13-Oct.-14: Impulse and Momentum

Purpose:

To verify the Impulse-Momentum Theorem with an elastic and inelastic collision between two masses.

Impulse Momentum Theorem - The change in momentum of a particle during a time interval equals the impulse of the net force that acts on the particle during that interval.

J = Δp

F•t = mΔv

Apparatus:

Equipment -
A rolling cart* - with a mass of 435-g and one cart fixed to a pole
a track - to guide the rolling cart into a collision,
a motion sensor - to find the velocity of the rolling cart,
a force sensor* - resting on the rolling cart to measure the force of the impact,
some clay - to create an inelastic collision in which the masses "stick"
a nail - attached to the rolling cart to penetrate the clay.
a clamp - to secure the clay in the desired position.
a known mass - 500 grams to rest on the rolling to do the experiment with a "different mass."

*combined mass of cart and sensor: 435-g

  

  





Experiment:

To do before the experiment:

• Leveling out the track - this required stacking sheet of paper beneath the track.
• Calibrating the force sensor -  accomplished by using the program's calibration option and hanging a known mass to tell the program how much mass it is experiencing.
• Adjustments for accurate data - We fixed the force sensor to the blue cart in a horizontal position by screwing the sensor to a metal plate that had been previously secured to the cart. we then needed to zero the sensor, which was done through the sensor's computer program.
• Adjusting the motion sensor - We switched the sensor into its "narrow beam" mode for our experiment and ensured that the beam was point in the direction of our cart, parallel to the track.
• Setting the amount of collections - We set the motion sensor to 50 measurements per second.

There were three parts to this experiment,

 A) An elastic collision

 B) an elastic collision with a different mass

 C) an inelastic collision

We note that, in this case, the velocity of the fixed mass is always zero - which leads us to the fact that its change in momentum is also zero.

PART A - Elastic Collision:

1. We gave the rolling cart an initial push.
2. The cart collided with a fixed mass and bounce back toward its origin.
3. During this collision, the motion sensor created a position-vs-time graph, which was then used to calculate the carts velocity.
4. The force sensor simultaneously recorded the force of the impact and the time duration of the impact.

Sensor data:
m_cart = 435-g

V_initial = 0.260-m/s

V_final = -0.223-m/s 

Calculating the change in momentum:

PART B - Elastic Collision #2:

1. We placed a 500 gram mass onto the cart.
2. We gave the rolling cart an initial push.
3. The cart collided and reacted just as it did in part A.
4. The motion sensor gave us new data for velocity.
5. The force sensor gave us new data for the force and time.

Sensor data:
m_cart = 935-g

V_initial = 0.337-m/s

V_final = -0.246-m/s

Calculating the change in momentum:

PART C - Inelastic Collision:

1. We attached a nail with its pointed end directed in the same direction as the carts motion. The nail was secured to the force sensor's "sensor point" using some tape.
2. We gave the cart an initial push
3. The cart, now with a nail, collided into a ball of clay without bounce back.
4. The motion sensor gave us an initial velocity only - the clay stopped the cart.
5. The force sensor gave us new data for the force and time.

Sensor data:
m_cart = 435-g

V_initial = 0.728-m/s

V_final = 0-m/s

Calculating the change in momentum:

Integrating the values for force that our sensor recorded gives us a value for the impulse of the collision.

PART A:

J = -0.2405-N•s

Calculated Δp = -0.210-N•s

PART B:

J = -0.7538-N•s

Calculated Δp = -0.562-N•s

PART C:

J = -0.2779-N•s

Calculated Δp = -0.317-N•s

Conclusion:

The Impulse data and the change in momentum we calculate, with some uncertainty, are about equal.

This verifies the Impulse momentum theorem which states: J = Δp

A Great Day for Physics.

(10/20/14, 7:17am)