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

the coefficients of static friction is 0.577

the coefficients of fkinetic friction is 0.54

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` +
`(1)/(2) at^(2)`

`v_(0) t` = 0

S =
`(1)/(2) at^(2)`

a =
`(2S)/(T^(2) )` =
`(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