Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
a. Consider the adjacent diagram in which the bob B is displaced through an angle θ and released.
At t = 0, suppose bob B is displaced by θ = 10° to the right. It is given potential energy E1 = E. Energy of A, E2 = 0
When B is released, it strikes A at t = T/4. In the head-on elastic collision between B and A comes to rest and A gets the velocity of B. Therefore. E1 = 0 and E2 = E. At t = 27T/4, B reaches its extreme right position when KE of A is converted into PE = E2 = E. Energy of B, E1 = 0.
At t = 3T/4, A reaches its mean position. when its PE is converted into KE = E2 = E. It collides elastically with B and transfers the whole of its energy to B. Thus, E2 = 0 and E1 = E. The entire process is repeated.
b. The values of energies of B and A at different time intervals are tabulated here. The plot of energy with time 0 ≤ t ≤ 2T is shown separately for 8 and A in the figure below.
| Time (t) | Energy of A (E1) |
Energy of B (E2) |
| 0 | E | 0 |
| T/4 | 0 | E |
| 2T/4 | 0 | E |
| 3T/4 | E | 0 |
| 4T/4 | E | 0 |
| 5T/4 | 0 | E |
| 6T/4 | 0 | E |
| 7T/4 | E | 0 |
| 8T/4 | E | 0 |
APPEARS IN
संबंधित प्रश्न
Answer carefully, with reason:
In an inelastic 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 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.
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.
Solve the following problem.
A marble of mass 2m travelling at 6 cm/s is directly followed by another marble of mass m with double speed. After a collision, the heavier one travels with the average initial speed of the two. Calculate the coefficient of restitution.
What is inelastic collision? In which way it is different from an elastic collision. Mention a few examples in day-to-day life for inelastic collision.
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 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 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 ______.
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.
A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses `(m/M)` is `1/x`. The value of 'x' will be ______.
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?
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?
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 ______.
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 ______.
What is a collision?
