Return to Physics IndexNewton'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) 485-7600Objectives:

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 calculatorsStrategy:

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*t^{2}.

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/t^{2})

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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*APerformance 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.