# Work

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 velocity.

(Hint: For parts 1 to 4 above, graph the force vs. time.)

5. Answer the following question. A 4 kg ball moving at 3 m/s bounces off a wall and is observed to be moving at 3 m/s in the opposite direction. What was the total impulse on the ball?

Apparatus

Pasco 750 Interface

1.2 meter dynamics track

Force sensor attached to the Force sensor bracket with attachments (hook, rigid spring, less rigid spring, rubber bumper, magnetic bumper)

Dynamic cart (without plunger) and mass block

Motion sensor (set on "narrow beam')

Pulley and clamp

Large table clamp

Mass holder and 500 grams of masses

Thread

Mass block to elevate track

Detailed Procedure and Analysis for the Impulse – Momentum Experiment

I. Program Selection and Preparation

Turn on the Pasco Science Workshop Interface, then the computer, and login.

Launch the Data Studio program, choose Create Experiment, select Force Sensor, and Motion Sensor.

Connect the Force Sensor lead to Channel A on the Science Workshop Interface box. Double click on the Force Sensor. In the Sensor Properties window, choose General, then select Fast Force Changes, and increase the sample rate to 1000 Hz. Under Measurement, de-select all choices and select Force (only Force should be checked). Click OK.

Connect the yellow motion sensor plug into digital channel 1, and the other plug into channel 2. Double click on the Motion Sensor. In the Sensor Properties window, choose Measurement, then de-select Position and Acceleration, so only Velocity is selected. Choose Motion Sensor,and set the trigger rate to 100. Click OK.

To set up the graphs, drag the Force Sensor from the Data window to the Graph in the Displays window.

Click and drag the Motion Sensor from the Data Window to the graph set up in the previous step. Two graphs should appear in the same window.

To align the time origins of the graphs, click on the button at the top of the...

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