Question

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches 30o , the box starts to slip and slides 2.5 m down the plank in 4.0 s. Calculate the coefficients of friction.

Answer 1

Answer:

the coefficients of static friction is 0.577

the coefficients of fkinetic friction is 0.54

Step-by-step explanation:

given information

θ = 30°

S = 2.5 m

t = 4 s

- Static friction

F - F(friction) = 0

W sin θ = μs W cos θ  

μs = sin θ/ cosθ

   = tan θ

   = tan 30°

   = 0.577

- kinetic friction

S = $v_{0} t$ + $\frac{1}{2} at^{2}$

$v_{0} t$ = 0

S = $\frac{1}{2} at^{2}$

a = $\frac{2S}{T^{2} }$ = $\frac{2 x 2.5}{4^{2} }$

  = 0.3 $m/s^{2}$

F - F(friction) = m a

W sin θ - μ W cos θ  = m a

mg sin θ - μk mg cos θ  = m a

g sin θ - μk g cos θ  = a

μk = g sin θ  - a / g cos θ

    = 9.8 sin 30° - 0.3 / 9.8 cos 30°

    = 0.54