Newton's Second Law; Mass-Acceleration Relationship with Dynamics Carts

D. James Chichester            Lincoln-Way High School
                               1801 East Lincoln Highway
                               New Lenox IL 60451
                               (815) 485-7600

Objectives:

Students will form their own hypothesis about the relationships between force, 
mass, and acceleration for their dynamics cart system.  First they will 
qualitatively evaluate a cart system, then collect actual data, then express the 
data in graphical format to visualize the relationships.  This mini-teach is  
geared for the high school physics student.  Minor adaptations can be used for  
lower grades.  CBL units can also be implemented for more advanced high school   
physics students. 

Materials Needed:

Classroom set:
2   different mass automobiles (van & car)
2   bathroom scales (cheap flat ones)
7   dynamics carts
7   table clamp pulleys
7   1.8 meter lengths of string
7   100 gram masses
28  1 kg masses
7   startwatches
7   dynamics cart stoppers
7   calculators

Strategy:

     The concepts of force, mass, and acceleration are reviewed with students
first.  Question: If I push on a car with a constant force, then push on a van 
with the same constant force, which will accelerate at a higher rate?  Let's try 
it! 
     Have two students push on a small car with bathroom scales under their 
hands against the bumpers.  Have them push straight ahead, trying to keep the 
scales at a constant force.  Students qualitatively measure the car's 
acceleration rate.  Now two students push on a mini-van with bathroom scales 
under their hands against the bumper.  Students again qualitatively measure the 
van's acceleration rate.  The teacher should be "secretly" calculating the 
actual acceleration rate of both vehicles using d = 1/2*a*t2. 
     Ask students to formulate their own conjectures about the relationship 
between mass and acceleration for objects being pushed or pulled.  Students will 
now complete the following lab. 

                 NEWTON'S 2ND LAW: MASS-ACCELERATION RELATIONSHIP
DIRECTIONS:
1. Assemble your dynamics cart system as follows, be certain cart does not hit 
pulley.  Connect string to cart and hang 100 gram mass over edge of pulley. 
Place wood stopper block in front of pulley to stop the cart from smashing it.  
Pull car back on table top until hanging mass is just below pulley, mark the 
front of the cart's position on the table with tape.  Let cart travel one meter 
in a straight line towards the pulley, mark one meter traveled position on the 
table.  Be certain the hanging mass still has not touched the ground when cart 
is at the one meter position. 

2. Your cart will be allowed to travel one meter over your table surface.  The 
cart needs to travel the full meter before the attached hanging mass hits the 
ground.

3. With your startwatch, find the time from the release of the cart to the point 
that the cart has traveled exactly one meter.  Time each trial three times for 
each amount of mass added to the cart. 

4. Average your three time trials for each amount of mass added to the cart, 
then calculate the average acceleration rate of your cart by using acceleration 
= 1/(time)2. 

5. Complete the following data table with your group, then be prepared to graph 
your results.  Do you notice anything about the acceleration rate of the 
dynamics cart? 

                 Data Table:

Hanging Mass   Cart+Mass   Time 1   Time 2   Time 3   Avg Time    Acc (1/t2)
-----------------------------------------------------------------------------
 100 grams       cart
 100 grams     cart + 1kg
 100 grams     cart + 2kg
 100 grams     cart + 3kg
 100 grams     cart + 4kg

 6. After individual groups complete data table, they shall complete a graph of 
 acceleration vs. cart's mass on 2ft x 2ft dry erase boards.  

 7. Look for similarities and differences between the groups graphs, making 
 changes if necessary.

 8. From your table what can you say about mass-acceleration relationship?

 9. From your graph what can you say about mass-acceleration relationship?

10. Does the graph and table have a similar relationship for mass-acceleration?

11. Does the graph and table support or change your original conjecture?

Discussion:
Ok, Newton's 2nd Law says that the net force on an object is equal to the 
objects mass times the objects net acceleration.  Or, F=m*a.
Since we kept the net hanging force a constant size, what would happen to the 
acceleration if we made the mass larger?  F=M*a
What would happen to the objects acceleration if we made the mass small?
F=m*A

Performance Assessment:

Give students the acceleration rate of either the car or van from the opening 
activity.  Recall what force the scales showed, in pounds, then convert them to 
the metric units of force (Newtons).  Students now need to calculate the car or 
van's mass from this data.  After results are collected we can find the 
experimental error in the vehicles mass calculation.  If the performance 
assessment tool above is used, you will need to find the force of friction of 
the vehicle at a constant speed to obtain an accurate NET force of motion and 
calculate an accurate vehicle mass.