oblique collision

Mohammed Asif

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Topic : Ph : 9391326657, 64606657

OBLIQUE COLLISION IN CASE OF SMOOTH SURFACES

a) Common – Normal (C. N)Force is excerted in CN direction only. Both bodies exert equal and

opposite forces (action and reaction) on each other.

Hence momentum and velocities change accordingly in CN – direction.

Momentum changes in CN direction only.Apply e (coefficient of restitution) in the CN direction only.

b) Common – Tangent (C. T)f = 0 in case of smooth surfacef = u (Normal reaction) in case of rough surface. Then changed

velocity will be (e m) times.

Neither momentum nor velocity changes in C T – direction.

(Q) Two point particles A and B are placed in line on a frictionless horizontal plane. If particle A (Mass 1 kg) is moved with velocity 10 m/s towards stationary particle B (Mass 2 kg) and after collision. The two move at an angle of 450 with the initial direction of motion, then find

a) Velocities of A and B just after collision?b) Coefficient of restitution?

Sol: - The very first step to solve such problems is to find the line of impact which is along the direction of force applied by A on B, resulting the stationary particle B to move.

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Thus by watching the direction of motion of B, line of impact is along the direction of motion of B, (I e) 450 with the initial direction of motion of A.

a) Let us apply the principle of conservation of momentum along x - direction

Along y – direction

Solving the two equations

2) A smooth ball of mass 1 kg is projected with velocity 7 m/s horizontal from a tower of height 3.5 m. It collides elastically with a wedge of mass 3 kg and inclination of 450 kept on ground. The ball collides with the wedge at a height of 1 m above the ground. Find the velocity of the wedge and the ball after collision. (Neglect friction at any contact).Apply L. C. L. M in Horizontal direction

Sol: -

Let the ball rebounds with velocity V and v1 be the



velocity of the wedge.

Solving (1) and (2) , we get

3) After a totally inelastic – collision, two objects of the same mass and same initial speeds are found to move together at half of their initial speeds. The angle between the initial velocities of the objects is ____

Along x – axis

Along y – axis

Solving (1) and (2) we get

Required angle

4) A 8 gm bullet is fired horizontally in to a 9 kg block of wood and stick in it. The block which is free to move, has a velocity of , after the impact. Find the velocity of the bullet. Also calculate the heat dissipated in collision?

Sol: -

Heat dissipated = loss in k. t

= 809. 3 J

5) A ball of mass 1kg collides with another ball of mass 1 kg at an angle 300

with the x – axis with a velocity of 1 m/s. Find the final velocities if after collision both the masses go at 450 as shown in figure?

Sol: - Initial momentum along x – axis



Initial momentum along y – axis

finial momentum along x – axis

finial momentum along y – axis

Solving (1) and (2)

6) A rubber ball is released from a height h above the floor. It bounces repeatedly always rising to 0.81 times of the height through which it falls.a) Ignoring the practical fact that the ball has finite size, find the total distance it has

travelledb) Determine the time required for infinite number of bouncesc) Determine its average speed.

Sol: -

b)



c) Average speed

7) An explosion blows a rock into three parts. Two pieces go off at right angle to each other, 1 kg piece with a velocity of 12 m/sec and 2 kg piece with a velocity of 8 m/sec. The third piece flies off with a velocity 40 m/sec. Complete the mass of third rock?

Sol: - Initial momentum = 0Along x – axis

Along y – axis

Squaring and adding

8) A wedge of mass M rests on a horizontal surface. The inclination of the wedge is . A ball of mass M moving horizontally with speed u hits the inclined face of the wedge inelastically and after hitting slides up the inclined face of the wedge. Find the velocity of the wedge just after collision. (Neglect any friction)

Sol: - Let velocity of the wedge after collision is v1 and that of the ball is v2 with respect to wedge.

As the net impulse on the system in the horizontal direction = 0

Since common normal is along y1

therefore momentum of the ball remains constant along the incline (along x1 as F x

1 = 0 for ball)



From Eqn (1) and (2), we get

e = 0 is satisfied for perfectly inelastic collision. Also balls velocity will make angle less than with the horizontal.

9) A ball is thrown onto a rough floor at angle of . If it rebounds at the

same angle . Find the coefficient of kinetic friction between the floor and the ball. The coefficient of restitution, e = 0.6.

Sol: - along x – axis

Along y – direction

And

From (1) , (2) and (3) we get

10) A simple pendulum of mass M and length L is suspended from the trolley of mass M as shown in figure. If the system is released from rest at ,

find the velocity of trolley when . (Neglect friction)

Sol: - Let v = velocity of trolley at

Total energy of system = m g

L

Total energy at

L. C. Energy

M g L

L. C. L. M at



From (1) and (2), we get

M g L

11) Two blocks of mass 3kg and 6 kg respectively are placed m a smooth horizontal surface. They are connected by a alight spring of force constant K = 200 N/m. Initially the spring is un stretched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be by momentum con

Sol: - By energy conservation

12) A smooth ring is kept on a smooth horizontal surface. From point C of the ring a particle is projected at an angle to the radius vector at C. If e is the coefficient of restitution between the ring and the particle show that the particle will return to the point of projection

after two reflections if tan

Sol: - from figure

At point B,

And

Similarly, at point A,

And

As particles comes back at the original position,

(or)



(or)



oblique collision

Documents

velocity v

v cos45

v sin450

sin45 v sin

b a0a50v v cos

sv v soit

cn direction

y direction