Question

A 25kg box in released on a 27° incline and accelerates down the incline at 0.3 m/s2. Find the friction force impending its motion? What is the coefficient of kinetic friction?

A block is given an initial speed of 3m/s up a 25° incline. Coefficient of friction

Answer 1

a) μ = 0.475 , b) μ = 0.433

Step-by-step explanation:

a) For this exercise of Newton's second law, we create a reference system with the x-axis parallel to the plane and the y-axis perpendicular to it

X axis

Wₓ - fr = m a

the friction force has the expression

fr = μ N

y Axis

N -
`W_(y)` = 0

let's use trigonometry for the components the weight

sin 27 = Wₓ / W

Wₓ = W sin 27

cos 27 = W_{y} / W

W_{y} = W cos 27

N = W cos 27

W sin 27 - μ W cos 27 = m a

mg sin 27 - μ mg cos 27 = m a

μ = (g sin 27 - a) / (g cos 27)

very = tan 27 - a / g sec 27

μ = 0.510 - 0.0344

μ = 0.475

b) now the block starts with an initial speed of 3m / s. In Newton's second law velocity does not appear, so this term does not affect the result, the change in slope does affect the result

μ = tan 25 - 0.3 / 9.8 sec 25

μ = 0.466 -0.03378

μ = 0.433