A crate of weight Fg is pushed by a force on a horizontal floor.

(a) If the coefficient of static friction is μs, and is directed at angle θ below the horizontal, show that the minimum value of P that will move the crate is given by the following equation.

(Do this on paper. Your instructor may ask you to turn in this work.)

(b) Find the minimum value of P that can produce motion when μs = 0.450 and Fg = 145 N for the following angles.

θ = 0°
θ = 15.0°
θ = 30.0°
θ = 45.0°
θ = 60.0

3 answers

exactly what equation?

MINIMUM VALUE OF P THAT

To find the minimum value of P that will move the crate, we need to consider the forces acting on the crate and use the equation of equilibrium for the forces in the horizontal direction.

Let's break down the forces:

1. Weight (Fg): The weight of the crate is acting vertically downward and has a magnitude of Fg.
2. Normal force (N): The normal force is the force exerted by the floor on the crate. It acts perpendicular to the surface and has a magnitude equal to Fg.
3. Applied force (P): This is the force applied to the crate at an angle θ below the horizontal direction.

Now, let's analyze the forces in the horizontal direction:

The force of static friction (Fs) opposes the applied force P and prevents the crate from moving until P reaches a certain value, at which point the crate will start moving. The force of static friction can be determined using the equation:

Fs = μs * N

where μs is the coefficient of static friction.

Since the normal force N is equal to the weight of the crate (N = Fg), the equation for the force of static friction becomes:

Fs = μs * Fg

For the crate to start moving, the applied force P must overcome the force of static friction:

P > Fs

Substituting Fs = μs * Fg, we have:

P > μs * Fg

This inequality represents the condition for the crate to start moving. Therefore, the minimum value of P that will move the crate is given by:

P(min) = μs * Fg

Now, let's solve part (b) where we are given different values of θ, μs, and Fg.

For each angle θ, we can calculate the minimum value of P using the equation above.

For θ = 0°:
P(min) = μs * Fg = 0.450 * 145 N

For θ = 15.0°:
P(min) = μs * Fg = 0.450 * 145 N

For θ = 30.0°:
P(min) = μs * Fg = 0.450 * 145 N

For θ = 45.0°:
P(min) = μs * Fg = 0.450 * 145 N

For θ = 60.0°:
P(min) = μs * Fg = 0.450 * 145 N

You can calculate each of these values using a calculator.