7.7 - Acceleration on a Ramp
The experiment
Aim
To find out how the slope of a ramp affects the acceleration of a ball or trolley rolling down it.
Background
- An object on a slope is pulled down it by part of its own weight. The steeper the slope, the bigger that force, and the bigger the acceleration.
- You can't measure the acceleration directly, but you can time how long the object takes to roll a measured distance from rest.
- So in this practical you time a ball rolling 80 cm down a ramp at different heights, and work out its acceleration at each height.
Variables
- Independent variable - The height of the raised end of the ramp.
- Dependent variable - The time taken to roll between the two lines, which gives the acceleration.
- Control variables - The ball or trolley, the distance between the lines, and the ramp surface.
Method
- Set up the ramp - Rest one end of a wooden ramp, about 120 cm long, on a pile of blocks, so the raised end is 5 cm high.
- Mark the distance - Draw a start line and a finish line across the ramp in pencil, 80 cm apart.
- Release the ball - Hold a marble or a ball bearing still at the start line, and let go without pushing it.
- Time the run - Start the stopwatch as you let go, and stop it as the ball crosses the finish line.
- Repeat - Do three runs at each height and find the mean time.
- Change the height - Raise the ramp in equal steps up to about 15 cm, so you have five heights.
- Plot the graph - Work out the acceleration at each height, and plot acceleration against the height of the ramp.
Safety
- Catch the ball - Put a box or a tray at the bottom of the ramp, because a marble on the floor is a slip hazard.
- Protect your feet - If you use a trolley, stand a box of crumpled newspaper on the floor below the end of the ramp.
- Check the blocks - Make sure the pile is stable before letting go of the ramp.
Worked example - Acceleration down a ramp
A student released a ball from rest and timed it over the 80 cm between the two pencil lines, at five different ramp heights.
| Height of ramp (cm) | 5.0 | 7.5 | 10.0 | 12.5 | 15.0 |
|---|---|---|---|---|---|
| Mean time (s) | 2.00 | 1.63 | 1.41 | 1.26 | 1.15 |
Find the acceleration at each height, describe the graph and find its gradient, and work out how fast the ball was going as it crossed the finish line at the 10.0 cm height.
Step 1 - Work out the acceleration at each height
The ball starts from rest, so use this equation with = 0.80 m.
- At 5.0 cm, a = 1.60 ÷ 2.002 = 0.40 m/s2.
- At 7.5 cm, a = 1.60 ÷ 1.632 = 0.60 m/s2.
- At 10.0 cm, a = 1.60 ÷ 1.412 = 0.80 m/s2.
- At 12.5 cm, a = 1.60 ÷ 1.262 = 1.00 m/s2.
- At 15.0 cm, a = 1.60 ÷ 1.152 = 1.20 m/s2.
Step 2 - Plot and describe the graph
Plot acceleration on the y-axis against ramp height on the x-axis. The points lie on a straight line through the origin, and every extra 2.5 cm of height adds 0.20 m/s2. The acceleration is directly proportional to the height of the ramp, because raising the end increases the part of the ball's weight acting down the slope in proportion to the height. The average speed, 0.80 m ÷ the mean time, also rises with the height, but not in proportion. A graph of average speed against height is a curve through the origin that gets less steep.
Step 3 - Find the gradient
Each centimetre the ramp is raised adds 0.080 m/s2 to the acceleration.
Step 4 - Find the speed at the finish line
At the 10.0 cm height, the average speed is 0.80 ÷ 1.41 = 0.567 m/s. The ball started from rest and its speed rose steadily, so its speed at the finish line is twice the average.
Step 5 - Check the speed using the acceleration
Use , with = 0.
The two answers agree, which checks the working. It doesn't show the acceleration was steady, because both methods assume it.
Common exam questions
Question 1
Why is the ball released rather than pushed?
So that it starts from rest. A push would give it an unknown starting speed, and a = 2s ÷ t2 would no longer work.
Question 2
A ball starting from rest reaches 1.2 m/s in 3.0 s. Calculate its acceleration.
a = (v − u) ÷ t = (1.2 − 0) ÷ 3.0 = 0.40 m/s2.
Question 3
A student times the runs with a stopwatch. Give one advantage of using light gates instead.
The gates are triggered by the ball itself, so there's no reaction time in the measurement. The runs last only a second or two, so a person's reaction time is a noticeable fraction of each reading.
Question 4
Why should the ramp be as smooth as possible?
Friction acts against the ball's motion and reduces its acceleration. The smoother the surface, the closer the measured acceleration is to what the slope alone would produce.
Question 5
How would you change this experiment to test whether the mass of the trolley affects its acceleration?
Keep the ramp at one height and load extra masses onto the trolley. The mass becomes the independent variable, and the height of the ramp becomes a control variable.