Question

A block is given certain upward
velocity along the incline of
elevation a. The time of ascent to
upper point was found to be half the
time of descent to initial point. The
co-efficient of friction between
block and incline is:​

Answer 1

The coefficient of friction between  block and incline is μ  = 0.6 tanα  

Explanation:

• a1 = (g sin a + μg cos a)   -----(1)
• According to the second equation of motion  
• S = ut1 - 1 / 2 (gsin α + μg cos α)t1^2   ----(2)

Now  

t1 = t2 / 2

S =  1 / 2 (gsin α + μg cos α )t1^2

0 = u - (gsin α + μg cos α )t1^2

μ = gsinα + μg cos α )t1 ----(3)

t1 = √2s / gsinα + μg cos α  

t2 = √2s / gsinα -  μg cos α  

μ  = 3 /5 tan α

μ  = 0.6 tanα  

Thus the co-efficient of friction between  block and incline is μ  = 0.6 tanα