Stopping distance lab

1. Pick a release height. Click one of the height buttons, from 10 cm to 80 cm. The car's back wheels move to that height on the wooden ramp. The green marker shows where it starts. 80 cm is the top of the ramp.
2. Press Release the car. The car rolls down the ramp and through the photogate at the bottom. Then it rolls into the open end of the box at A and hits the far wall.
3. Read the speed. The photogate measures how fast the car is going at A, right before the crash. It shows up top as Speed at A.
4. Read the distance. The car pushes the box along the bench until both stop at B. The meter stick starts at A. Read where the open end of the box stops. That is the distance from A to B.
5. Check your trials. Each run adds a row to Your trials and a dot to each graph. Try every height, and run each one more than once.
6. Double the speed. Run 10 cm and 40 cm, or 20 cm and 80 cm. The speed at A doubles. The blue box above the graphs shows what happens to the distance.
7. Start over any time. Reset puts the car back. Delete last trial takes back one run. Clear trials empties the table (click it twice). Copy data copies the table for a spreadsheet.

A moving car has kinetic energy. Kinetic energy is the energy of motion. It depends on the car's mass and on its speed squared.

Squared means a number times itself. If the speed doubles, the energy goes up 2 × 2 = 4 times. If the speed triples, the energy goes up 3 × 3 = 9 times.

When the car hits the box, it pushes the box along the bench. Friction between the box and the bench pushes back. It is the same size on every run. Friction takes away a little energy for every centimeter the box slides.

So the box stops when friction has taken away all the energy. Four times the energy needs four times the distance. That is why twice the speed gives about four times the distance.

This is why drivers need much more room to stop at high speed. A car going 60 mph needs about four times the braking distance of a car going 30 mph.

Words to know

Kinetic energy

The energy an object has because it is moving. More mass or more speed means more kinetic energy.

Speed squared

The speed times itself. Kinetic energy grows with the speed squared, not just the speed.

Friction

A force that pushes against sliding. It slows the box down and turns its energy into heat.

Photogate

A light beam that times how long the car blocks it. That time gives the car's speed.

Stopping distance

How far something slides before it stops. Here it is the distance from A to B.

What each letter means

Letter	What it stands for	Unit
h	Release height, from the bench to the car's back wheels	m
g	Gravity's pull: always 9.8	m/s²
v	Speed of the car at A	m/s
m	Mass of the car: 0.100	kg
KE	Kinetic energy of the car at A	J
d	Distance from A to B	cm

Three steps

1. Speed at A. A higher start gives more speed. The 0.75 is there because the ramp and the wheels take away about a quarter of the energy.
   v = √(2 × g × h × 0.75)
2. Kinetic energy at A. The speed is squared.
   KE = ½ × m × v²
3. How far the box slides. The car hits the inside of the box's far wall. Then the car and the box move together, at half the car's speed (they have the same mass). Friction slows them at 1.67 m/s². The speed is squared again, so twice the speed gives four times the distance.
   d = (v ÷ 2)² ÷ (2 × 1.67) × 100

 

Your measured numbers are a little different from these, because of the real-lab wobble. Turn the wobble off and they will match.