfrac{1}{2}(6.0)(2.0)^2 = 12\) J. The collision loses 24 J.
(c) The friction force is \(\mu m g = (0.25)(6.0)(10) = 15\) N. The work by friction equals the kinetic energy: \(15\,d = 12\), so \(d = 0.80\) m.
Momentum is conserved in a collision. Kinetic energy is not, unless the collision is elastic. Carts that stick together lose kinetic energy.
It computes both values and names the type of collision.
What graders look for
- The statement of the principle, such as "momentum is conserved," before the equation.
- A system chosen so that outside forces are negligible.
- Units and signs, especially for velocities in opposite directions.
- A consistency check: energy after a collision cannot exceed energy before.
Common mistakes
- Conserving kinetic energy in an inelastic collision.
- Using the mass of only one cart after they stick together.
- Using the wrong mass in the friction force.
- Dropping a negative sign for a velocity in the opposite direction.
Frequently asked questions
When is kinetic energy conserved in a collision?
Only in an elastic collision. Most collisions in these problems are inelastic.
Is momentum always conserved?
For a system with no net external force during the collision, yes.
How do I find the work done by friction?
Multiply the friction force by the distance, with a negative sign for the work done on the object.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics courses ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a review with worked answers. These free lessons also build the skills the free-response section tests:
- Free lesson 1.2: displacement, velocity, and acceleration
- Free lesson 1.4: the constant acceleration equations
See the AP Physics 1 course Free lessons and lesson list
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Multiple choice
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