Impulse and momentum

Everyday, objects or people collide, sometimes by accident and sometimes on purpose.  In a collision, the momentum of each colliding partner changes in a very short time interval.  Each collision partner receives an impulse.  A momentum change or impulse requires a force.  For the momentum to change by an amount ∆p a force F must act for a time ∆t such that ∆p = F∆t.  The shorter the collision time, the larger are the forces acting on the collision partners.

Many safety devices, such as seat belts, airbags, crumple zones, etc, are standard equipment on modern cars.  The purpose of these devices is to increase the time it takes for a passenger's velocity to change by a large amount in the event of a collision.  In sports, pads are designed to increase the collision time and therefore reduce the force acting on a player during a collision which changes the player's momentum by an amount ∆p.  If a pad doubles the collision time, it decreases the force by a factor of 2.

In this session you will investigate the relationship between force, collision time and impulse, and you will also examine momentum conservation in elastic and inelastic collisions.

Equipment needed:

• Track
• Two Smart Carts
• Electronic balance

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  This log will form the basis of your lab report.

Experiment 1

A cart rolls down an inclined track and collides with a wood block at the end of the track.  The wood block is padded with another block made of metal, wood, or foam, for four different experimental runs.  Since the car is released from rest at the same position on the track every time, its speed when it makes contact with the block is approximately the same every time.  An acceleration sensor measures the acceleration as a function of time during the collision and a computer displays the output of the acceleration sensor.  The magnitude of the interaction force F is proportional to the acceleration, F = ma.  The output of the acceleration sensor under different collision conditions is shown below.

The cart collides with an aluminum block.  The magnitude of the maximum measured acceleration is ~22 m/s².  The collision lasts for ~0.09 s

  

The cart collides with a wood block.  The magnitude of the maximum  measured acceleration is ~21 m/s².  The collision lasts for ~0.1 s.

  

The cart collides with a high-density foam block.  The magnitude of the maximum measured acceleration is ~17 m/s².  The collision lasts for ~0.12 s.

  

The cart collides with another foam block.  This type of foam is used for packing fragile materials for shipping.  The magnitude of the maximum measured acceleration is ~14 m/s².  The collision lasts for ~0.15 s.

  

The mass of the cart with the attached acceleration sensor is 555 g. 
Fill in the table below.

In order to estimate the impulse during the collision, you need to find the area under the peak in the acceleration versus time graph (units m/s² * s = m/s) and then multiply by the mass of the cart.

• Paste the table into your log.
• Compare the impulse using the four different bumper blocks.  Is this what you expected?   What significance might this have in a real car collision?  Explain.
• Compare maximum forces and the interaction times for the four different collisions.  Is this what you expected?  What significance might this have in a real car collision?  Explain!

Experiment 2

You will now investigate elastic and inelastic collisions between two carts on a track.  In elastic collisions, the carts bounce off each other and in inelastic collisions they stick together.  The momentum of an object is the product of its mass and its velocity, p = mv.  If external forces acting in the horizontal direction (such as friction) can be ignored in the experiments of this lab, then the sum of the momenta of the two carts prior to a collision should be the same as the sum of the momenta of the carts after the collision.  You will explore the implication of momentum conservation under various collision conditions.

Procedure:

• You have a red and a blue Smart Cart.  Determine the mass of your carts using the electronic balance and record it.
• Turn on both Smart Carts.  In Capstone, click Hardware Setup and add both carts.  Choose to measure Position and Acceleration for both carts.
• Create a Graph Display by dragging the Graph icon onto the main display.  Add an additional plot to your graph.  For the x-axis of both plots choose time.  For the y-axis of one plot choose Velocity Red (m/s) and for the other plot choose Velocity, Blue (m/s).
• Place the carts on the track.
• Let the two carts collide with each other while recording the collision.  Record at least 3 elastic collisions with different initial conditions and 3 perfectly inelastic collisions with different initial conditions.  Make sure the carts do not all off the track.
• For the elastic collisions let the magnetic bumpers of the carts face each other.
  
• For the perfectly inelastic collisions let the Velcro patches on the carts face each other.
  
• Use the coordinate tool to determine the velocity of each cart just before and just after the collision.  (This minimizes changes to the velocities due to the external frictional force.) 
• Determine the momentum of each cart and the total momentum of both carts just before and just after the collision.  Enter these values into the table below.  Make sure that you enter them with the right sign.  (You have to keep track of the sign yourself.  Choose which direction you call positive.)
   

  	before the collision			after the collision
  	pcart 1	pcart 2	ptotal	pcart 1	pcart 2	ptotal
  Elastic 1
  Elastic 2
  Elastic 3
  Inelastic 1
  Inelastic 1
  Inelastic 1

Discuss your results!

• Paste the table into your log.
• Does the total momentum of the carts change in the elastic collision experiments?  Refer to your data.
• Does the total momentum of the carts change in the inelastic collision experiment?  Refer to your data.
• Did your experiments reproduce the expected results?  If not, speculate on the reasons for any discrepancies.

Experiment 3

Discuss the following situation with your partners and record your predictions.
Assume you place a wide textbook on the floor and stand on it.  Then you jump off the book onto the floor two different times.  The first time you land normally, allowing your knees to bend.  The second time you land stiff-legged, not allowing your knees to bend.  Will these jumps feel different to you?  Explain!

Now make some measurements using the acceleration sensor in the Smart Cart.  Choose one of the carts.

• In Capstone add a new page and the Graph icon onto the display.
  For the x axis choose time.  For the y axis of one plot choose Acceleration - x (m/s²) for your chosen cart.
• Have the jumper stand on a stack of two textbooks.  The jumper should hold the Smart Cart vertically against their body, with the arrow pointing straight down.
• Once the jumper is completely stationary, zero the acceleration sensor.  Then start collecting data.  The initial acceleration should be zero.  After about 1 s, have the jumper scoot off of the books without jumping up any more than necessary and land on the floor while keeping the knees straight and stiff.
• Identify the different regions of the plot.  When was the jumper accelerating upward at the beginning of the jump, when was the jumper accelerating downward because of gravity, when was the jumper accelerating upward again because of the contact with the floor?
• Repeat this at least twice to insure that the data is repeatable and that you have a good data set.
• Record the maximum acceleration of the jumper during the landing and the interaction time with the floor in the table below. 
• Repeat the experiment, but this time have the jumper land as gently as possible, allowing the knees to bend.
• Record the maximum acceleration of the jumper during the landing and the interaction time with the floor in the table below.
• Estimate the jumper's mass and the maximum force and the impulse for both types of jump.

Discuss your results with your partner.  Compare and contrast the maximum forces, interaction times, and the total impulses given to the jumper in the two different kinds of landings.  Relate these results to the observations in experiment 1.

Convert your log into a lab report.

Name:
E-mail address:

Laboratory 5 Report

• In one or two sentences, state the goal of this lab.
• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots.
• Add a reflection at the end of your report in a short essay format.

Save your Word document (your name_lab5.docx), go to Canvas, Assignments, Lab 5, and submit your document.