Achair 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.

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

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