Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θ C , called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μ s n for angles less than θ C ? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θ c ? (c) Show that the coefficient of static friction is given by μ s = tan θ c . (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θ c ’ ≤ θ c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction? Figure P4.82
Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θ C , called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μ s n for angles less than θ C ? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θ c ? (c) Show that the coefficient of static friction is given by μ s = tan θ c . (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θ c ’ ≤ θ c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction? Figure P4.82
Solution Summary: The author explains how the friction force, normal force and weight are the forces acting on the coin.
Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θC, called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μsn for angles less than θC? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θc? (c) Show that the coefficient of static friction is given by μs = tan θc. (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θc’ ≤ θc such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction?
Figure P4.82
Definition Definition Force that opposes motion when the surface of one item rubs against the surface of another. The unit of force of friction is same as the unit of force.
Statistical thermodynamics. The number of imaginary replicas of a system of N particlesa) cannot be greater than Avogadro's numberb) must always be greater than Avogadro's number.c) has no relation to Avogadro's number.
Lab-Based Section
Use the following information to answer the lab based scenario.
A student performed an experiment in an attempt to determine the index of refraction of glass.
The student used a laser and a protractor to measure a variety of angles of incidence and
refraction through a semi-circular glass prism. The design of the experiment and the student's
results are shown below.
Angle of
Incidence (°)
Angle of
Refraction (º)
20
11
30
19
40
26
50
31
60
36
70
38
2a) By hand (i.e., without using computer software), create a linear graph on graph paper
using the student's data. Note: You will have to manipulate the data in order to achieve a
linear function.
2b) Graphically determine the index of refraction of the semi-circular glass prism, rounding your
answer to the nearest hundredth.
Use the following information to answer the next two questions.
A laser is directed at a prism made of zircon (n = 1.92) at an incident angle of 35.0°, as shown in
the diagram.
3a) Determine the critical angle of zircon.
35.0°
70°
55
55°
3b) Determine the angle of refraction when the laser beam leaves the prism.
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