# Investigating motion on a sloping surface

##### Demonstration

When free to move, a trolley on an inclined plane will accelerate down the slope. If it is given a velocity up the slope it will decelerate. This experiment allows both acceleration and deceleration to be investigated by datalogging the output from a motion sensor.

#### Apparatus and materials

Motion sensor, interface and computer

Dynamics trolley

Runway

Wooden block and clamp

#### Health & Safety and Technical notes

If a full length runway (2 m long) is used, two people should handle it to avoid back strain.

Prop up the runway at one end to create an inclined plane. Clamp a wooden block at the lower end to make a solid barrier.

The dynamics trolley with its spring plunger pointing forwards is allowed to roll down the runway.

Place a motion sensor at the top of the runway and connect it via an interface to a computer.

Take care that the girders to the sides of the runway do not protrude too high. This would interfere with the ability of the sensor to distinguish sonic reflections from the trolley.

Configure the data-logging software to measure the distance of the trolley from the sensor and present the results as a graph of distance against time.

#### Procedure

Data collection
a
Position the trolley near the top of the runway, about 30 cm from the motion sensor.

b Start the data-logging software and release the trolley. The trolley should bounce off the wooden block and move up and down the runway several times.

The distance travelled by the trolley reduces after successive bounces.

Analysis
c Depending upon the software, the results may be displayed as a distance versus time graph whilst the experiment proceeds.

Observe the shape of the graph as a succession of half loops.

Identify on the graph:

1 The points corresponding to the collision of the trolley with the block.

2 The parts of the graph representing the trolley movement down the runway.

3 The parts of the graph representing the trolley movement up the runway.

There are several interesting features of the graph which invite explanation:

1 The graph shows curves rather than straight lines.

2 Successive half-loops reduce in size.

3 Each half-loop is asymmetrical.

4 Distances are from the sensor rather than from the wooden block where collisions occur.

You could study the velocity of the trolley more directly. Do this by setting the program to calculate and plot the rate of change of distance against time. This reveals both positive and negative velocities.

These change linearly, indicating uniform acceleration and deceleration. Note that the magnitude of the deceleration is slightly larger than the acceleration.

#### Teaching notes

1 This experiment illustrates the value of rapid collection and display of data in assisting thinking about the phenomenon under investigation. Data is collected within a few seconds and the graph is presented simultaneously. This helps students to make connections between features on the graph and the actual motion of the trolley.

In general, it is a useful teaching strategy to ask students to make a prediction about the appearance or shape of a graph, before the program actually plots the result. Comparing the result with the prediction is a simple ploy for prompting discussion.

2 The collisions show up as rapid reversals in the direction of motion. One side of the loop corresponds to the downward motion and the other side corresponds to the upward motion.

These associations may be confirmed by separate informal experiments pushing the trolley up and down the runway by hand. Similar hand-controlled experiments can confirm the connection between the speed of the trolley and the gradient of the graph.

3 The shape of the graph is such that it shows distance increasing as the trolley rolls down the runway. For some students this is counter intuitive. They may think that upward graph line indicates upward movement on the runway. Emphasize that the graph shows not velocity butdistance, which is measured down the slope.

4 Software tools for taking readings from the graph and measuring gradients at several points are useful for testing out ideas about the motion. For example: 'Is the gradient immediately before the collision the same as the gradient immediately after?' This prompts thinking about the change of velocity at each collision.

The asymmetry of each loop can also be investigated. Further experiments can establish that the degree of asymmetry depends upon the mass of the trolley and the angle of slope. The presence of friction has a role in explaining the asymmetry, as discussed below.

5 A particularly useful software function is to calculate the velocity for all points on the graph and plot these as a new graph. The linear changes observed confirm uniform acceleration and deceleration. There are plenty of opportunities for discussion here.

• The gradients of the velocity versus time graph are observed to be different according to the direction of travel.
• The deceleration when the trolley is moving up the slope is found to be slightly larger than theacceleration when the trolley is moving down the slope. For an explanation of this, prompt students to think about the direction of the force of friction and the component of its weight acting along the ramp.
• For the downward motion, friction opposes the component of gravity. For the upward motion friction is in the same downward direction as the component of gravity. The resulting force and acceleration are different in each case.

How Science Works Extension: This experiment provides ample opportunities for extension work, illustrating various aspects of ‘How Science Works’. For example, students could investigate how the acceleration of the trolley depends on its mass. In principle, the mass of the trolley is irrelevant; in a frictionless situation, the trolley will have an acceleration equal to the component of g down the slope. However, friction reduces the acceleration and the effect is greater for a trolley with a small mass.

Because the electronic equipment can determine the value of the acceleration, students are able to focus their attention on the experiment rather than on the manipulation of ticker-tapes or on complicated calculations.

Frictional effects are more significant for a ramp with a small angle of slope, so students should consider this in the design of their experiment.

Because the effects of friction are small, students will need to work carefully, making repeat measurements if they are to show up any clear effects. This is a good test of experimental technique.

This experiment was safety-checked in May 2006