Impulse Virtual Lab: Force–Time Graphs and Crash Safety

This impulse virtual lab turns the momentum and car-safety content of GCSE, A-level and AP Physics into a practical. A cart with a bumper runs along an air track into a wall fitted with a force sensor, and light gates time it on the way in and out. Students keep the mass and speed fixed, swap between a soft spring, a hard spring, a crumple zone and an airbag, and read the peak force, contact time and impulse for each run. The area under the force–time graph matches the change in momentum from the light gates every time. The lesson ends with a design task: protect an egg on a moving cart.

Curriculum links

• AQA GCSE Physics 4.5.7.3 (changes in momentum): F = mΔv/Δt and safety features such as air bags, seat belts and crumple zones. The light gates work as in the GCSE trolley practicals.
• AQA A-level Physics 3.4.1.6 (momentum): impulse as the area under a force–time graph.
• AP Physics 1 Unit 4 (linear momentum), topic 4.2 on change in momentum and impulse.
• NGSS HS-PS2-3: design a device that minimizes the force on an object during a collision.

Simulic is not affiliated with or endorsed by AQA, the College Board or any exam board.

Before the lab (5 min)

Ask students to commit to a prediction, on paper or as question 1 of the class link:

"A 1 kg cart at 3 m/s hits a wall, first with a soft spring bumper, then with a hard spring. Both times it bounces back at 3 m/s. How does the peak force on the wall compare?"

Many students say the force is the same, because the change in momentum is the same. Don't correct them yet.

Method in the simulation

1. Press Force sensor & crash test. Keep Collides with on "Wall with force sensor", Mass m₁ 1.0 kg, Velocity u₁ 3.0 m/s and Bumper depth 20 cm.
2. Choose Bumper: Soft spring and press Launch. The run plays in slow motion during contact, then adds a row to the table.
3. Repeat with Hard spring, Crumple zone and Airbag. Keep m₁ and u₁ the same every time.
4. For each run, record u and v from the light gate, Δp, the impulse J (the shaded area), the contact time Δt and the peak force Fmax.
5. Compare the red graph (force on the wall) with the blue graph (force on the cart).

Bumper	u (m/s)	v (m/s)	Δp (kg·m/s)	J (N·s)	Δt (ms)	Fmax (N)
Soft spring
Hard spring
Crumple zone
Airbag

Expected results

All values come from the simulation, which has no random error, so every group gets the same numbers.

Bumper	v (m/s)	Δp = J (kg·m/s)	Δt (ms)	Fmax (N)	F̄ = J/Δt (N)
Soft spring	−3.00	−6.000	157.1	60.0	38.2
Hard spring	−3.00	−6.000	44.4	212.1	135.0
Crumple zone	−0.24	−3.245	56.6	60.0	57.4
Airbag	−0.82	−3.820	232.5	62.4	16.4

• The impulse from the sensor always equals Δp from the light gate.
• The two springs give the same Δp, but the soft spring's contact lasts 3.5 times longer and its peak force is 3.5 times smaller.
• The crumple zone and the airbag barely rebound, so Δp is about half as large. They also absorb about 4.2 to 4.5 J of kinetic energy.
• The red and blue curves are mirror images: the wall pushes on the cart as hard as the cart pushes on the wall.

Questions for students

1. (Prediction, asked again after the lab) How does the peak force with a soft spring compare with a hard spring?
2. Which quantities must stay the same while you compare bumpers?
3. With a hard spring, m₁ = 1.0 kg and u₁ = 3.0 m/s, what is the peak force?
4. How many times longer is the soft-spring contact time than the hard-spring contact time?
5. Use momentum to explain why an airbag reduces the force on a driver in a crash.

Answers for teachers: (1) The soft spring gives a smaller peak force (60 N against 212 N), because the contact lasts longer. (2) The mass m₁ and the velocity u₁, so the change in momentum is comparable. (3) 212 N (accept ±2). (4) 157.1 ÷ 44.4 ≈ 3.54. (5) The driver's change in momentum is fixed by their mass and speed. Force = change in momentum ÷ time, so an airbag that makes the stop last longer gives a smaller force.

Common misconceptions

• "The same change in momentum means the same force." The impulse is the same, but force = Δp/Δt. Spread the change over more time and the force falls.
• "A softer bumper is always safer." Set Velocity u₁ to 4.5 m/s with the soft spring: it is squashed completely and the force spikes to about 1210 N. A safety feature must be soft and deep enough.
• "The heavier object pushes harder." Choose Cart 2 at rest: the forces on the two carts are equal and opposite whatever their masses.

Extension

• Design challenge (NGSS HS-PS2-3): set Task to Design challenge. A 2 kg cart carrying an egg hits the wall at 3 m/s; keep Fmax at or below 100 N with a bumper no deeper than 15 cm. In the simulation, no spring passes: soft enough springs bottom out. A 15 cm airbag passes with 88 N; a crumple zone with a 90 N crush force passes with exactly 90 N.
• Choose Collides with "Cart 2 at rest" and check that J₁ = −J₂ for both carts.

FAQ

Can the class link open straight on the force sensor screen?

Yes. On the Share page, pin Screen to "Force sensor & crash test" in the link's starting values. You can also pin Bumper and Collides with. Otherwise the first step of the method tells students to press the button.

Why is J negative?

The cart moves toward the wall in the positive direction, and the wall pushes it back. So the impulse on the cart and its change in momentum are both negative.

Where is the conservation of momentum part?

Press Back to air track for two carts colliding elastically or inelastically. The forces and motion lesson plan covers the force side in more depth.

Related simulations and guides

Collision lab – momentum and kinetic energy in collisions Newton's second law – pulling a block on a surface

For more physics activities, see interactive physics lesson ideas.