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Rough Surface with: Ms = 0.8 HK = 0.4

(a) Find the magnitude of the

force F needed to prevent the

book from sliding down the

rough wall.

F

M = 1.5 kg

600

(b) Find the minimum force F

needed to set the book in

motion up the rough wall with

constant velocity

2 Answers

5 votes

Final answer:

To prevent the book from sliding down, the force F equals the static friction force, which can be calculated using the coefficient of static friction and the gravitational force component. To move the book upward at constant velocity, F needs to overcome both gravitational and kinetic friction forces.

Step-by-step explanation:

Static and Kinetic Friction

To find the magnitude of the force F needed to prevent the book from sliding down a rough wall, we need to consider the force of static friction and the gravitational force acting on the book. Given that the coefficient of static friction (µs) is 0.8, and the book has a mass (M) of 1.5 kg inclined at 60° to the horizontal, the gravitational force acting down the wall is M * g * cos(60°), where g is the acceleration due to gravity (9.8 m/s²). The static friction force can then be calculated using F = µs * N, where N is the normal force, which in this case is the horizontal force F itself because it must balance the component of the gravitational force that acts perpendicular to the wall (M * g * sin(60°)). Thus, F can be found by solving the equation F = µs * (M * g * sin(60°)).

For part (b), to set the book in motion up the wall with constant velocity, the horizontal force F must overcome not only the gravitational force but also the force of kinetic friction, with a coefficient of µk = 0.4. Since the velocity is constant, the net force is zero, which means the applied force has to balance both the downward gravitational force and the kinetic friction force, leading to the equation F = M * g * cos(60°) + µk * (M * g * sin(60°)). Solving for F gives the minimum force needed to move the book upwards at constant velocity.

User PorridgeBear
by
4.3k points
1 vote

Answer:

a) F = 18.375N, b) F = 24.5 N

Step-by-step explanation:

This exercise can be solved using the translational equilibrium equations.

Let's start by fixing a reference system with the horizontal x axis and the vertical y axis, from the statement of the exercise I understand that the wall is vertical and the book is supported on it, therefore the applied force is in the direction towards the wall

a) In this part the force that does not allow the movement of the book is requested, therefore the static friction coefficient must be used (μ_s = 0.8)

X axis

F - N = 0

N = F

Y axis

fr - W = 0

W = fr

where W is the weight of the book.

The friction force has the formula

fr = μ_s N

we substitute

mg = μ_s F

F =
(mg)/(\mu_s )

let's calculate

F = 1.5 9.8 / 0.8

F = 18.375N

b) In this case the book is moving so the friction coefficient to use is kinetic ( μ_K = 0.6)

F =
(mg)/(\mu_K )

we calculate

F = 1.5 9.8 / 0.6

F = 24.5 N

User Menol
by
4.1k points