Engineering Mechanics

(^566) „„„„„ A Textbook of Engineering Mechanics
Notes.1.In such cases, we do not apply the principle of momentum (i.e., equating the initial mo-
mentum and the final momentum), since the fixed plane has infinite mass.
2.If a body is allowed to fall from some height on a floor, then the velocity, with which the
body impinges on the floor, should be calculated by the relations of plane motion as dis-
cussed below :
Let H = Height from which the body is allowed to fall.
∴ Velocity with which the body impinges on the floor,
ugH= 2

3. If a body is first projected upwards from the ground with some initial velocity, it will
   reach the greatest height and will return to the ground with the same velocity, with which it was
   projected upwards.
   Example 27.8. From a point, on a smooth floor of a room, a toy ball is shot to hit a wall. The
   ball then returns back to the point of projection. If the time taken by the ball in returning is twice the
   time taken in reaching the wall, find the coefficient of restitution between the ball and the wall.
   Solution.
   Let s = Distance between the point of shot and the wall, and
   t = Time taken by the ball in reaching the wall.
   ∴Time taken by the ball in returning to the point of shot
   = 2t ...(given)
   Let e = Coefficient of restitution between the ball and the wall.
   Since the ball is rolling on a smooth floor, therefore its velocity will remain constant.
   ∴ Velocity, with which the ball will hit the wall,
   Distance
   Time

s

u

t

== ...(i)

and velocity with which the ball will rebound after hitting,

Distance

Time 2

s

v

t

== ...(ii)

We know that the velocity after hitting (v),

2

ss

eu e

tt

==×

∴

1

0.5

2

e== Ans.

Example 27.9. A ball is dropped from a height h 0 = 1 m on a smooth floor. Knowing that the

height of the first bounce is h 1 = 81cm, determine

(a) coefficient of restitution, and

(b) expected height h 2 after the second bounce.

Solution. Given : Height from which the ball is dropped (h 0 ) = 1m and height to which the

ball rose after first bounce (h 1 ) = 81 cm. = 0.81 m.

(a) Coefficient of restitution

Let e = Coefficient of restitution.

We know that the velocity with which the ball impinges on the floor,

ugh g==×=2212m/s 0 g ...(i)