Advertisements
Advertisements
Question
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°.
Advertisements
Solution
Consider the diagram below for a general collision.
By the principle of conservation of linear momentum,
P = P1 + P2
For inelastic collision, some KE is lost, hence `p^2/(2m) > p_1^2/(2m) + p_2^2/(2m)`
∴ `p^2 > p_1^2 + p_2^2`
Thus, p, p1 and p2 are related as shown in the figure.
θ is acute (less than 90) `(p^2 = p_1^2 + p_2^2 "would given" θ = 90^circ)`
APPEARS IN
RELATED QUESTIONS
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.
Total energy of a system is always conserved, no matter what internal and external forces on the body are present.
Answer carefully, with reason:
If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy.)
A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s–1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?
Answer the following question.
Obtain its value for an elastic collision and a perfectly inelastic collision.
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.
Define the following:
Coefficient of restitution
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 ______.
Two bodies of masses 3 kg and 2 kg collide bead-on. Their relative velocities before and after collision are 20 m/s and 5 m/s respectively. The loss of kinetic energy of the system is ______.
During inelastic collision between two bodies, which of the following quantities always remain conserved?
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 ______.
A ball of mass m, moving with a speed 2v0, collides inelastically (e > 0) with an identical ball at rest. Show that for head-on collision, both the balls move forward.
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.
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 ______.
A sphere of mass 'm' moving with velocity 'v' collides head-on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is ______. ( e is coefficient of restitution and collision is inelastic)
Before collision, what is the position of objects?
Which of the following real-life scenarios is the best example of a collision as defined in the source?
