 # Newton s second law of motion cart experiment

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. 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.

## Investigating Newton's second law of motion

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.

Connect the light gate via an interface to a computer running data-logging software.

• How does this affect the acceleration of the cart when you apply the same forces that you did in step 1 and 2?
• You can "zero" it by sliding the scale up or down;
• Fix a 1 kg mass on the trolley with Blu-tack to make the total mass trolley plus mass of about 2 kg;
• What happens if you apply an even larger force like 2 Newtons?

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.

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. Release the trolley from the same starting point as before. Repeat this several times. 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. 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.

## Newton's Second Law

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.

• It is informative to display successive measurements on a simple bar chart;
• Set the software to record data, then release 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;
• If the force is doubled, this results in a doubling of the acceleration, and so on;
• This avoids preoccupation with the calculation process, and greatly assists thinking about the relationship between acceleration and force;
• Choose a length of string such that the mass does not touch the ground until the trolley nearly reaches the pulley.

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. 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. This may be conducted to provide data for the complementary relationship indicated by Newton's second law: This experiment was safety-checked in November 2006. 