Chapter 3 – Newton’s 2nd Law of Motion
Relationship between force, mass, and acceleration
Constant Force and Changing Mass
Materials
cart
track
4 – 500g bar masses
1 – 50g hook mass
pulley
string
stopwatch
Safety
None
Purpose
To investigate the effect of increasing mass on an accelerating system.
Procedure
Step 1: Set up the pulley-cart system
a.) Set the aluminum track over the edge of the lab table.
b.) Fasten the pulley to the edge (wheel up) making sure not to over-fasten the screw.
c.) Tie one end of the string to the cart and thread it over the pulley.
d.) Add the 50g hook mass to the hanging end of the string.
Step 2: Set up the timing system
a.) Roll the cart backward (away from the pulley) until the string’s knot touches the pulley.
b.) Mark this distance on the track with a piece of masking tape. This is your starting point.
c.) Roll the cart forward (toward the pulley) until the hanging mass touches the floor.
d.) Mark this distance with a piece of masking tape. This is your ending point.
Step 3: Data Collection
a.) Move the cart to its starting point and let go, stopping it at its ending point.
b.) Use a stopwatch to collect the time it takes to travel this distance. Record the time in your data table.
c.) Repeat two more times for a total of three trials.
d.) Add a 500g bar mass to the cart and repeat steps a-c until all 4 bars are used.
Step 4: Calculations
a.) Average the times by finding the sum and dividing by 3. Record the average time in your data table.
1
b.) Calculate the acceleration of the system by rearranging the equation 𝑑 = 2 𝑎𝑡 2 and solving for a.
2𝑑
𝑎= 2
𝑡
Data Table
Distance = ___________________m
Mass of system
(kg)
Trial 1
Time to Cover Distance (seconds)
Trial 2
Trial 3
Average
Acceleration
(m/s2)
(car)
(car+1)
(car+2)
(car+3)
(car+4)
Analysis
1. Make a graph of acceleration (vertical axis) vs. mass (horizontal axis).
2. Describe your graph of acceleration vs. mass. Is it a straight-line graph or a curve? Is it directly or inversely proportional?
3. For a constant applied force, how does increasing the mass of an object affect its acceleration?
4. Develop an equation to describe the relationship between acceleration and mass.
Chapter 3 – Newton’s 2nd Law of Motion
Relationship between force, mass, and acceleration
Constant Mass and Changing Force
Safety
None
Materials
Same as above
4 – 20g hook masses
Purpose
To investigate the effect of increasing force on an accelerating system.
Procedure
Step 1: Set up the pulley-cart system
a.) Same as above
Step 2: Set up the timing system
a.) Same as above
Step 3: Data Collection
a.) Set all of the 20g masses onto the pan of the cart.
b.) Move the cart to its starting point and let go, stopping it at its ending point.
c.) Use a stopwatch to collect the time it takes to travel this distance. Record the time in your data table.
d.) Repeat two more times for a total of three trials.
e.) Remove one of the 20g masses from the cart and set it on the hanging mass.
e.) Repeat above steps b-e until all masses have been moved from the cart to the hanger.
Step 4: Calculations
a.) Calculate the force on the hanger by taking the mass and multiplying by gravity’s acceleration. Record the
force in the data table.
b.) Average the times by finding the sum and dividing by 3. Record the average time in your data table.
1
b.) Calculate the acceleration of the system by rearranging the equation 𝑑 = 𝑎𝑡 2 and solving for a.
2
2𝑑
𝑎= 2
𝑡
Data Table
Distance = ___________________m
# of masses in
the cart
Mass of
falling hanger
(kg)
Force on falling
hanger
(N)
Time to Cover Distance (seconds)
Trial 1
Trial 2
Trial 3
Average
Acceleration
(m/s2)
4
3
2
1
0
Analysis
1. Make a graph of acceleration (vertical axis) vs. force (horizontal axis).
2. Describe your graph of acceleration vs. force. Is it a straight-line graph or a curve? Is it directly or inversely proportional?
3. Does the acceleration of the cart increase or decrease as the force increases?
4. Was the mass of the accelerating system (cart + falling weight) the same in each case?
5. Develop an equation to describe the relationship between acceleration and force.
6. Combine the two equations of force-acceleration and mass-acceleration to write a general equation between force,
mass, and acceleration.