Physics Education:Impulse and Momentum.

The following is a great example of using a data logger to do a physics experiment, which would otherwise be very difficult to achieve. It involves the use of two sensors – a photo gate and a force sensor. We will attempt to show that the change in momentum during a collision is equal to the impulse during the collision. We will determine the impulse by finding the area under the force vs time curve. Please read on ……
This experiment was conducted using the Ezilog USB data logger.

Aim:

To investigate the relationship between impulse and momentum.

Theory:

To change an object's motion we need to apply a force for a period of time.  This quantity of force x time is known as impulse.  For an object experiencing a constant force we can find an equation for impulse by using Newton's Second law (F=ma) and the equations of motion as follows

Where F is the force acting on the body, DP is the change in momentum, m is the mass of the body and v1, v2 are the velocities of the body before and after impulse.  Note that momentum, force, acceleration and velocity are all vector quantities and so impulse has the same direction as the force that produced it.

In this experiment a trolley collides with a force sensor and the change in momentum is compared to the impulse.

The impulse is found by calculating the area under the force vs time graph (the integral of the force) measured by the sensor.

A photo gate is used to measure the velocities of the trolley before and after the collision.

Equipment: Force and photo gate sensors connected to an interface or data logger, linear airtrack and glider (or ramp and dynamics trolley) and a computer.


Data Logger Setup:
  Input 1: Photo Gate
  Input 2: Force Sensor
  Samples: 50,000
  Rate: 10,000 samples/ Sec


Method:

I. Setup the equipment as shown

II. Connect the data logger or interface to the computer and start the software.

III. Place the glider or trolley on the track as shown in the diagram with a glider flag (10 cm).

IV. Start logging and immediately push the trolley towards the force sensor. Make sure that the initial push is strong enough: after the collision the trolley must pass back through the photo-gate so that its velocity after the collision can be calculated.

V. If you are using the Ezilog USB set the sample rate to 50 samples/s and sample time to 2 s. Select the Run button and after the graph appears release the glider. Use the cursors to measure the time for the flag to break the first gate and the second gate, or use the Convert to Times button to automate this for you.

VI. Measure the mass of the trolley. Record this value.


Analysis:

1. Calculate the impulse:
Display a graph of force vs time.  The area under the curve is the Impulse.

2. Calculate the change in momentum:
In the graph created by the photo gate identify the times when the light was blocked by the glider flag.

dt1 the first time interval during which the light was blocked by the glider flag. Record dt1 .
Repeat the above step to measure dt2 the second time interval when the light was blocked. Record dt2 .

Use the length of the glider flagand the time intervals dt1,dt2 to calculate the velocities of the trolley before and after the impulse:

Note that as velocity is a vector a negative sign for v2   indicates opposite direction to v1.

Multiply the velocities by the mass m to calculate the momentum before and after the impulse:

Calculate the difference in momentum:

Record this value.

Discussion:

Compare the amount of impulse to the change in momentum

1. Is the change in momentum equal to the impulse?

2. Would the impulse be different if the mass of the glider was changed? Explain your answer.

3. Discuss any sources of error that may have affected your results.