Question

A chair of mass 14.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force F = 43.0 N that is directed at an angle of 38.0 degrees below the horizontal and the chair slides with constant velocity along the floor.(a) Draw clearly labeled free-body diagram for the chair.(b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.(c) Find the coefficient of kinetic friction.

Answer 1

Answer: a) 110.3N b) 0.39

Explanation:

a) The normal reaction force acts in the vertical direction opposite the weight of the object(check attachment for diagram).

Since the object is inclined at 38° to the horizontal, the weight (W) will become Wcos38°.

Since the body is not moving vertically, its acceleration I'm the vertical direction will be zero.

According to newton's first law,

F = ma

Since we have two forces acting in the vertical direction, we will take their sum

R - Wcos38° = m(0)...1

Note that normal reaction (R) is acting in the positive y direction while the weight is in the negative y direction.

From 1,

R - Wcos38° = 0

R = Wcos38°

R = mg cos38°

R = 14×10×cos38°

R = 140cos38°

R = 110.3N

b) For the coefficient of friction,

Taking the sum of forces along x -direction

Fm - Ff = ma

Since a = 0(constant velocity)

Fm = Ff  = 43N

Note that Fm is the moving force (force that causes the body to move)

Ff = frictional force

Since Ff = nR

n is the coefficient of friction

43 = n× 110.3

n = 43/110.3

n = 0.39

Coefficient of kinetic friction = 0.39