Question

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively :

Answer 1

Direct apply the concept of

Angle of repose.Thanks

Answer 2

Answer:

The coefficient of static friction of the wood on the tilted plank at 30° is 0.6 whereas for the kinetic friction it's 0.5.

Explanation:

Step 1 : Write down the relevant formulas to work out this question.

Let Mk be the coefficient of kinetic friction whereas Ms be the coefficient of static friction and © Be the angle of inclination.

The respective formulas are:

Ms = Tan ©

S = ut + ½at²

a = g(Sin © - MkCos©)

S = ut + ½gt²Sin© - ½gt²MkCos ©

S - ut - ½gt²Sin © = - ½gt²MkCos ©

Dividing through by - 1:

ut + ½gt²Sin © - S = ½gt²Mk Cos ©

Mk = (ut + ½gt²Sin © - S) / (½gt² Cos ©)

Step 2 : Identify the given values in the question.

© = 30°

S = 4 m

t = 4 seconds

g = 10 m/s²

u = 0 m/s (box starts from rest)

Step 3: Substitute the values in the formula.

Ms = Tan 30 = 0.5774

Mk = (½ × 10 × 4² × Sin 30 - 4) / (½ × 10 × 4² × Cos 30)

= 0.5196

Lets round off the values to 1 decimal place each.

Ms = 0.6

Mk = 0.5