Calculating Coefficient of Static Friction for a 770-kg Block

What is the coefficient of static friction for a 770-kg block on a horizontal floor?

Let μ_s be the coefficient of static friction between the block and the floor.

We have the force equation:

F = μ_s * m * g

Given that the force applied is 12.0 N and the mass of the block is 770 kg, we can calculate the coefficient of static friction:

μ_s = F / (m * g)

Plugging in the values, we get:

μ_s = 12.0 / (770 * 9.8)

Calculating the above expression gives us:

μ_s = 0.255

Calculation of Coefficient of Static Friction

In this scenario, we have a 770-kg block at rest on a horizontal floor. When a horizontal force of 12.0 N is applied to the block, it just starts to move. This situation indicates that the force of friction acting on the block is equal to the force applied, hence the block begins to move.

Coefficient of static friction (μ_s):

The coefficient of static friction (μ_s) measures the resistance to motion between two surfaces that are not moving relative to each other. In this case, it represents the friction between the block and the floor when they are at rest.

Calculation:

We use the equation of static friction, which relates the force of friction to the normal force and the coefficient of static friction: F_friction = μ_s * N

Given: - Applied force (F) = 12.0 N - Mass of the block (m) = 770 kg - Acceleration due to gravity (g) = 9.8 m/s²

Using the equation F = μ_s * m * g, we can solve for the coefficient of static friction (μ_s):

μ_s = F / (m * g)

Substitute the known values:

μ_s = 12.0 / (770 * 9.8) = 0.255

Therefore, the coefficient of static friction between the block and the floor is 0.255.