This lab primarily aims at investigating Newton’s laws of motion. It involves the experiment on mass, velocity, time, and the acceleration of a cart. The experimental values of acceleration are compared with those of the theoretical ones.
Theory
The lab involves experimenting with a cart that is self-propelled using a fan. Other procedures carried out include a cart on a horizontal and the one on include track, pulled by a rope attached to a mass that is hanging. Newton's laws of motion help in describing the effects of force on a motion of a system or object. In brief, the acceleration of a system occurs in a manner governed by the mass and the net force of the system if there is an imbalance of all the forces acting on the system. This experiment uses the acceleration of a cart for the examination of Newton's laws of motion.
Data
Tables 1: A Cart Self-Propelled by a Fan
Mass (kg)
Acceleration of cart (m/s2)
F = mass x acceleration of cart (N)
From v vs. t graph
From x vs. t graph
Average
0.518
0.303
0.153
0.228
0.118
0.997
0.155
0.078
0.117
0.117
Table 2: A Cart on Horizontal Track
Mass (Kg)
MASS (KG)
Acceleration of cart (m/s2)
T (N)
Experiment
Theory
% error
From v vs. t graph
From x vs. t graph
Average
0.532
0.01
0.206
0.109
0.158
0.003
5166
0.002
0.02
0.383
0.192
0.228
0.008
2750
0.004
1.04
0.01
0.106
0.052
0.079
0.0008
4775
0.0008
0.02
0.195
0.097
0.146
0.003
4766
0.003
Table 3: A Cart on an Inclined Track
Mass (Kg)
MASS (KG)
θ (degrees)
Sine θ
Acceleration of the cart (m/s2)
T (N)
Experiment
V vs. t graph
x vs. t graph
Average
Theory
% error
1.04
0.2
3.04
0.053
0.941
0.519
0.73
0.085
758.8
0.129
6.43
0.112
0.395
0.302
0.449
0.5
1396.6
0.084
9.38
0.163
0.197
0.047
0.147
0.004
3575
0.029
Sample Calculations
From table 1, it is apparent acceleration, α = varies inversely with mass (m). For example, a mass of 0.518 kg produces an average acceleration of 0.228 m/s2. Also, a mass of 0.997 kg has an acceleration of 0.117 m/s2.
Force, F = mα = 0.518 x 0.228 = 0.118 N.
For the second mass, F = 0.997 x 0.117 = 0.117 N.
The average value of force = 0.1175 N.
Graphs
Figure 1: Graph of Acceleration versus Sine θ
In this graph, R2 = 0.7949 and y = 7.5x – 0.37
Questions and Answers
Question 1
Figure 1: Free Body Diagram
If m = 1.04 kg and M = 0.2 kg, then sine θ = (100 – 30)/ 95 = 0.7
T = (1.04 x 0.2)/ (1.04 + 0.2) x 9.8 = 1.64 N
1.64 – (0.2 x 9.8 x 0.7) = 0.268 N
If T – mg x sine θ = and ma cart F, then the nominal force of the cart = 0.268 N
Equation (8), a = g [M-(m x sine θ)]/ [m + M]
= 9.8[0.2-1.04 x 0.7)]/ [1.04 + 0.2] = 5.1744/ 1.24 = 4.173
Equation (9), T = Mmg (1+ sine θ)/ (m + M)
= [(0.2 x 1.04 x 9.8)] x [(1 + 0.7)/ (1.04 + 0.2)] = 2.0384/ 1.37 = 1.488
Question 2
Figure 2: Schematic Diagrams
Question 3
The force of the cart F depends on its mass. The answers agree with the results in Table 1.
Question 4
In such a scenario, the hanging mass’ acceleration would be equal to that of gravity 9.8 m/s2
because of the free fall.
Question 5
The cart’s acceleration would be close to that of the gravity 9.8m/s2 due to the free fall on the frictionless ramp. The acceleration = angle of inclination would be = g x sine θ.
Conclusion
This experiment helped in showing how a net force is produced by the forces acting on the cart. Even though the lab achieved it objective of investigating Newton's laws of motion, there were some significant errors in the experimental values.
Obstacles/ Errors
As can be seen in all the three tables, the percentage errors are quite significant. Lengthy calculations faultiness of the equipment might have resulted in these uncertainties.
