Question

A force of 36.0 N is required to start a 3.0-kg box moving across a horizontal concrete floor. Part A) What is the coefficient of static friction between the box and the floor? Express your answer using two significant figures. Part B) If the 36.0-N force continues, the box accelerates at 0.54 m/s^2. What is the coefficient of kinetic friction? Express your answer using two significant figures.

Answer 1

Answer:

A) 1.2

B) 1.1

Explanation:

A)

F = force required to start the box moving = 36.0 N

m = mass of the box = 3 kg

$F_{g}$  = weight of the box = mg = 3 x 9.8 = 29.4 N

$F_{n}$  = normal force acting on the box by the floor

normal force acting on the box by the floor is given as

$F_{n}$  = $F_{g}$ = 29.4

$F_{s}$  = Static frictional force = F = 36.0 N

$\mu _{s}$ = Coefficient of static friction

Static frictional force is given as

$F_{s}$  = $\mu _{s}$ $F_{n}$

36.0  = $\mu _{s}$ (29.4)

$\mu _{s}$ = 1.2

B)

a = acceleration of the box = 0.54 m/s²

F = force applied = 36.0 N

$f_{k}$ = kinetic frictional force

$\mu _{k}$ = Coefficient of kinetic friction

force equation for the motion of the box is given as

F - $f_{k}$ = ma

36.0 - $f_{k}$ = (3) (0.54)

$f_{k}$ = 34.38 N

Coefficient of kinetic friction is given as

$\mu _{k}=\frac{f_{k}}{F_{n}}$

$\mu _{k}=\frac{34.38}{29.4}$

$\mu _{k}$ = 1.1