- #1

Jimmy87

- 686

- 17

## Homework Statement

We were given two methods to look into Newton's 2nd Law and evaluate them by looking at where sources of error may have come from. They both involved accelerating a car across a table. A plastic track was used to guide the car along a straight path to make sure it went through the light gate. String was attached to the car which was put over a bench pulley and we hung slotted masses to provide the force. We only had one light gate so we used it to measure the time it took the car to go through. We stuck card on the top of the car which was used to break the light beam. We found the velocity by dividing the length of the card on top of the car by the time recorded at the light gate. We started the car 20cm away from the light every time for method 1 (this was 's'). We used the equation below to work out the acceleration. The initial velocity was zero so the acceleration was just v^2/2s. The length of the card on top of the car in method one was 2cm.

The second method was very similar except that the card on top of the light gate started off right at the light gate instead of 20cm away. Therefore the distance 's' was just the length of the card which was 8cm in method 2. We used the time at the light gate and the length of the card to work out the average velocity instead of the final velocity. We then doubled this value to give the final velocity as it was a constant acceleration that started at rest. I just wanted some pointers on why the results were all over the place for method 1 but not for method 2. For both experiments we varied the masses on the end so we had a set of 5 different masses and 5 different accelerations. We used this data to find the mass of the car we accelerated. We measured the true mass afterwards which was 40 grams. Using method 1, all five values for the mass were between 130-260 grams! Using method 2 they were between 25-51 grams. Why is method 1 so awful?

## Homework Equations

v^2 - u^2 = 2as

## The Attempt at a Solution

The only thing I can think of is that there is a bigger distance for drag to slow down the car in method 1? Or maybe the length of the card in method 1 (2cm) is too big to give an accurate value for the final velocity which we should try to get as close to an instantaneous value as possible? This is all I can think of. The cars did accelerate very nicely and smoothly in both methods so I cannot see why method 1 gives such bad results. Here is one set of results for method 1 and 2:

Method 1:

Distance from car to light gate ('s') = 20cm

Length of card = 2cm

Time at light gate = 0.021s

Final velocity = 0.95 m/s

Acceleration = 0.95^2 / 0.4 = 2.26

Mass on hanger = 50g = 0.49N

Mass of car = 0.49/2.26 = 216g (true mass in both was 40g)

Method 2:

Length of card = 8cm

Distance ('s') = 8cm (as started right at the beam)

Time at light gate: 0.137s

Average velocity = 0.08/0.137 = 0.58 m/s

Final velocity = 0.58 x 2 = 1.16 m/s

Acceleration = 1.16^2 / 0.08 = 16.82

Mass on hanger = 50g = 0.49N

Mass of car = 0.49/16.82 = 29g (true mass in both was 40g)

As you can see method one gives a much smaller acceleration even though the force etc is the same as method 2.

Thanks for any help