Question

The coefficient of kinetic friction between an object and the surface upon which it is sliding is 0.6. The

mass of the object is 12 kg. What is the force of friction

Answer 1

70.56 N

Step-by-step explanation:

The formula for kinetic friction is fₖ = μₖ * n, where μₖ is the coefficient of kinetic friction and n is the normal force.

The question gives us the value of the coefficient of kinetic friction, but it does not explicitly give us the normal force.

Let's draw a free-body diagram to see the forces that are acting on the object. I attached an image of what the free-body diagram should look like.

We can see that there are three forces being applied to the object: the normal force, weight force, and the (kinetic) friction force.

Since the object has a net force of 0 in the y-direction (it is not moving vertically), we can use Newton's 2nd Law to prove that the normal force and the weight force are equal to each other.

Newton's 2nd Law of Motion tells us that F = ma, so we can apply it in this instance by saying the sum of all forces in the y-direction is equal to 0, since there is no acceleration in the vertical direction.

• ∑F_y = 0
• ∑F_y = n - w = 0

The two forces acting on the object in the y-direction must subtract to become 0 since the net force must be 0.

Therefore, by adding w to both sides of the equation, we get:

• ∑F_y = n = w

We know that n = w, so by solving for the weight force we can find the normal force.

The weight force w can also be written as mg, where m = mass (kg) and g = 9.8 m/s² (acceleration due to gravity).

We are given the mass of the object, so we can plug it into mg to solve for the weight force.

• w = mg = (12 kg)(9.8 m/s²)
• w = 117.6 N

The weight force is equal to 117.6 N, and since the normal force is equal to the weight force, we can say that the normal force is also equal to 117.6 N.

Now that we have the normal force, we can plug it into the formula for the force of kinetic friction:

• fₖ = μₖ * n

• fₖ = (0.6) * (117.6)

• fₖ = 70.56 N

The force of kinetic friction between the object and the surface is 70.56 N.

FBD:

Answer 2

`F_s^(k) = 70.56 \ N`

General Formulas and Concepts:

Physics 1 - Newton's Law of Motion

• Gravity: 9.8 m/s²
• Static/Kinetic Friction Formula:
  `F_s^k = F_n \cdot U_k`
• Free Body Diagram

Step-by-step explanation:

Step 1: Define Variables

`Mass = 12 \ kg`

`U_k = 0.6`

Step 2: Find Normal Force

See Attachment for FBD.

1. Substitute: Fg = (12 kg)(9.8 m/s²)
2. Multiply: Fg = 117.6 N
3. Redefine: Fn = 117.6 N

Step 3: Find Kinetic Friction

1. Substitute: Fs = (117.6 N)(0.6)
2. Multiply: Fs = 70.56 N