Investigating Newton's second law of motion

Demonstration

A trolley experiences an acceleration when an external force is applied to it. The aim of this datalogging experiment is explore the relationship between the magnitudes of the external force and the resulting acceleration.

Apparatus and materials

Light gate, interface and computer

Dynamics trolley

Pulley and string

Slotted masses, 400 g

Mass, 1 g

Clamp

Ruler

Double segment black card (see diagram)

Health & Safety and Technical notes

Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.

Pass a piece of string with a mass hanging on one end over a pulley. Attach the other end to the trolley so that, when the mass is released, it causes the trolley to accelerate. Choose a length of string such that the mass does not touch the ground until the trolley nearly reaches the pulley. Fix a 1 kg mass on the trolley with Blu-tack to make the total mass (trolley plus mass) of about 2 kg. This produces an acceleration which is not too aggressive when the maximum force (4 N) is applied.

The force is conveniently increased in 1 newton steps when slotted masses of 100 g are added. Place the unused slotted masses on the trolley. Transfer them to the slotted mass holder each time the accelerating force is increased. This ensures that the total mass experiencing acceleration remains constant throughout the experiment.

Fit a double segment black card on to the trolley. Clamp the light gate at a height which allows both segments of the card to interrupt the light beam when the trolley passes through the gate. Measure the width of each segment with a ruler, and enter the values into the software.

Connect the light gate via an interface to a computer running data-logging software. The program should be configured to obtain measurements of acceleration derived from the double interruptions of the light beam by the card.

The internal calculation within the program involves using the interruption times for the two segments to obtain two velocities. The difference between these, divided by the time between them, yields the acceleration.

A series of results is accumulated in a table. This should also include a column for the manual entry of values for 'force' in newtons. It is informative to display successive measurements on a simple bar chart.

Procedure

Data collectiona Select the falling mass to be 100 g. Pull the trolley back so that the mass is raised to just below the pulley. Position the light gate so that it will detect the motion of the trolley soon after it has started moving.

Set the software to record data, then release the trolley. Observe the measurement for the acceleration of the trolley.

b Repeat this measurement from the same starting position for the trolley several times. Enter from the keyboard '1'( 1 newton) in the force column of the table

c Transfer 100 g from the trolley to the slotted mass, to increase it to 200 g. Release the trolley from the same starting point as before. Repeat this several times. Enter '2' (2 newtons) in the force column of the table.

d Repeat the above procedure for slotted masses of 300 g and 400 g.

Analysis
Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the relative increase in values of acceleration as the slotted mass is increased.

The relationship between acceleration and applied force is investigated more precisely by plotting an XY graph of these two quantities. (Y axis: acceleration; X axis: force.) Use a curve-matching tool to identify the algebraic form of the relationship. This is usually of the form 'acceleration is proportional to the applied force'.

This relationship is indicative of Newton's second law of motion.

Teaching notes

1 This is a computer-assisted version of the classic experiment. The great advantage of this version is that the software presents acceleration values instantly. This avoids preoccupation with the calculation process, and greatly assists thinking about the relationship between acceleration and force. Each repetition with the same force gives a similar acceleration. If the force is doubled, this results in a doubling of the acceleration, and so on. The uniform increases in the acceleration can be confirmed by using cursors to read off corresponding values from the graph.

2 The resulting straight line fit on the graph should be scrutinized for sources of error. The quality of the fit is reduced if the suggested procedure for maintaining the total mass constant is ignored. Also, a common outcome is a very small intercept near the graph origin. The most likely cause of this is neglect of the effect of friction on the motion of the trolley.

3 The gradient of the line may be correlated with 1/mass of the system (trolley and slotted masses).

4 There is a variation of this experiment, in which the force is held constant but the mass of the trolley is altered by attaching further masses. This may be conducted to provide data for the complementary relationship indicated by Newton's second law: for a given applied force, the acceleration of the trolley is inversely proportional to its mass.

This experiment was safety-checked in November 2006