As we’ve seen and used, gravity pulls things down to the ground. It causes what physicists call uniform acceleration. This means the object accelerates the same amount each second or unit of time.

Another way of saying this is that the object going speed in meters/second [m/s] per second moving [1/s] or acceleration [a] is m/s^{2}.

In another Project we found gravitational acceleration is the same for large or small masses. Air can slow the object down due to friction. Remember the paper airplanes and the fan?

In this Project we will try to measure gravitational acceleration in two ways. This will require doing some math. Both ways require the stopwatch start when the ball is released so the ball starts from rest or velocity equal to zero.

**Question:** What is the value of gravitational acceleration?

**Materials:**

Ramp

Ball

Meter stick

Stopwatch

**Procedure:**

This is the hardest way. You drop the ball while timing how long it falls. The farther it falls, the easier it is to start and stop the stopwatch as the ball hits the ground. You must know exactly how far in meters the ball falls.

Mark the height you will drop the ball from.

Measure the distance from the floor to the mark in meters

Stand with the ball in one hand and the stopwatch in the other hand or have a friend help

Start the stopwatch at the same time you drop the ball

Stop the stopwatch when the ball hits the floor

Do this at least three times

If you remember other Projects, running the ball down the ramp makes it take longer to get to the ground. This makes timing the ball easier. You must know exactly how far the ball rolls down the ramp to the ground.

Set up your ramp

I used a ramp two meters long propped and taped to a chair.

Mark your starting line on the ramp

Measure the distance from your mark to the floor in meters

Hold the ball in one hand at the starting line and the stopwatch in your other hand or have a friend help

Let the ball go at the same time you start the stopwatch

Stop the stopwatch when the ball reaches the floor

Do this at least three times

**Observations:**

Time for the ball to fall:

1st:

2nd:

3rd:

Time for the ball to go down the ramp

1st:

2nd:

3rd:

**Analysis:**

Find the average time for the ball to fall

Find the average time for the ball to go down the ramp

[Remember you add up all the times then divide by the number of times to find the average.]

To calculate the gravitational acceleration we will use the formula: a = v/t = d/t/t

The a is acceleration.

The v is the velocity of the ball when it hits the floor. You don’t know the velocity but velocity is distance divided by time and you do know these.

The d is the distance the ball travels in meters.

The t is the time in seconds.

Calculate the acceleration by dividing the distance in meters by the time in seconds then the quotient by the time in seconds again to get the acceleration for one second.

Use the same formula and the distance down the ramp and time for the ramp to calculate the acceleration down the ramp.

**Conclusions:**

Why is measuring the distance so important?

Why is measuring the time accurately so important?

Why do you use an average time?

Would it be better to have more times to use to get your average time? Why do you think so?

Why should the acceleration you calculate for the two methods of timing be about the same?

Were your two times the same? Why do you think this was the case?

The gravitational acceleration is thought to be 9.8 m/s^{2}. Were your calculated accelerations close to this? Why do you think this was the case?

**What I Found Out**

This project seems so easy to do. I measured my ramp carefully so it was 2 m long. It was set up with a steep slope.

When I tried to time the ball going down the ramp, I had problems. It was easy to start the ball and the stopwatch at the same time. It wasn’t so easy to stop the stopwatch when the ball got to the floor.

Dropping the ball was even harder. Again it was easy to start the ball and the stopwatch at the same time. I’m positive the ball bounced before I got the stopwatch stopped.

This is definitely a project requiring two people to do it well.

The formula required two measurements. One was the distance the ball went. Since this distance is divided by the square of the time, a little mistake in measuring the distance can make a big difference in the answer.

The time is squared or multiplied by itself. Any mistake in the time becomes very big.

I measured the time four times each way the ball went. The times were very similar for going down the ramp with a span of only .03 sec between the lowest and highest times.

The times for dropping the ball had a range of .1 sec between the lowest and highest time. The range of the squares would be .19 sec^{2} to .29 sec^{2}. That much difference would make a big change in the acceleration I calculated.

Using an average time smoothed out these extremes to give me a better time for my calculations.

The procedure said to use three time measurements. I chose to use four because my measurements were so different. If the three measurements had been more similar, I would have used only three.

I think the number of measurements you use depends on how similar they are.

When I calculated my accelerations I got 1.5 m/s^{2} for dropping the ball and 1.3 m/s^{2} for the ramp. Since the pull of gravity was the same for both methods, the acceleration should be about the same.

My calculated acceleration was very different from the accepted gravitational acceleration of 9.8 m/s^{2}, not even close. I am not sure why my values were so different.

One possibility is the time. It was very hard for me to get a good time even though my values were similar.

What I would like to do is repeat this project with someone to help me. I would make two other changes.

First I would lower the angle of the ramp so the ball would go down a little slower making timing it easier.

Second I would lengthen the distance to at least two meters dropping the ball. This would give a little more time to stop the stopwatch before the ball bounced.