2. The Energy Car -Newton’s second law
In this investigation students will examine how small variations in Earth’s orbit and axial tilt effect seasonal variation of light intensity, and how that variation ultimately is responsible for the seasons.

3. Key question
What is the relationship between force and motion?

4. Newton’s laws
The relationships between force and motion are known as Newton’s laws.
These are among the most widely used relationships in all of physics.
This investigation is about the second law which relates the force acting on an object to the object’s change in speed and its mass.

5. Changing force with constant mass
For the first part of the investigation you will use different amounts of force to launch the car.
What do you think will happen?
As the force gets larger, what happens to the speed of the car?

6. Changing force with constant mass
Set up the long straight track with a rubber band on one end and a clay ball on the other end.

7. Changing force with constant mass
Adjust the screw so the rubber band deflects about two centimeters.
Put one photogate about 20 cm away from the rubber band.
Put 1 marble in the center of the car

8. Changing force with constant mass
Adjust the screw so the rubber band deflects about two centimeters.
Put one photogate about 20 cm away from the rubber band.
Put 1 marble in the center of the car

9. Changing force with constant mass
Use the screw to launch the car using the same deflection of the rubber band each time.
This means the same force is applied to each launch.

10. Changing force with constant mass; Calculating speed
The width of the flag on the car is one centimeter.
speed = distance/time
The easiest way to calculate the speed of the car is to divide 1.0 centimeter by the time it takes to pass through a single photogate.

11. Changing force with constant mass
Try to get three launches with times that are within seconds of each other.
Record your three closest results in Table 1.
Repeat the experiment with two and three rubber bands
Number of rubber bands
Time through photogate (sec)
Speed
(cm/sec) 1 2 3

12. Changing force with constant mass
Try to get three launches with times that are within seconds of each other.
Record your three closest results in Table 1.
Repeat the experiment with two and three rubber bands
Number of rubber bands
Time through photogate (sec)
Speed
(cm/sec) 1
0.0121
82.6 2
0.0092
108.7 3
0.0066
151.5

13. Stop and think
a. During which portion of the car’s motion is the rubber band affecting its speed?
Only the very first 2 cm, because that is the only time the car is contact with the rubber band.

14. Stop and think
b. Make a graph showing the speed of the car on the y-axis and the number of rubber bands on the x-axis. As the force was increased, what happened to the speed of the car??
The speed of the car increased as the force was increased

15. Stop and think
a. Why was the same mass used for all trials (with different force)?
The mass of the car was one of the control variables. The experimental variable in this part was the number of rubber bands.

16. Changing mass with the constant force
Put a single rubber band on the launching end of the track.
Leave the photogate in the same place as it was (20 centimeters in front of the rubber band).

17. Changing mass with the constant force
With the screw in the same place, launch cars of four different masses and observe their speeds when they pass through the photogate.
Measure the mass of the car with 0, 1, 2, and 3 steel balls

18. Changing force with constant mass
Table 2: Changing mass data
Mass of car (kg)
Time through photogate (sec)
Speed
(cm/sec)

19. Changing force with constant mass
Table 2: Changing mass data
Mass of car (kg)
Time through photogate (sec)
Speed
(cm/sec)
0.0568
0.0101
99.0
0.0851
0.0123
81.3
0.1133
0.0142
70.4
0.1415
0.0156
64.1

20. Applying what you learned
a. Use Table 2 to graph the speed of the car (y) against the mass (x). Does your graph show a direct relationship or an inverse relationship?
The graph shows an indirect relationship. The greater the mass of the car, the lower its speed.

21. Applying what you learned
b. Why did the speed change when the same launching force from the rubber band was applied to carts of different mass? How do your observations support your answer?
The speed changed because more mass requires more force to achieve the same speed. We observed that as we increased mass with the same amount of force, the speed decreased.

22. Applying what you learned
c. Do you think the force applied to an object causes speed itself or causes changes in speed? Support your answer with at least one sentence of explanation for why you believe your answer is correct.
The force causes a change in speed. Once the car left contact with the rubber band, it did not seem to go any faster. The force applied by the clay stopped the car, a clear change in speed.

23. Applying what you learned
When an object’s speed changes we say the object accelerates. Acceleration occurs whenever speed changes. To be precise, acceleration means the “change in speed divided by the change in time”

24. Applying what you learned
e. Based on your experimental results, propose a mathematical relationship between the variables F (force), a (acceleration), and m (mass).
Force = mass x acceleration