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The Physics of a Cart Rolling along a Ramp

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Introduction

The Physics of a Cart Rolling along a Ramp

BY: Tahmid Zaman.

Group: Javeria, Nida

Table of Contents

  1. Purpose                                                                        3
  2. Materials                                                                        3        
  3. Diagram of Apparatus                                                        3
  4. Procedure                                                                        4
  5. Results                                                                        5
  1. Position –Time Data                                                5
  2. Isolated Charts                                                        6
  3. Position – Time Graph                                        6
  4. Average velocity – Average Time Graph                7
  1. Calculations                                                                7
  1. Theoretical                                                        7
  2. Experimental                                                        9
  1. Coefficient of Friction                                                        10
  2. Percentage Difference                                                        11
  3. Source of Errors                                                                11
  4. Discussions                                                                12
  5. Conclusions                                                                13
  1. Appendix i                Symbols                                                 13

Purpose:

The purpose of this lab was to calculate coefficient of rolling friction of a cart along a ramp using the theoretical acceleration using Newton’s 2nd Law and experimental acceleration using ticker-tape data analysis.

Materials:

  • Ticker-tape timer
  • Ticker-tape
  • Transparent tape
  • 0.839kg Cart with three wheels
  • 0.500kg weight
  • 0.200kg weight
  • A ramp approximately 2 m in length with a pulley attached at the end
  • Ruler – 1m
  • Two desks (labeled 1,2 according to the diagram)
  • 1 Approximately 2m long string

Diagram of Apparatus:

image00.png

Procedure:

  1. The apparatus was set up as shown on Figure 1.
  2. Firstly, the string was attached to the front of the cart and the other end of the string looped and suspended over the pulley.
  3. A long piece of ticker-tape was attached to the back end of the cart and pulled through the ticker-tape timer.
  4. The 200g or 0.200 kg weight was hooked on to the loop of the string, which was the falling end of the string.
  5. The 500g or 0.500 kg weight was placed on top of the 839g or 0.839 kg cart.
  6. Then everything was set with the 200g weight suspended and the cart held in position.
...read more.

Middle

10.30

0.1

1.05

103

66

1.1

61.8

11.50

0.1

1.15

115

72

1.2

73.3

12.40

0.1

1.25

124

78

1.3

85.7

13.50

0.1

1.35

135

84

1.4

99.2

14.40

0.1

1.45

144

90

1.5

113.6

15.20

0.1

1.55

152

96

1.6

128.8

15.20

0.1

1.65

152

102

1.7

144.0

8.20

0.1

1.75

82

108

1.8

152.2

2.50

0.1

1.85

25

114

1.9

154.7

Isolated Charts:

Time (s)

Position ∆d

0.0

0.0

0.1

0.8

0.2

2.6

0.3

5.3

0.4

9.0

0.5

13.7

0.6

19.4

0.7

26.0

0.8

33.6

0.9

42.0

1.0

51.5

1.1

61.8

1.2

73.3

1.3

85.7

1.4

99.2

1.5

113.6

1.6

128.8

1.7

144.0

1.8

152.2

1.9

154.7

tav (s)

vav (cm/s)

vav (m/s)

0.05

8

0.8

0.15

18

1.8

0.25

27

2.7

0.35

37

3.7

0.45

47

4.7

0.55

57

5.7

0.65

66

6.6

0.75

76

7.6

0.85

84

8.4

0.95

95

9.5

1.05

103

10.3

1.15

115

11.5

1.25

124

12.4

1.35

135

13.5

1.45

144

14.4

1.55

152

15.2

1.65

152

15.2

1.75

82

8.2

1.85

25

2.5

Position-Time Graph:

image01.png

Average Velocity – Average Time Graph:

image02.png

Calculations:

Theoretical:

Weight (0.200 kg)

Cart (1.339 kg)

Let “w” represent the Weight that was dropped

m w  = 0.200 kg

a = g = 9.80 m/s²

Fnet = ma

Replacing acceleration with gravity as it is falling

         Fnet  w = m w g – FT

                   FT = m w g – F

...read more.

Conclusion

        This experiment was not nearly as perfect as one could hope, but the surface of the ramp and the friction of the wheels were fairly low as a mass close to 13 % of the cart could exert such a high force and accelerate the at such a high rate. Even though the surface was very smooth, it came with some visible bumps and dents that could have caused increased friction. So, a smoother surface would allow more accuracy. All in all this experiment was a success as the surface was very with a very low coefficient of friction.

Conclusion:

After the experiment being carried out, the coefficient of friction was deduced at 0.015 derived from the experimental acceleration at 0.967 m/s². The theoretical acceleration at 1.274 m/s² was 27.4% more than that of the experimental acceleration.

Appendix i: Symbol

w (subscript)                Representation of the Weight dropped

c (subscript)                Representation of the Cart

m w                        Mass of weight, Kg

m c                        Mass of the cart, Kg

a                        Acceleration  m/s2

g                        Acceleration due to gravity m/s2

Δd                        Change in Position (displacement)

d                        Position (displacement)

Fnet                        Net force

Vavg                        Average Velocity

Tav                        Average Time

μ                        Coefficient of friction

FN                        Normal Force

Fg                        Force of Gravity

Ff r                        Force of Rolling Friction

Fapp                        Force Applied

FT                        Forceof Tension

Physics Lab #1 – Motion

BY: Tahmid Zaman

...read more.

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