Advertisements
Advertisements
प्रश्न
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.)
Advertisements
उत्तर
The potential energy depends on the separation distance between centres; this means that during the collision, the force acting between the bodies is conservative; therefore, energy will be conserved. Thus, the collision will be elastic.
APPEARS IN
संबंधित प्रश्न
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 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.
Arrive at an expression for elastic collision in one dimension and discuss various cases.
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 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?
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.
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls (i.e., when they are in contact).
- Kinetic energy.
- Total linear momentum?
Give reason for your answer in each case.
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°.
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.
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 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 ______.
Answer carefully, with reason:
Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?
What do the objects do "after collision"?
Before collision, what is the position of objects?
