Advertisements
Advertisements
प्रश्न
Answer the following question.
Discuss the following as special cases of elastic collisions and obtain their exact or approximate final velocities in terms of their initial velocities.
- Colliding bodies are identical.
- A very heavy object collides on a lighter object, initially at rest.
- A very light object collides on a comparatively much massive object, initially at rest.
Advertisements
उत्तर
The final velocities after a head-on elastic collision is given as,
`"v"_1 = "u"_1 [("m"_1 - "m"_2)/("m"_1 + "m"_2)] + "u"_2["2m"_2/("m"_1 + "m"_2)]`
`"v"_1 = "u"_1["2m"_1/("m"_1 + "m"_2)] + "u"_2[("m"_2 - "m"_1)/("m"_1 + "m"_2)]`
- Colliding bodies are identical
If m1 = m2, then v1 = u2 and v2 = u1. Thus, objects will exchange their velocities after head on elastic collision. - A very heavy object collides with a lighter object, initially at rest.
Let m1 be the mass of the heavier body and m2 be the mass of the lighter body i.e., m1 >> m2; the lighter particle is at rest i.e., u2 = 0 then,
m1 ± m2 ≅ m1 and `"m"_2/("m"_1 + "m"_2) ~= 0,`
∴ v1 ≅ u1 and v2 ≅ 2u1
i.e., the heavier colliding body is left unaffected and the lighter body which is struck travels with double the speed of the massive striking body. - A very light object collides on a comparatively much massive object, initially at rest.
If m1 is the mass of a light body and m2 is the mass of a heavy body i.e., m1 << m2 and u2 = 0. Thus, m1 can be neglected.
Hence v1 ≅ - u1 and v2 ≅ 0.
i.e., the tiny (lighter) object rebounds with the same speed while the massive object is unaffected.
APPEARS IN
संबंधित प्रश्न
In an inelastic collision of two bodies, the quantities which do not change after the collision are the ______ of the system of two bodies.
State if the following statement is true or false. Give a reason for your answer.
In an elastic collision of two bodies, the momentum and energy of each body is conserved.
State if the following statement is true or false. Give a reason for your answer.
In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V. If the collision is elastic, which of the following figure is a possible result after collision?
Which of the following potential energy curves in Fig. cannot possibly describe the elastic collision of two billiard balls? Here r is distance between centres of the balls.
Define coefficient of restitution.
Solve the following problem.
A spring ball of mass 0.5 kg is dropped from some height. On falling freely for 10 s, it explodes into two fragments of mass ratio 1:2. The lighter fragment continues to travel downwards with a speed of 60 m/s. Calculate the kinetic energy supplied during the explosion.
In Rutherford experiment, for head-on collision of a-particles with a gold nucleus, the impact parameter is ______.
A ball of mass 0.1 kg makes an elastic head-on collision with a ball of unknown mass, initially at rest. If the 0 .1 kg ball rebounds at one-third of its original speed, the mass of the other ball is ______.
A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of mass 3 kg is 16 m/s, The kinetic energy of mass 6 kg is ____________.
A particle of mass 'm' collides with another stationary particle of mass 'M'. A particle of mass 'm' stops just after collision. The coefficient of restitution is ______.
A bullet fired from gun with a velocity 30 m/s at an angle of 60° with horizontal direction. At the highest point of its path, the bullet explodes into two parts with masses in the ratio 1:3. The lighter mass comes to rest immediately. Then the speed of the heavier mass is
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V as shown in figure.
If the collision is elastic, which of the following (Figure) is a possible result after collision?
A cricket ball of mass 150 g moving with a speed of 126 km/h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001s, the force that the batsman had to apply to hold the bat firmly at its place would be ______.
Two blocks M1 and M2 having equal mass are free to move on a horizontal frictionless surface. M2 is attached to a massless spring as shown in figure. Iniially M2 is at rest and M1 is moving toward M2 with speed v and collides head-on with M2.
- While spring is fully compressed all the KE of M1 is stored as PE of spring.
- While spring is fully compressed the system momentum is not conserved, though final momentum is equal to initial momentum.
- If spring is massless, the final state of the M1 is state of rest.
- If the surface on which blocks are moving has friction, then collision cannot be elastic.
A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that for a general collision, the angle between the two velocities of scattered balls is less than 90°.
The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in figure.
If the length of the pendulum is 1 m, calculate
- the height to which bob A will rise after collision.
- the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.
Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (Figure). One of the bobs is released after being displaced by 10° so that it collides elastically head-on with the other bob.
- Describe the motion of two bobs.
- Draw a graph showing variation in energy of either pendulum with time, for 0 ≤ t ≤ 2T, where T is the period of each pendulum.
A particle of mass m with an initial velocity u`hat"i"` collides perfectly elastically with a mass 3m at rest. It moves with a velocity v`hat"j"` after collision, then, v is given by :
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and required 1 s to cover. How long the drunkard takes to fall in a pit 13 m away from the start?
An insect moves with a constant velocity v from one corner of a room to other corner which is opposite of the first corner along the largest diagonal of room. If the insect can not fly and dimensions of room is a × a × a, then the minimum time in which the insect can move is `"a"/"v"`. times the square root of a number n, then n is equal to ______.
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms-1 gets embedded in it, then loss of kinetic energy will be ______.
An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is ______.
Three identical blocks A, B and C are placed on horizontal frictionless surface. The blocks A and C are at rest. But A is approaching towards B with a speed 10 m/s. The coefficient of restitution for all collision is 0.5. The speed of the block C just after the collision is ______.
Before collision, what is the position of objects?
