You need to move a 128-kg sofa to a different location in the room. It takes a force of 99 N to start it moving. What is the coefficient of static friction between the sofa and the carpet?
F=μmg
μ=F/mg=99/128•9.8= 0.079
To determine the coefficient of static friction between the sofa and the carpet, we can use the formula:
Coefficient of static friction (μ_s) = Force required to start the object moving (F_s) / Normal force (N)
The normal force is the force exerted by a surface perpendicular to the object. In this case, it is equal to the weight of the sofa, which can be calculated using the formula:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given:
Mass of the sofa (m) = 128 kg
Force required to start the sofa moving (F_s) = 99 N
Acceleration due to gravity (g) = 9.8 m/s^2
First, we can calculate the weight of the sofa:
Weight (W) = mass (m) * acceleration due to gravity (g)
W = 128 kg * 9.8 m/s^2
Next, we can calculate the coefficient of static friction:
Coefficient of static friction (μ_s) = Force required to start the object moving (F_s) / Normal force (N)
μ_s = F_s / W
Now we can substitute the given values and solve for the coefficient of static friction:
μ_s = 99 N / (128 kg * 9.8 m/s^2)
Calculating this expression will give us the coefficient of static friction between the sofa and the carpet.