Discussion

Impulse, momentum, and the impulse-momentum relationship are defined and discussed in the text. The momentum of an object with mass m and velocity [pic] is

[pic].

The impulse of a resultant force from time t1 to time t2 is When the force is plotted versus time, the impulse is the area under the curve between t1 and t2.

[pic]

The impulse-momentum relationship states that if an object with mass m is acted on by a force over the time interval from t1 to t2, the impulse is equal to the change in momentum:

[pic].

This can easily be derived from Newton’s second law

[pic].

Multiplying both sides of the equation by dt we obtain,

[pic].

Integrating from time t1 to time t2,

[pic].

In this experiment, a moving cart collides with a stationary “force sensor.” The force sensor measures the collision force as it varies with time throughout the collision. A motion sensor detects the position of the cart versus time, enabling its velocity to be calculated as a function of time. The computer graphs force versus time, and also the cart’s velocity versus time.

A statistics package is used to integrate the force versus time curve to obtain the impulse. In addition, the initial and final (maximum and minimum) velocities can be obtained, making it easy to calculate initial and final momentum, and test the impulse-momentum relation.

Pre-Lab Assignment

Complete the following problem, using the impulse-momentum relationship. A 4kg mass is initially moving in the x direction at 5 m/s. A force in the positive x direction acts on the mass for 7 seconds as follows: a. The force grows linearly from 0 to 8 Newtons in 2 seconds. b. The force stays constant at 8 Newtons for 3 seconds. c. The force decreases linearly to 0 in 2 seconds.

1. Calculate the initial momentum.

2. Calculate the total impulse.

3. Calculate the final momentum.

4. Calculate the final