PHYS 1405 – Conceptual Physics I

Conservation of Momentum

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

Pasco Dynamics Track                                     LabPro

1 x collision cart (w/o plunger)                          Laptop

      and (w/o force probe adapter)                   

1 x dynamics cart (w/ plunger)                          2 x Photogates

Masking tape                                                    2 x 2.5 cm flags for air track cart

 

Introduction

      In this lab we will explore conservation of momentum in a system of objects.  Remember that we define momentum as mass × velocity or in symbols p = m×v.

 

Q1.  Is momentum a vector or a scalar quantity (i.e. does direction matter)?

 

 

Q2.  If a 0.50 kg cart moves to the right at 3.0 m/s, what is its momentum?  Include units.

 

 

Q3.  If the same cart moves to the left at 3.0 m/s, how is your answer different than in Q2?

 

 

Momentum is an important quantity in Physics because under certain conditions the total amount of momentum in a system doesn’t change.

 

Q4.  Define a system.

 

 

      In this experiment we will collide two carts on the Pasco Dynamics track.  We will use a probe called a photogate to measure the speed of each of the carts before and after the collision.  We will then compare the total momentum of the system before and after the collision.

 

Q5.  Describe the system that we are studying in this experiment.  (Note there is more than one correct answer to this question, but there is a best answer.)

 

 

 

 

Procedure

1.  Setup

      Make sure that the Pasco track is level.  Place a cart on it and see of it rolls.  If it does, then adjust the foot so that when you place a cart on the track it doesn’t roll.

 

      On the side of the cart, place a piece masking tape to label the carts.  Label the cart with the plunger as 1 and the cart without as 2.  Use the electronic balance to measure the mass of each of the carts and record below.

 

Mass of cart 1:  m1 = ______________ kg

Mass of cart 2:  m2 = ______________ kg

 

      Make sure that the LabPro and laptop have the AC adapters connected and plugged in.  Connect the LabPro to the laptop using the provided USB cable, and connect the photogates to DIG/SONIC 1 and DIG/SONIC 2 on the LabPro.

 

2.  Setup the Photogates.

 

      Note which of the photogates is plugged into DIG/SONIC 1.  For the photogates to work correctly, you always want a cart to pass through that photogate first.  If you look at the photogates you will observe two small holes opposite each other.  In one hole there is a light source and in the other there is a light detector.  When objects pass between the holes, they block the light getting to the detector.  The computer can time how long the light is blocked and if it knows how long the object is can use v = d/t to calculate how fast the object is moving.  Place a flag into the hole on the top of each of the carts so that the flag passes with its width facing the photogate.  Position the height of the photogates so that the as the cart passes through them the flag will block the photogate.

      Measure the width of the flags on each cart.

 

Width of flag 1:  d1 = ____________ m

Width of flag 2:  d2 = ____________ m

 

Start up LoggerPro 3.1.  Click OK to close the Tip box and then click on the open file and then double click on the Probes and Sensors folder, then the Photogates folder and then double click on the file titled 2 gate timing.

      Click on the LoggerPro button.  A window (called the sensor set-up window) like the following should appear.

 

Right click on the Photogate icon under DIG/SONIC 1 and choose Set Distance or Length   The following window will appear

 

 

Choose User Defined from the drop down box and then enter the width of the flag in meters and then click on OK.

      Repeat for the photogate icon under DIG/SONIC 2, then close the sensor set-up window.

 

Data Acquisition

When you hit the collect button, the computer will wait for a cart to pass through photogate 1.  It will measure the velocity of a cart each time it passes through a photogate. 

 

Collision 1

Position the cart without the plunger between the two photogates.  Hit the collect button.  Once the computer is ready, start the cart with the plunger extended so that it passes through photogate 1 and collides with the other cart via the plunger.  The computer should record the velocity of the first cart before the collision and the second cart after.

 

Q6.  Next to each other, draw two pictures showing both carts - one before the collision and the other just after.  Label the carts with their velocities before and after the collisions.  (For simplicity, hereafter I will refer to a sketch like this as before and after sketch.)

 

 

 

 

 

 

Q7.  What was the velocity of cart 2 before the collision?

 

 

Q8.  What was the velocity of cart 1 after the collision?

 

 

The total momentum of the system we define as the sum (taking into account direction) of the individual momentums.

 

Q9.  Fill in the table below with the details before the collision.  Note a subscript of b refers to before the collision and t refers to total.  Include units.

