**Lab Activity: Kinematics**

Before performing this lab please read the Lab Notebook requirements. Click here.*It is very important that, at the end of this experiment, you answer the questions regarding experimental error. Do not skip this section. Questions about experimental error will be a part of the AP* Physics C exam.*

**Goal**: Determine the validity of the kinematic equations for a marble or ball rolling down a ramp.

**Materials**:

1. A heavy marble (preferred) or a golf ball

2. Two long pieces of wood (preferably two meter sticks)

3. Books or a box of Kleenex

4. A ruler (preferably a meter stick)

5. A protractor (optional)

6. A stopwatch (or a cell phone with a stopwatch function... or you can use the virtual stopwatch at http://www.online-stopwatch.com/)

**Activity:** Set up a ramp system (2 pieces of wood set close enough together to create a grove-like track) as you see in the images below. If you are not using meter sticks to make the ramp, use the ruler to mark a line at the starting point and at 70 cm from the starting point. Using your protractor, measure the angle of the ramp (θ). If you don’t have a protractor, use your ruler to measure the height and length of the ramp to calculate the angle trigonometrically.

Now, using the stopwatch, measure the time it takes for the marble to roll 70 cm down the ramp. Make sure that you release the marble (from rest) at the exact instant you start the watch. Stop the watch the moment the 70 cm mark is reached. Record your measurement in a data table such as the one you see below. Repeat this procedure for 7 trials all at different angles. Don’t use angles less than 10 degrees or greater than 30 degrees.

**Data Table**:

Trial | Ramp Angle | Measured Time (s) | Calculated Time (s) | % difference |

1 | ||||

2 | ||||

3 | ||||

4 | ||||

5 | ||||

6 | ||||

7 |

**Analysis:** The acceleration that the marble undergoes is related to the gravitational acceleration that we discussed in the presentations. The magnitude of the acceleration of the marble on the ramp can be calculated by the following equation:

a = (5/7)gsinθ

where θ is the angle of the ramp and g = 9.8 m/s

^{2}

The derivation of this equation can be done using an analyis of force and Newton's Laws which are discussed in a future lesson.

*(Note: The acceleration would be a = gsinθ if the marble only slid down the ramp and did not roll. Because the rolling involves both linear movement down the ramp and rotation at the same time, the linear acceleration is diminished somewhat.)*

** Use this acceleration in the 2 ^{nd} kinematics equation to calculate the time it “should” take for the marble to roll 70 cm. Record your calculations for each angle you used in the lab.**

**Error Analysis:** Calculate the percent difference between your measured and calculated times (relative to the calculated time) for each trial using the following formula:

C = Calculated Time

M = Measured Time

% difference = [(M – C)/C] x 100%

Think about why there might be a difference between the measured times and the calculated times. Approximate the amount of error you judge to be a part of the distance determination that is used to calculate the time for the motion. For example, the distance in each trial should have been 70 cm, but what range of distances do you think was possible based on the experimental design? If you judge the possible error in that measurement to be about 1 cm, then the distance may have been as low as 69 cm and as high as 71 cm. Determine the amount of error this would mean for the calculation of time. Do the same analysis for the measurement of the angle. Which measurement, distance or angle, is most likely to be the greater contributor to error in the calculation of time for this lab?