9.3.1 Relativistic Momentum

Question 1

Relativistic Momentum

Answer 1

• While different observers in different reference frames may not agree on the value of a system’s momentum, they will always agree that momentum is conserved.
• The classical definition of momentum, , is not consistent with conservation of momentum at relativistic speeds.
• The relativistic definition of momentum is .
• The relativistic form of Newton’s second law is , where pis the relativistic momentum.

Question 2

According to Newton’s laws, in an isolated system, momentum is conserved. The conservation of momentum principle can be expressed in several equivalent forms. Which of the following is not equivalent to the momentum conservation law?

Answer 2

p = 0

Question 3

In the non-relativistic case, as v increases, the momentum of p also increases. Because v has no upper limit,t he momentum can increase definitively. Evaluate the following as true or false. In the relativistic case, because v < c, the momentum cannot grow without limit.

Answer 3

false

Question 4

Two objects A and B have equal momenta. The mass of A is half that off B. Based on Newton’s laws, what can you conclude about the velocities vA and vB?

Answer 4

vA = 2vB

Question 5

Which of the following is the relativistic momentum of a particle that is moving with speed v = 0.886c? Assume that the rest mass is m0.

Answer 5

5.2*10^8 m0

Question 6

A particle has rest mass m0 in an inertial frame. How is the mass of m affected if the particle is moving with velocity v?

Answer 6

m > m0

Question 7

Which of the following relationships describes the relativistic definition of momentum?

Answer 7

p = gm0v

Question 8

An observer O notes a particle moving to the right with velocity v. Another observer O’ is moving with the speed of v relative to O along the direction of the motion of the particle. Which of the following are values of mass measured by O and O’?

Answer 8

O measure m and O’ measures m0

Question 9

According to Newton’s second law, an unbalanced force causes an object to accelerate: F = ma. An alternative view of force is obtained by expressing the right-hand side as d/dt(mv); therefore, F = d(mv)/dt. If F /= 0, what happens to the momentum of an object?

Answer 9

Momentum changes.

Question 10

True or false?
In Newtonian physics, momentum is defined as the product of mass and velocity. The momentum of an object is the same for all inertial observers.

Answer 10

false