In a frame at rest with respect to the billiard table, a billiard ball of mass m moving with speed v strikes another billiard ball of mass m at rest. The first ball comes to rest after the collision while the second ball takes off with speed v in the original direction of the motion of the first ball. This shows that momentum is conserved in this frame. (a) Now, describe the same collision from the perspective of a frame that is moving with speed v in the direction of the motion of the first ball. (b) Is the momentum conserved in this frame?
In a frame at rest with respect to the billiard table, a billiard ball of mass m moving with speed v strikes another billiard ball of mass m at rest. The first ball comes to rest after the collision while the second ball takes off with speed v in the original direction of the motion of the first ball. This shows that momentum is conserved in this frame. (a) Now, describe the same collision from the perspective of a frame that is moving with speed v in the direction of the motion of the first ball. (b) Is the momentum conserved in this frame?
In a frame at rest with respect to the billiard table, a billiard ball of mass m moving with speed v strikes another billiard ball of mass m at rest. The first ball comes to rest after the collision while the second ball takes off with speed v in the original direction of the motion of the first ball. This shows that momentum is conserved in this frame. (a) Now, describe the same collision from the perspective of a frame that is moving with speed v in the direction of the motion of the first ball. (b) Is the momentum conserved in this frame?
A particle of mass m (particle #1) is fired head-on at speed 48 m/s toward another particle of mass 3m (particle #2) which is at rest. The result of this collision is that #1 comes to a complete stop, and #2 moves forward. (a) At what speed does particle #2 emerge from the collision? (b) What fraction of the original kinetic energy is lost during this process?
An atomic nucleus suddenly bursts apart (fission) into two pieces. Piece A with mass ma travels to the left with a speed of vA. Piece B with mass mg travels to the right with
speed vg. Show the velocity of piece B in terms of ma, mg and VA.
Solution:
Consider that the nucleus is not acted by an external force. Thus, momentum is conserved, so:
PBf + PAf = 0
Substituting the expression for momentum results to
mBV
mAV
= 0
Deriving the expression for the velocity of piece B results to
=(mA/m
VA
A cannon of mass M fires a projectile of mass m. The energy liberated in firing is E. Assume the projectile is discharged horizontally and that the cannon is mounted on wheels of a negligible mass. Using the fact that the energy E is taken up by both cannon and projectile and that momentum is conserved in the firing, do the following: A) Find the velocity of the projectile in terms of the masses and the energy E. B) By writing the velocity of the recoiling cannon in terms of the velocity of the projectile, find a relationship between the energy liberated, E, and the energy of the projectile. C) Explain what happens as M gets very large compared to m.
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