Analysis
Static Friction In the first part of this experiment, you will determine, from your data, the coefficient of
static friction between the hockey puck and the board. The inclination angle at which the puck loses
balance and starts sliding down the incline is referred to as θs. At this angle, the force of static friction
reaches its maximum value (µs mg sin θs) and becomes equal to the component of the gravitational
force down the incline, as stated in Equation (7.1). From this equation, derive a simple relation
(independent of the weight) between µs and θs.
Next, use the measured heights hs (from the five trials) and the length of the board, to calculate the
corresponding inclination angles θs. The average of these five trials is the experimental measurement of
θs and the largest deviation from the average is an estimate of the experimental error (∆θs). After that, it
should be straightforward to calculate the coefficient of static friction µs between the puck and the
board.
To estimate the uncertainty (∆µs) you need to use the general theory of errors, which states that if y is a
function of x, then
∆y = (dy/ dx) ∆x
Note that for the tangent function, the uncertainty is given by
∆(tan θ) = d dθ (tan θ) ∆θ
= (1/ cos θ)^2 ∆θ
where ∆θ is in radians (not degrees). Length of board = 124 cm
Hs (m)
34.5
41
35
40
36 Ѳs (Degrees) Kinetic Friction
To calculate the coefficient of kinetic friction µk between the sliding puck and the board, you need first
to calculate the acceleration for a particular inclination angle and then substitute into Equation (7.3). The
acceleration can be calculated from the measured time (t) and distance (d) of the sliding puck (i.e. d = 1 2
at2 ). From the five timing trials, calculate the values of t and ∆t for each inclination angle θ. Then,
calculate the acceleration corresponding to each inclination angle. Complete Table 7.2 and comment on
your results. For example, does µs appear independent of θ? Compare your values for µs and µk.
Distance between start and end point = 113 cm
Inclination
Ѳ
41.5 31 53 Time
t
2.03
2.1
2.05
1.97
1.85
14.76
14.25
15.2
13.6
12.94
1.19
1.21
1.33
1.20
1.21 Average time
t ± ∆t Acceleration
a ± ∆a µk Inclination
Ѳ
13 20.5 24 Time
t
2.4
2.06
1.97
1.4
1.5
1.4 Average time
t ± ∆t g sin Ѳ Acceleration
a ± ∆a 1.32
1.26
1.2 29.5 1.13
1.07
1.06 41.5 .93
.9
.93 17 1.52
1.46
1.46 Questions
1. Show that the acceleration of a solid cylinder rolling down an incline, making an angle θ with the
horizontal, is given by Equation (7.4). Hint: You can use the principle of conservation of mechanical
energy.
2. Two spheres look identical and have the same mass. However, one is hollow and the other is solid.
Describe an experiment to determine which is which.

 

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