Momentum: two trolleys collide
Send trolley A into trolley B so they stick together. Change their masses and velocities, and check that the total momentum is the same before and after, while some kinetic energy is lost.
Core concept
Momentum is mass × velocity; in a collision the total momentum before equals the total after, so trolleys that stick move at (m₁v₁ + m₂v₂) ÷ (m₁ + m₂), and some kinetic energy turns into sound and heat
Topic: Force and laws of motion
Momentum is mass: How much matter something has, measured in grams or kilograms. It is the same everywhere. All key words × velocity, p = mv, measured in kg·m/s. Velocity has a direction, so a trolley moving to the left has a negative velocity and a negative momentum. When two objects collide, they push on each other with equal and opposite force: A push or a pull. Forces can start, stop or turn things. All key words (Newton's third law) for the same time, so whatever momentum one gains, the other loses: the total momentum before the collision equals the total after. If the trolleys stick together they move off at one velocity, v = (m₁v₁ + m₂v₂) ÷ (m₁ + m₂). Kinetic energy: What is needed to make things move, heat up, light up or grow. All key words, ½mv², is not kept in such a collision: some of it becomes sound, heat and the work of denting.
What you will learn
- Calculate momentum as mass × velocity, with a sign for direction.
- Use the conservation of momentum to find the velocity after a collision.
- Show that kinetic energy is lost when colliding objects stick together.
Before you start
- Know that velocity is speed in a given direction.
Materials
- Two toy trolleys, clay or tape to make them stick, and a smooth floor
Equipment
- A metre scale and a stopwatch
Procedure
- Record a 2 kg trolley at 4 m/s hitting a 2 kg trolley at rest.
- Make trolley B come towards A at 3 m/s and record.
- Make A 3 kg and 6 m/s and record.
How this simulation is simplified
- There is no friction, and the trolleys stick together after the collision; right is positive.