Q35 of 42 Page 35

When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

Here, we have two cases, one with friction and one without friction. The distance travelled by the block in both cases is same.

Let the distance travelled by the block be “s” the mass of the block be “m”, the coefficient of friction be “μ” and the acceleration due to gravity be “g”. The angle made by the incline with the ground is θ .


Case:1 No friction


The equation of motion is



Here, initial velocity, u = 0



Acceleration in the incline frame of reference is, a=g(sinθ)




Case:2 With Friction


Here, we first calculate the acceleration.


From the free body diagram,




Using this acceleration in the equation of motion. The time taken is given by t’.




We know t’=pt


Substituting the values of t’, and t



Squaring both sides and simplifying,




Given, θ=45°



More from this chapter

All 42 →
33

A person in an elevator accelerating upwards with an acceleration of 2 m s-2, tosses a coin vertically upwards with a speed of 20 m s1. After how much time will the coin fall back into his hand? (g = 10 m s-2)

 34

There are three forces F1, F2 and F3 acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.

(a) Show that the forces are coplanar.


(b) Show that the torque acting on the body about any point due to these three forces is zero.


 36

Figure 5.9 shows (vx ,t ),and( (vy ,t) diagrams for a body of unit mass. Find the force as a function of time.


 37

A racing car travels on a track (without banking) ABCDEFA (Fig. 5.10). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m s-1. Find the minimum time for completing one round.