The Efficiency of a Ramp

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[pic 9]

The Work Out was calculated using the formula for the gravitational potential energy: [pic 10]

Example: When the angle of the ramp was , the height of the ramp was . The mass was constant at and the force of gravity is .[pic 11][pic 12][pic 13][pic 14]

[pic 15]

The Efficiency was calculated using the formula: [pic 16]

Example: When the Work In was , the Work Out was .[pic 17][pic 18]

[pic 19]

Using the results from Fig 4, the following graph can be plotted.

[pic 20]

Fig 5: Angle vs Efficiency of a Ramp

From the results gained above, it can be seen that as the slope of the ramp increases, the efficiency also increases. From Fig 1, it was established that the two forces acting upon an object on a ramp is the force of gravity and the normal force. The force of gravity is constant for each test as the mass was a controlled variable and the gravity on earth’s surface is always . Therefore, this does not change the amount of friction acting on an object. However, the normal force which can be calculated by the formula causes the friction acting on the object to differ each time due to the different angles. [pic 21][pic 22][pic 23]

Using , where and , the normal force is calculated for the five different angles measured and is displayed in Fig 6. [pic 24][pic 25][pic 26]

Angle of the Ramp (⁰)

Normal Force (N)

3.87

7.43

5.02

7.42

7.10

7.39

9.98

7.34

10.6

7.32

Fig 6: The normal force

From Fig 6, it can be seen that as the angle of the ramp increases, the normal force decreases. Since the normal force is decreasing, the overall friction acting between the cart and the ramp also decreases causing less energy to be lost to heat. As less energy is lost, there will be more energy output making the efficiency greater.

Ramps allow objects to be lifted at a certain height as a substitution of physically lifting the object. An advantage of ramps is that less force is required to slide the object to a certain level. While lifting, a greater amount of force needs to be exerted on the object to displace it. However, a disadvantage of ramps is that while relocating objects, more work needs to be done in order to overcome the frictional force over a longer distance. While lifting, there is no frictional force as the object does not come in contact with another surface, hence no friction will be generated.

In the practical conducted, there were both random and systematic errors that may have affected the reliability of the results gained. A possible random error could have occurred while taking readings from the ruler or the spring scale. If such random error occurs, then the results will be inaccurate and unreliable. In order to avoid this, it is important to take readings from eye level to avoid parallax error. Another possible error could be that the cart was not being pulled up at a constant speed. If this was the case, the spring scale would provide inaccurate forces which will affect the results and it will not be considered accurate. In order to mitigate this error, it is vital to pull the cart using equipment that can be set to a constant speed so that there is no scope of error.

Along with random errors, systematic errors are also a possible way the results could be affected. One such example of systematic errors is the usage of uncalibrated equipment. If the equipment used in the practical were uncalibrated, then the results will not be accurate or reliable. Therefore, to avoid such influences on results, it is important to use calibrated results and do several trials with different equipment to confirm the accuracy of the results.

The aim of this practical was to explore the effects different angles have on the efficiency of a ramp. It was earlier hypothesised that as the angle increases, the efficiency will also increase. Through conducting this practical and analysing results, it was found that the hypothesis is supported because the efficiency will be greater at greater inclination.