 

m1

v1b

p1b = m1v1b

m2

v2b

P2b = m2v2b

ptb = p1b + p2b

 

 

 

 

 

 

 

 

Q10.  Fill in the table below with the details after the collision.  Note a subscript of a refers to after the collision and t refers to total.  Include units.

 

m1

v1a

p1a = m1v1a

m2

v2a

p2a = m2v2a

pta = p1a + p2a

 

 

 

 

 

 

 

 

 

Q11.  Did the total momentum of the system change appreciably after the collision compared to before?  In other words, compare the last columns of the two tables you have just completed.

 

 

 

Q12.  It may have changed a little bit.  What forces might have affected the momentum of the carts.

 

 

 

 

Q13.  If you define your system as the two carts, then is friction an internal force (between the carts) or external force (between the carts and something else)?  Explain.


Q14.  If you could eliminate friction do you think the total momentum of the system would change from before to after the collision?

 

 

 

Collision 2

Push the plunger in completely until it clicks.  Position the carts between the photogate with the cart with the plunger nearer to photogate 1 than the other cart is to photogate 2.   The plunger should be between the two carts.

      Hit the collect button.  Once the computer is ready, push down on the button on top of the cart with the plunger so that the plunger releases. The computer should record the velocity of each cart after the collision.

 

Q15.  Next to each other, draw two pictures showing both carts - one before the collision and the other just after.  Label the carts with their velocities before and after the collisions.  (For simplicity, hereafter I will refer to a sketch like this as before and after sketch.)

 

 

 

 

 

 

Q16.  What was the velocity of cart 1 before the collision?

 

 

Q17.  What was the velocity of cart 2 before the collision?

 

 

The total momentum of the system we define as the sum (taking into account direction) of the individual momentums.

 

Q18.  Fill in the table below with the details before the collision.  Note a subscript of b refers to before the collision and t refers to total.  Include units.

 

m1

v1b

p1b = m1v1b

m2

v2b

P2b = m2v2b

ptb = p1b + p2b

 

 

 

 

 

 

 

 

Q19.  Fill in the table below with the details after the collision.  Note a subscript of a refers to after the collision and t refers to total.  Include units.  Take into account the direction of each cart after the collision.

 

m1

v1a

p1a = m1v1a

m2

v2a

P2a = m2v2a

pta = p1a + p2a

 

 

 

 

 

 

 

 

 

Q20.  Did the total momentum of the system change appreciably after the collision compared to before?  In other words, compare the last columns of the two tables you have just completed.

 

 

 

Q21.  If you could eliminate friction do you think the total momentum of the system would change from before to after the collision?

 

Collision 3

Push the plunger completely in until it clicks.  Experiment with the orientation of the two carts with respect to each other.  In one orientation, you will find that the two carts repel each other and in the other, you will find that they attract each other.  Position the carts so that they attract each other.  Hit the collect button and gently push cart 1 so that it passes through photogate 1 and then collides with cart 2.

 

Q22.  Next to each other, draw two pictures showing both carts - one before the collision and the other just after.  Label the carts with their velocities before and after the collisions.  (For simplicity, hereafter I will refer to a sketch like this as before and after sketch.)

 

 

 

 

 

 

 

Q23.  What was the velocity of cart 2 before the collision?

 

 

Q24.  How is this collision different from the previous two?

 

The total momentum of the system we define as the sum (taking into account direction) of the individual momentums.

 

Q25.  Fill in the table below with the details before the collision.  Note a subscript of b refers to before the collision and t refers to total.  Include units.

 

m1

v1b

p1b = m1v1b

m2

v2b

p1b = m1v1b

ptb = p1b + p2b

 

 

 

 

 

 

 

 

Q26.  Fill in the table below with the details after the collision.  Note a subscript of a refers to after the collision and t refers to total.  Include units.

 

m1

m2

va

pta = (m1 + m2) va

 

 

 

 

 

 

Q27.  Did the total momentum of the system change appreciably after the collision compared to before?  In other words, compare the last columns of the two tables you have just completed.

 

 

 

Q28.  If you could eliminate friction do you think the total momentum of the system would change from before to after the collision?

 

 

Q29.  At this point, we have examined three different collisions.  In each did the momentum change appreciably before and after the collision?

 

Q30.  Was friction force an internal or an external force?

 

Q31.  If you could eliminate the externals forces like friction, would the momentum have changed before and after the collision?

 

When a physical quantity remains constant we say that it is conserved.

 

Q32.  Complete the following statement.  If the ______________ forces on a system can be ignored, then the total momentum of the system is __________________.