When we release a cart at the top of an inclined ramp, we know the cart will roll down because of gravity. But what happens if we change the tilt of the ramp, or add weight to the cart? What parameters can we alter to change the results, and what does that tell us about gravity, friction, and the forces that act on the cart?

It's pretty easy to see that a cart sitting on a flat table isn't going anywhere. It's also easy to see that if you drop a cart down a vertical wall it's going to accelerate due to gravity at about 9.81 m/s². If we say that the flat table is a ramp with no tilt, and the wall is a ramp tilted to pi/2 radians (90 degrees), we can start to see that there might be a relationship between the acceleration of the cart and how far the surface it's on is tilted.

What about adding weight to the cart? Think about what causes the cart to roll down the ramp, and how adding mass might change that. You may be familiar with some famous experiments that could give us clues here as well. Let's form some hypotheses about how the cart will behave:

Now we're going to setup the equipment for our experiments. You should already have a cart and a ramp with sensors placed 1 meter apart. You'll need to be able to adjust the height of one end of the ramp. You can prop it up with a few books or something similar.

In each experiment you'll set the length and height of the ramp, and we'll use that to calculate the angle the ramp makes with the floor. Take a look at the image above to see how we're measuring length and height. The height is measured from the propped up end to the floor. The length is measured end to end.

To measure how fast the cart is moving, we need to know how long it is. Measure the cart as shown in the image above, and enter the length below.

In the next sections we'll use sensors to gather some data. Please plug in your Arduino if you haven't already and attach the IR sensor at the top of the ramp to pin 2. Then attach the IR sensor at the bottom of the ramp to pin 4.

First, prop up one end of your ramp with a few books or something similar. Then, enter the height and length of your ramp in centimeters. You can look back at the setup instructions to make sure you're using the correct measurements. The angle that your ramp makes with the table or floor will be calculated automatically using these measurements. Adjust the height by adding or removing books until the ramp angle is between 0.03 and 0.26 radians.

Next, for each row in the table below, we'll measure the velocity of the cart in two spots. Here's the procedure we'll follow:

1. Place the cart at the top of the track.
2. Add the mass for the next row in the table to the cart.
3. Click Record for that row and release the cart. Sensor Status will change to "Recording"
4. Catch the cart at the bottom of the ramp.
5. Sensor Status will change back to "Ready". Now you can record another row.

The sensors will record how fast the cart was moving when it passed each sensor, and the total time it took to travel between the sensors. We can use this information to calculate the average acceleration of the cart between the sensors and plot a graph of acceleration versus mass.

If you wait longer than about 5 seconds before triggering the first sensor, it will record a 0 and move to the next sensor. After 5 more seconds, this will also record a 0 and the sensors will reset. If this happens, just wait for the status to change back to "Ready" and try again.

In this section we'll change the ramp height but leave the mass of the cart alone. We need to increase the angle a little for each row in the table, but we want the ramp angle to stay between 0.03 and 0.26 radians. So start with just one book under the ramp and measure the height and length. Then adjust the height by adding or removing books until the angle is 0.03 radians or a little more.
The angle that your ramp makes with the table or floor will be calculated automatically using the height and length you enter, and they'll be stored in the table when you click record for a row.

Next, for each row in the table below, we'll measure the velocity of the cart in two spots. Here's the procedure we'll follow:

1. Adjust the height of the track and enter it in the Ramp Height block. The new ramp angle will be calculated automatically.
2. Place the cart at the top of the track.
3. Click Record for that row and release the cart. The current ramp angle will be recorded for you, and Sensor Status will change to "Recording"
4. Catch the cart at the bottom of the ramp.
5. Sensor Status will change back to "Ready". Now you can record another row.

The sensors will record how fast the cart was moving when it passed each sensor, and the total time it took to travel between the sensors. We can use this information to calculate the average acceleration of the cart between the sensors and plot a graph of acceleration versus angle.

We've just gathered data for different cart masses with a constant ramp angle and different ramp angles with a constant mass. This data can help us understand the relationship between mass, ramp angle, and acceleration.