# To study motion of a metal sphere on an inclined plane and determine the average frictional force offered by the plane to a metal ball.

Aim: To study motion of a metal sphere on an inclined plane and determine the average frictional force offered by the plane to a metal ball.

Equipment used: Meter Ruler/ measuring tape, inclined plane, metal ball, clamps, stands, table, stop clock etc.

Diagram:

Data:

- Mass of marble: 0.01811g ± 0.00001

- Angle of inclination: sinα=height/displacement

sinα=0.083/1.739

α=2.736

- Acceleration of gravity: 9.81ms 2

Formulae used:

- S=(1/2)(v+u)*t

- Average time=(t1+t2+t3)/3

- Kinetic energy=(1/2)mv2

- Potential energy=mgH

- mgH=(1/2)mv2+Fs

- Work done against friction: mgh-(1/2)mv2

Data collection and processing

Work done against distance travelled

0.00700

f(x) = 0x + 0

0.00600

Work done against friction

f(x) = 0x + 0

f(x) = 0x + 0

0.00500

0.00400

0.00300

0.00200

0.00100

0.00000

0.9

1

1.1

1.2

1.3

1.4

Distance travelled (m)

Sample calculation

(using data from observation 1)

Average time

t=(t1+t2+t3)/3

=(3.53+3.60+3.57)/3

=3.57s

1.5

1.6

1.7

1.8

Uncertainty of time

∆t=[(t-t1)+(t-t2)+(t-t3)]/3

=[(3.57-3.53)+(3.57-3.60)+(3.57-3.57)]/3

=0.00724

Velocity

S=(1/2)(v+u)*t

v=2S/t

=(2*1.739)/3.57

=0.974

Uncertainty of velocity

∆v=[(∆S/S)+(∆t/t)]*v

=[(0.001/1.739)+(0.00724/3.57)]*0.974

=0.00724

Kinetic energy

KE=0.5mv2

=0.5*0.01811*0.9742

=0.00859J

Uncertainty of kinetic energy

∆KE=(∆m/m)+(2*∆v/v)

=(0.00001/0.01811)+(2*0.00724/0.974)

=0.0154

Potential energy

PE=mgh

=0.01811*9.81*0.083

=0.0147J

Uncertainty of potential energy

∆PE=(∆m/m)+(∆h/h)

=(0.00001/0.01811)+(0.001/0.083)

=0.0126

Work done against frictional

Fs=mgh-0.5mv2

=0.0147-0.00859

=0.00615J

Uncertainty of work done

∆Fs=[(2*∆m/m)+(∆h/h)+(2*∆v/v)]*Fs

=[(2*0.00001/0.01811)+(0.001/1.739)+(2*0.00724/0.974)]*0.00615 =0.00172

Calculation of friction

From graph, y=0.0014x+0.0035

Slope=0.0014

Frictional force offered by the plane to the metal ball = 0.0014J Maximum slope = 0.0035

Minimum slope = 0.0014

∆slope = (0.0035-0.0014)/2

=0.00105

Percentage Precision

=(1-0.00105/0.0014)*100%

=25%

Conclusion and evaluation

The experiment is done by releasing a metal ball at a specific height on the inclined plane and measuring the time required for the ball to cover the distance on the plane. Velocity is then determined by the time required and distance travelled. After collecting and processing the data, a graph of work done against distance travelled is obtained. By the equation W=FS, F=W/S, ie friction is calculated by the slope of the graph. The calculated percentage precision is 25%, which is hardly acceptable. The lack in precision may be caused by certain errors.

First of all, the slope of the plane is adjusted by ourselves. The slope may not be at an angle which the ball rolls at constant speed. Air resistance may be included, thus increasing the result of friction. This may be a reason for systematic error, which affect the accuracy of the results. Also, a stopwatch is used to measure the time required for the metal ball to cover the distance on the plane. The measurement is based on eye observation. The time measured by stopwatch is inaccurate due to the reaction time of human. To add on to that, reaction time varies with different people. When calculating the final velocity, we assumed that u=0 in the equation S= (u+v)*t/2. However, the initial velocity may be 0 in the actual experiment. We may exert a force onto the marble when we release the marble by hand. This contributes to the initial velocity. Therefore, the calculation of final

velocity may be inaccurate.

In addition to that, the path in which the marble rolls may not be a straight line. This increases the distance travelled. Therefore, the distance travelled obtained may not be accurate, which affects the calculation of the friction.

In order to improve the results of the experiment, we should slide the ball for more times to ensure that we can...

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