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.
A block of mass M is suspended at rest by two strings attached to walls, as shown in the figure. The left string is horizontal with tension force T2 and and the right string with tension force T1 makes an angle θ with the horizontal. g is the magnitude of the gravitational acceleration. Which of the following statements is true? Select all apply.
The net force along the y-component is zero.
The acceleration along the y-component is non-zero.
The net force along the y-component is non-zero.
The net force along the x-component is zero.
The acceleration along the y-component is zero.
The acceleration along the x-component is non-zero.
The acceleration along the x-component is zero.
The net force along the x-component is non-zero.
A 75-kg crane is suspended through a frictionless pulley to a massless pole at two points, each point is an end of two cables, and the left cable has an angle to the pole of 25 degrees while that of the right angle has an angle of 15 degrees. Each cable passes over a frictionless pulley. What is the tension force of the left cable? What is the tension force of the right cable?
Draw a free-body diagram of the problem.
Identify the known information.
Identify the unknown information.
Write the equations to solve for the unknown information.
Calculate.
Encircle your final answer with the appropriate units.
A block of mass m is on an inclined ramp. The ramp makes anangle θ with respect to the horizontal, as shown. The ramp hasfriction, with coefficient of kinetic friction μk and static friction μs.This experiment takes place on earth.The block has an initial speed of v up the ramp. It travels adistance d along the ramp before it stops.Answer using variables, please.a) Draw a free body diagram clearly showing all the forces acting on the block while it is movingup the ramp.b) Calculate the work done by the Normal force as the block travels the distance d.Is it positive, negative, or zero?c) Calculate the work done by the Weight force as the block travels the distance d.Is it positive, negative, or zero?d) Calculate the work done by the Friction force as the block travels the distance d.Is it positive, negative, or zero?e) If the block comes to rest, how far has it travelled?Use the work-energy principle and your results of parts b), c), and d).f) Briefly (one sentence) explain why this…
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