Impulse and Momentum: Guided Inquiry

Objectives:

- Measure a cart's change in momentum and compare it to the impulse it receives 

- Compare average and peak forces in impulses 

Key Terms:

- Impulse

- Momentum

- Force

- Velocity

- Average

Pre-Lab Discussion:

As discovered in the previous Momentum and Collisions Lab, we have learned that collisions are composed of a beginning, middle, and end. This lab deals with the impulse-momentum theorem, which relates and objects impulse: (force/time) to the change in momentum: (mass*change in velocity). In this lab, we will prove that an object's change in momentum is equal to its impulse. 

Procedure: 

Results:

In the following graphs, we found the force, velocity, and position (m)

Elastic 1: Beginning

Elastic 1: Middle 

Elastic 1: End 

Elastic 2: Beginning

Elastic 2: Middle

Elastic 2: End 

Data Table:

This graph measures the final velocity, initial velocity, average force, duration (s), and the calculated impulse, found by finding the average force/time. 

When we calculate the momentum of the car...

Knowing that Mass of cart = 0.51 kg.

Elastic 1: mass * velocity = (0.51 kg)(1.4957) = 0.764, which is about equal to the value we found for impulse (0.740).

Elastic 2: mass * velocity = (0.51)(2.394) = 1.223, which is about equal to the value we found for impulse (1.16).

Takeaways:

By calculating the impulse and momentum of the trials, it is simple to see how the two are equal, providing the impulse-momentum theorem. The numbers may slightly be off due to friction and/or repositioning of equipment in between trials. 

Momentum and Collision

Objectives:

• To investigate and calculate momentum

Key Terms:

• displacement
• velocity
• momentum
• friction
• collision

Pre Lab Discussion:

What is momentum and how is it calculated?

Momentum can be defined as "mass in motion", or the quantity of motion an object has. All objects have motion so, if they are in motion, they had momentum. Momentum can be calculated with the formula: m(mass) * v(velocity) = P(momentum)

Here's the video that we used (Mr. Eschelbacher's new hit single: Momentum & Collisions Lab ft. Vernier)

https://www.youtube.com/watch?v=3VyBnJRSzZo

Materials:

• Two Vernier cars
• Car track
• LabQuest
• Two motion detectors

Trials and Graphs:

TWO COLLIDING

Beginning 

During 

End

PERCENT DIFFERENCE: 

ONE AT REST, ONE IN MOTION 

ONE AT REST, ONE IN MOTION: VELCRO

Analysis:

Graph 1: 

This graph analyzes the velocity of the cars before they collide. We know the mass of the cars (0.5098 kg) and the velocities before the crash. With this, we can calculate their momentum: 

Car 1: m*v = (0.5098 kg) * (.3462 m/s) = 0.1765 kg*m/s

Car 2: m*v = (0.5098 kg) * (-0.3583 m/s) = -0.1827 kg*m/s

Net Momentum: P1+P2= -0.0062 kg*m/s

Total Momentum: |P1+P2| = 0.3592 kg*m/s

Graph 2:

Collision

Car 1: m*v = (0.5098 kg) * (-0.0415 m/s) = -0.0212 kg*m/s

Car 2: m*v = (0.5098 kg) * (.1239 m/s) = 0.0632 kg*m/s

Net Momentum: P1+P2= 0.0042 kg*m/s

Total Momentum: |P1+P2| = 0.0844 kg*m/s

Graph 3:

End of collision. This data depicts the momentum lost due to friction. Friction slows the velocities of the cars, therefore changing the momentum. 

Car 1: m*v = (0.5098 kg) * (-0.2469 m/s) = -0.1259 kg*m/s

Car 2: m*v = (0.5098 kg) * (0.2136 m/s) = 0.1089 kg*m/s

Net Momentum: P1+P2= -0.017 kg*m/s

Total Momentum: |P1+P2| = 0.2348 kg*m/s

Graph 4:

Graph four depicts the transfer of momentum from the moving cart to the stationary cart. The velocity of the first cart is zero and the velocity of the second cart equals the magnitude of the first cart prior to the collision. 

Graph 5:

In graph five, due to the Velcro on the carts, the two carts collide and essentially become one entire mass, meaning they share the same velocity after the collision. Though the velocity may be reduced by half, it is simply because the mass has doubled (0.5098 kg * 2) in the collision. Momentum is still conserved. 

Overall Analysis:

This lab has shown us the beginning, middle, and after aspects of a collision. With friction taken in to account, is it clear that momentum is a conservative force and can be transferred between two objects. Momentum is, again, the quantity of motion an object has and can be calculated by multiplying the mass by the velocity. This humorous gif explains how momentum changes:

Energy of a Tossed Ball

Objectives: 

Key Terms

- potential energy

- kinetic energy

- work

- force

- law of conservation of energy

Pre Lab Discussion

Materials

- Vernier Motion Detector

- 0.4029 kg ball

- LabQuest app

Procedure 

1. Place motion detector on the floor

2. Hold ball approximately one meter above the detector

3. Throw ball up above motion detector, make sure the detector doesn't catch your hands

4. Catch ball before it hits the motion detector

5. Analyze graphs 

Graphs:

How do these graphs represent the concept of the Law of Conservation of Energy?

These graphs represent the transformation of energy throughout the experiment and how the two components, kinetic and potential energy, come together to form the total energy (minus friction)

Analysis:

In this lab, we discussed...

Potential Energy:

     How to find it:

    Ball application: The potential energy of the ball is determined by its position, rather than its motion. 

     When the ball is thrown up, it will reach a maximum height based on how much kinetic energy it.

     has. At this point, all energy is potential. As the ball falls, potential energy turns in to kinetic. 

Kinetic Energy: 

     How to find it:

     Ball application: The kinetic energy of the ball is determined by its motion. When the ball is thrown 

     up, the ball will travel based on the amoun of kinetic energy. Once at the top of its path, the 

     kinetic energy is zero. The kinetic energy will then increase as the ball travels back down. 

How do these relate to total energy? What concept does this lab cover? 

The total energy of a system is calculate by adding kinetic energy, potential energy, and non conservative forces together (see graph above) This lab covers the concept of the Law of Conservation of Energy, which states that the energy in a system remains constant. Energy cannot be created or destroyed, but can be transformed in to different forms. In this lab, we saw the energy transform to potential and kinetic energy. Additionally, in this system, energy was "lost" due to friction.