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


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


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
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.

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

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?

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?

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.

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