Advertisements
Advertisements
प्रश्न
Define coefficient of restitution.
Advertisements
उत्तर
For two colliding bodies, the negative of the ratio of the relative velocity of separation to the relative velocity of approach is called the coefficient of restitution.
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.
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)?
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 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?
Consider the decay of a free neutron at rest : n → p + e–
Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution in the β-decay of a neutron or a nucleus
Answer the following question.
Obtain its value for an elastic collision and a perfectly inelastic collision.
Answer the following question.
A bullet of mass m1 travelling with a velocity u strikes a stationary wooden block of mass m2 and gets embedded into it. Determine the expression for loss in the kinetic energy of the system. Is this violating the principle of conservation of energy? If not, how can you account for this loss?
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.
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.
Define the following:
Coefficient of restitution
Arrive at an expression for elastic collision in one dimension and discuss various cases.
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 block of mass 'm' moving on a frictionless surface at speed 'v' collides elastically with a block of same mass, initially at rest. Now the first block moves at an angle 'θ' with its initial direction and has speed 'v1'. The speed of the second block after collision 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 ____________.
In inelastic collision, ____________.
A block of mass 'm' moving along a straight line with constant velocity `3vec"v"` collides with another block of same mass at rest. They stick together and move with common velocity. The common velocity is ______.
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.
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 ball of mass 10 kg moving with a velocity of 10`sqrt3` ms–1 along the X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis.
The configuration of pieces after the collision is shown in the figure.
The value of θ to the nearest integer is ______.
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 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 ______.
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)
Answer carefully, with reason:
Is the total linear momentum conserved during the short time of an inelastic collision of two balls ?
In a collision, what type of interaction occurs between objects?
