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Effect of Height on Velocity | Experiment

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Extended Experimental Investigation

MOTION ON AN INCLINE

DUONG, Phong (Nathan)

Contents

1.0 Introduction:

1.1 Research Question and Aim

1.2 Theory Review

1.2.1 Gravity

1.2.2 Forces

1.2.3 Ramp physics

1.2.4 Newtons law

1.3 Hypothesis

2.0 Methods

2.1 Safety

2.2 Equipment

2.3 Procedures

3.0 Results and Analysis

3.1 Results

3.1.1 The inclined angle of the ramp

3.1.2

3.2 Analysis

3.3 Error Analysis

4.0 Discussion

5.0 Conclusion

6.0 Appendices

Appendix 1:

Appendix 2:

Appendix 3:

Appendix 4:

Appendix 5:

7.0 References

1.0 Introduction:

1.1 Research Question and Aim

The aim of this extended experimental investigation is to find how gravitational energy and kinetic energy apply on the toy car rolling down the steep ramp. How does the ramp height affect the velocity of the car?

1.2 Theory Review

Basically, when a ramp has a small angle of incline, the force of friction between the car and the ramp has greater potential to prevent the car from moving. When an object rests on a surface like the ramp, the ramp exerts a force called 'normal force' on the object, and this force is greater when the angle of incline is smaller. The reason for this is that the force of gravity on the car has to be split between horizontal and vertical components. If the ramp is steep, the force of gravity can more easily overcome the force of friction. Obviously gravity will cause an object on an incline to move down the slope faster than a flat slope.

1.2.1 Gravity

Gravity acts vertically downwards, and the body during its free fall is accelerated due to the force of gravity. A body moving upward is undergoing negative acceleration, or deceleration, as its speed decreases and it momentarily comes to rest at the highest point of its ascent where its velocity becomes zero due to retardation obtained by the opposing force of gravity. As the gravity increases the motion of an object during its free fall and decreases the motion of an object as it travels in an upward direction.

1.2.2 Forces

All moving objects have a type of energy called kinetic energy (Ek) as well as the potential energy (PE) which stored in an object. These two forces have the potential to do work and gravity gives potential energy to object whereas kinetic energy of an object depends only upon its mass and its speed. The formula for potential energy due to gravity isPE=mgh. As the object gets closer to the ground, its potential energy decreases while its kinetic energy increases. The difference in potential energy is equal to the difference in kinetic energy.

1.2.3 Ramp physics

A ramp works like this inclined plane, the steeper the ramp the larger the amount of the sliding force. , when the ramp is (vertically) only the sliding component is left and equals the weight force. On the other extreme (the ramp is horizontal) the sliding force vanishes and only the component of the normal force is left.

1.3 Hypothesis

It is hypothesised that as the angle of the ramp increases the speed of the car travels will also increase which results in shorter time for the car to travel down the ramp. This is predicted according to the theory of gravitational potential energy converting to kinetic energy.

2.0 Methods

2.1 Safety

Must handle the retort stand with care as it could cause injuries if it drops on the lower bodies (legs, knees, foots...etc.) as well as the ramp because they are quite heavy.

2.2 Equipment

  1. Retort stand - For the ramp to rest on, to increase the height of theramp summit to any height
  2. Ramp- for the toy car to roll down
  3. Stop watch- to time the toy car (starts and finishes)
  4. Note book- to record the results on
  5. Measurements tape-to measure out 1 metre on the ramp
  6. Chalk- To mark the starting points and finish lines

2.3 Procedures

1. Set out equipment as shown in the diagram. 2. Ensure the height at the start line (the summit of the ramp) is 30 cm using the metre stick. 3. Ensure there are no extra weights attached to thetoy car. 4. Hold the toy car with its front touching the start line. 5. Simultaneously start the stop clock and release the toy car (becareful not to push it or exert any extra force on it).

6. Stop the clock when the front of the toy car reaches the finish line. 7. Record the time taken for the toy car to reach the finish, next to the relevant height, in a table. 8. Repeat from step 4 four times so you end up with five results for the same height then continue onto step 9. 9. Add all these results together and divide the answer by five to obtain the average time. 10. Record this average in the table. 11. By placing more books underneath the raised end of the ramp, increase the height at the summit by 10cm. Use the metre stick to check 12. Repeat from step 4 until you have obtained results for height from 30cm through to 50cm

3.0 Results and Analysis

3.1 Results

The average time for different heights and distance

Ramp Length (cm)

Heights of the ramp (cm)

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Average time (seconds)

Speed (m/s)

Acceleration (m/s)

Velocity(m/s)

100

30

0.79

0.87

0.81

0.85

0.84

0.832

1.2

3

2.5

40

0.68

0.84

0.66

0.67

0.68

0.706

1.42

3.97

50

0.65

0.63

0.64

0.64

0.62

0.636

1.57

4.87

95

30

0.79

0.78

0.76

0.77

0.78

0.776

1.21

3.22

2.8

40

0.67

0.66

0.72

0.65

0.65

0.67

1.41

4.18

50

0.6

0.65

0.58

0.64

0.61

0.616

1.54

5.03

90

30

0.72

0.75

0.71

0.74

0.72

0.728

1.23

3.43

3.1

40

0.71

0.67

0.72

0.73

0.68

0.702

1.28

3.99

50

0.64

0.59

0.59

0.61

0.58

0.602

1.5

5.15

3.1.1 The inclined angle of the ramp

Heights of the ramp (cm)

Angle of inclination (degrees)

30

16.7

40

21.8

50

26.6

3.1.2

Figure 1

3.2 Analysis

The results show that when the ramp is higher (50cm) the car went fasterdown the slope at (3.1m/s). This is because gravity is pulling the car straight down andfriction is pulling the car back up the ramp, opposite to direction ofmotion. The ramp is pushing the car straight up in the oppositedirection of gravity. The ramp is also pushing it horizontally awayfrom the ramp. The net force (the sum of the weight and normal force)acting on the car is large enough to make the car to accelerate downthe ramp. If the ramp were horizontal the net force would be zerotherefore the car would not move. So the higher an object goes the more gravitational potential energyit gains. When it falls, its potential energy is converted intokinetic energy and; since energy can neither be created or destroyed,only converted then it will move at a faster speed.

