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 :
Answers
Direct apply the concept of
Angle of repose.Thanks
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