Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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.
Answer carefully, with reason:
In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?
A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?
A bullet of mass 0.012 kg and horizontal speed 70 m s–1 strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.
Answer the following question.
Obtain its value for an elastic collision and a perfectly inelastic collision.
Solve the following problem.
A ball of mass 100 g dropped on the ground from 5 m bounces repeatedly. During every bounce, 64% of the potential energy is converted into kinetic energy. Calculate the following:
- Coefficient of restitution.
- The speed with which the ball comes up from the ground after the third bounce.
- The impulse was given by the ball to the ground during this bounce.
- Average force exerted by the ground if this impact lasts for 250 ms.
- The average pressure exerted by the ball on the ground during this impact if the contact area of the ball is 0.5 cm2.
Two different unknown masses A and B collide. A is initially at rest when B has a speed v. After collision B has a speed v/2 and moves at right angles to its original direction of motion. Find the direction in which A moves after the collision.
A ball moving with velocity 5 m/s collides head on with another stationary ball of double mass. If the coefficient of restitution is 0.8, then their velocities (in m/s) after collision will be ____________.
A mass M moving with velocity 'v' along x-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3v. After collision, the velocity of the combination 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 body of mas 'm' moving with speed 3 m/s collides with a body of mass '2m' at rest. The coalesced mass will start to move with a speed of ______.
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 head-on collision, both the balls move forward.
Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C and D in which the relation between potential energy V, kinetic energy (K) and total energy E is as given below:
Region A : V > E
Region B : V < E
Region C : K > E
Region D : V > K
State with reason in each case whether a particle can be found in the given region or not.
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.
A ball falls from a height of 1 m on a ground and it loses half its kinetic energy when it hits the ground. What would be the total distance covered by the ball after sufficiently long time?
A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is ______ m. (g = 10 m/s2)
