1. Project Presentation Alvaro Giraldo
Newton’s Second Law
Project Presentation
Alvaro Giraldo

2. Objectives Study Newton’s Second Law of Motion
Investigate the relationship between the mass of an object and its acceleration

3. Introduction
In 1687, Sir Isaac Newton published Book I of his Philosophiae Naturalis Principia Mathematica1.
Included three laws of motion.
Newton’s Second Law of Motion:
The net force on a body is equal to the product of its mass and its acceleration.

4. Equipment Used Balance Cart and Track Inelastic String Weight Hanger
Two Photogates with Timer
Pulley
Small Plastic Fence
Masses of varying magnitude

5. Setup Measured mass of cart (M).
Placed four 10 g masses on top of cart.
String was threaded over pulley, attached to cart at one end and weight hanger on the other.
Masses were placed on weight hanger so that its total mass (m) would be 15 g.
Placed photogates 0.50 m apart.
Placed fence on cart.
Placed first dark line of fence just before photogate sensor.

6. Data Collection
Cart was held back with a finger and timer was started.
Cart was released and allowed to move freely and time was recorded.
Reset cart to its initial position and recorded a total of 5 different time measurements.
10 g mass was moved from the cart to the weight hanger and process was repeated.
The above procedure was repeated until there were no masses left on the cart.

7. Diagram of Experiment
Pulley M
Photogates m

8. Results Mass of Cart = 512.5 g = 0.5125 kg
Total Initial Mass of Cart (M) = g + 40 g = 552.5g = kg
Initial Mass of Weight Hanger (m) = 15 g = kg
Displacement (Δx) = 0.80 m – 0.30 m = 0.50 m

9. Results Data Collected Trial M [g] m [g] T1 [s] T2 [s] T3 [s] T4 [s]
Tavg [s] 1
552.5 15
1.9985
2.0805
2.0200
1.9796
2.0218
2.0201 2
542.5 25
1.5597
1.4747
1.4825
1.4875
1.4851
1.4979 3
532.5 35
1.2401
1.2244
1.2495
1.2272
1.2162
1.2315 4
522.5 45
1.0774
1.0993
1.0987
1.0771
1.0647
1.0834 5
512.5 55
0.9910
0.9717
0.9760
0.9841
0.9790
0.9804

10. Experimental Calculations
Use kinematics equation with constant velocity:
x – x0 = at2/2 + v0t
Assume v0 = 0
x – x0 = Δx
Rearrange equation:

11. Results Experimental Results Trial Displacement [m] Tavg [s] m [g]
Weight Applied [N]
Acceleration [m/s2] 1
0.50
2.0201 15
0.15
0.25 2
1.4979 25
0.45 3
1.2315 35
0.34
0.66 4
1.0834 45
0.44
0.85 5
0.9804 55
0.54
1.04

12. Theoretical Calculations
Use Newton’s Second Law:
Since force and accelerations are both vectors, we need to examine the components of each force and acceleration.
To help visualize this, we need to draw Free Body Diagrams for each object in the system.

13. Free Body Diagrams M FN T1 Mg T2 m mg

14. Theoretical Calculations
Since the string is assumed to be inelastic, then:
If the above is true, then:
This simplifies the calculations and we can substitute T from the first equation into the last:
Rearranging the equation and solving for the acceleration gives:

15. Results Theoretical Results Trial M [g] m [g] Weight Applied [N]
Acceleration [m/s2] 1
552.5 15
0.15
0.26 2
542.5 25
0.25
0.43 3
532.5 35
0.34
0.61 4
522.5 45
0.44
0.78 5
512.5 55
0.54
0.95

17. Conclusions
The greater the force acting on an object, the larger the acceleration.
For a constant force, the less massive a body, the greater the acceleration.
Experimental results were close to the predictions made by Newton’s Second Law.

18. Discrepancies
First value of experimental data was lower than predicted by Newton’s Second Law.
May be due to friction between the cart and the track or the string and the pulley.
Experimental acceleration was higher than theoretical acceleration.
May be due to error in set up (v0 > 0)
As mass was added to weight hanger, the string fell from the pulley providing an additional, unaccounted force.

19. In real life…
Newton’s Second Law is applied to various situations in the real world.
Aerospace engineers use Newton’s Second Law to calculate the force required to overcome earth’s gravity and the drag force of the atmosphere.
Astronomers use Newton’s Second Law to predict the paths of celestial bodies by using the force of gravity exerted on the bodies by nearby planets, stars, or moons.

20. Reference
Tuckerman, M. (2002, Sep 14). Newton’s laws of motion. Retrieved from: ures/lecture_1/node2.html