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.
1. An arrangement of three charges is shown below where q₁ = 1.6 × 10-19 C, q2 = -1.6×10-19 C,
and q3 3.2 x 10-19 C.
2 cm
Y
93
92
91
X
3 cm
(a) Calculate the magnitude and direction of the net force on q₁.
(b) Sketch the direction of the forces on qi
(Figure 1)In each case let w be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight w
Find the direction of the force exerted on the strut by the pivot in the arrangement (a).
Express your answer in degrees.
Find the tension Tb in the cable in the arrangement (b).
Express your answer in terms of w.
Find the magnitude of the force exerted on the strut by the pivot in the arrangement (b).
Express your answer in terms of w.
(Figure 1)In each case let ww be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight w.
Find the direction of the force exerted on the strut by the pivot in the arrangement (b).
Express your answer in degrees.
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