3.3 Error Analysis

There are many gaps of errors when conducted this experiment such as careless error, random error, human error (reaction time) and systematic errors. These are due to mistakes in reading scales or careless setting markers; they can be eliminated by repetition of readings by one or two observers. Whereas the random error could be the observer’s position when recording the data and it could spread the results further away to the true value which will increase in anomalies. The results weren’t really accurate because air resistance and friction energy wasn’t taken in to the account, with these taken in to the calculation then it would be more accurate for the speed of the car.

4.0 Discussion

The experiment worked well after the preliminary experiment, the experiment indicates that if the height of the ramp is too high it would not produce very goodresults. Assume the results were accurate and the methodworked. Due to human error and reaction time, these results could notbe relied on completely, but did give a rough idea of how the experiment would have worked. If the conduction of the experiment was to be done again, it would be more accurate by producingresults using the computer system with light gate.

The air resistance was neglected because if the resistance to be present, the results would be decrease but not very much throughout the experiment. The car was suffering from the friction of a ramp, something that would seriously affect the car due to it having a small mass.

There were certainly some places where the experiment was lacking in some accuracy and it could have improved. The first area to highlight is the car, where most of the accuracies were caused. The car certainly had friction occurring in the wheels of the car, and with the surface it was going down. This is one of the major problem to solve because a frictionless car is impossible, to encounter this problem is to find a better car with better bearings is the wheels and more therefore less friction, causing less wasted energy through sound and heat. There was also some accuracy lacking areas which couldn’t improve either without better equipment. If the conduction of the experiment were to happen again, experimenting withdifferent surfaces of ramp would be a changed. The main problem established in the experiment wasthat the toy car kept swaying to the side, creating a longer journeyand hitting the edge majority of the time. This also could have been caused dueto uneven flooring of the ramp. If the right equipment could be accessed to calculatingthe speed using light gates and determining if it produces theoreticallyperfect results, also eliminating any other opposingforces, such as friction, polishing surfaces etc. (no air resistance) and noticing ifthis changes the results.To take the potential/kinetic energy element even further,looking into elastic potential energy and identify if it works on the sameprinciple as gravitational potential energy.

5.0 Conclusion

In conclusion, the experiment demonstrated that the ramp set on (50cm) height at the distance of (90cm) had a greater velocity (speed) and acceleration than other heights. This suggests that the car had a greater velocity and lowest time was because of the steepness of the ramp that was set on. The longer of the ramp, along with gravity had a huge impact on the car movement from the top of the ramp to the bottom. The hypothesis is supported by scientific theory of motion on an incline.

 

6.0 Appendices

Appendix 1:

  • 1 metre (100cm) long ramp

Heights of the ramp (cm)

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

30cm

0.79

0.87

0.81

0.85

0.84

40cm

0.68

0.84

0.66

0.67

0.68

50cm

0.65

0.63

0.64

0.64

0.62

  • 95 cm long ramp

Heights of the ramp (cm)

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

30cm

0.79

0.78

0.76

0.77

0.78

40cm

0.67

0.66

0.72

0.65

0.65

50cm

0.6

0.65

0.58

0.64

0.61

  • 90 cm long ramp

Heights of the ramp (cm)

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

30cm

0.72

0.75

0.71

0.74

0.72

40cm

0.71

0.67

0.72

0.73

0.68

50cm

0.64

0.59

0.59

0.61

0.58

Appendix 2:

Example 1: Given height = 30 cm and the length or the ramp = 100 cm

Example 2: Given height = 40 cm and the length or the ramp = 100 cm

Example 3: Given height = 50 cm and the length or the ramp = 100 cm

Appendix 3:

  • Velocity of (30 cm=0.3m) height ramp, g=9.8 m/s (constant)

  • Velocity of (40 cm=0.4m) height ramp, g=9.8 m/s (constant)

  • Velocity of (50 cm=0.5m) height ramp, g=9.8 m/s (constant)

Appendix 4:

 

Appendix 5:

When the height at 30 (cm), velocity=2.5m/s

7.0 References

Silverman, Buffy (2009).Simple Machines: Forces in Action, 4th Ed.. USA: Heinemann-Raintree Classroom. p.7.ISBN978-1-4329-2317-4

Reilly, Travis (November 24, 2011)."Lesson 04:Slide Right on By Using an Inclined Plane".Teach Engineering. College of Engineering, Univ. of Colorado at Boulder. Retrieved September 8, 2012

Smith, Crosbie (1998).The Science of Energy - a Cultural History of Energy Physics in Victorian Britain. The University of Chicago Press.ISBN0-226-76420-6.

Feynman, Richard P. (2011)."Work and potential energy".The Feynman Lectures on Physics, Vol. I. Basic Books. p.13.ISBN978-0-465-02493-3.


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