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.
1 answer:
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
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