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A careful quantitative study of the relationship between the velocity of a trolley down a slope and the angle of the slope.

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Introduction

A careful quantitative study of the relationship between the velocity of a trolley down a slope and the angle of the slope.

The velocity of trolley as it rolls down a slope will vary depending on the size of the angle of the slope relative to the ground. This theory comes from the general formula for gravitational potential energy:

Where GPE is gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height at which the object is from the ground. The gravitational potential energy increases as the height of the object increases and is proportional to the increase in velocity.

The gravitational potential energy lost is equal to the kinetic energy gained. This means that, as the trolley’s displacement from the ground decreases, i.e. it moves down the slope, h becomes less significant and the GPE decreases, thus increasing the KE. This increase in KE means that the trolley is moving at an increased speed, thus the velocity increases as it travels down the slope.

The GPE decreases constantly as the body moves down the slope; the velocity is also increasing constantly, which means that it is accelerating.

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Middle

away from the true value. This inaccuracy is not huge, so the results are reliable. The biggest problem with using a ruler is the parallax. In doing the experiment, the measurements were consistently taken from the same angle of vision thus reducing the effect of the parallax. This effect, however, could have been reduced slightly further by using a piece of paper on the table top, perpendicular to the ruler, to use as a better guide to an accurate measurement.

The percentage uncertainty in measuring the height of point A was reduced as the ramp was raised. This is because the measurement increased whilst the error remained constant, making the ratio between the two increase.

The time for the trolley to get from point A to point B could have been reduced by increasing the distance between the two points. This would have lessened the effect of the uncertainty, as the ratio between the two values would have been increased.

The wheels on the trolley add complications to the effect of the angle of the slope on the velocity of the trolley. This is because the smoothness of the wheels to rotate would have changed the outcome of the experiment and added to the friction.

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Conclusion

Time (s)

Velocity (m.s-1)

0.971

0.412

0.998

0.401

0.102

0.393

0.997

0.401

Average = 0.767

Average = 0.402

Height 3: 0.05m                                     Height 4: 0.06m

Time (s)

Velocity (m.s-1)

0.847

0.472

0.873

0.458

0.906

0.442

0.936

0.434

Average = 0.891

Average = 0.452

Time (s)

Velocity (m.s-1)

0.922

0.434

0.929

0.431

0.909

0.440

0.947

0.422

Average = 0.927

Average = 0.432

Height 5: 0.07m

Time (s)

Velocity (m.s-1)

0.691

0.579

0.726

0.551

0.704

0.568

0.702

0.570

Average = 0.706

Average = 0.567


Calculating the angle of the slope

Height 1: 0.03m

Height 2: 0.04m

Height 3: 0.05m

Height 4: 0.06m

Height 5: 0.07m


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image03.png

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