Exercises on Conservation of Momentum

Helena Dedic

Beware: Many of the solutions to these exercises use $g=10m/s^{2}$ !

Exercise 1

Consider a 20-g bullet (B) and a 60-kg athlete (A).

(a) If they have the same momentum, what is the ratio of their kinetic energies $K_{B} \over K_{A}$ ?

(b) If they have the same kinetic energy, what is the ratio of their momenta $p_{B} \over p_{A}$ ?

SOLUTION EX 1

Exercise 2

What is the change of momentum of a particle when a net force of 1000 N pointing in the direction 37° West of North acts on it for one millisecond?

SOLUTION EX 2

Exercise 3

The total momentum of a system of three particles has zero y-component. The momentum of the first particle has a magnitude of 96 ${\tfrac {kgm}{s}}$ and points in the direction of 60° East of South. The momentum of the second particle has a magnitude of 167 ${\tfrac {kgm}{s}}$ and points in the direction of 53° North of East. The third particle moves in the direction of 60° South of West. Determine the magnitude and the direction of the total momentum of the system and the magnitude of the momentum of the third particle.

SOLUTION EX 3

Exercise 4

A 10,000-kg truck moves at 30 m/s. At what speed would a 1200 kg car have the same value of

(a) linear momentum;

(b) kinetic energy?

SOLUTION EX 4

Exercise 5

A 6-kg bomb moving at 5 m/s in the direction 37° South of East explodes into three pieces. A 3-kg piece moves off at 2 m/s at 53° North of East while a 2-kg piece moves West at 3 m/s. What is the velocity of the third fragment? Assume all motion occurs in a horizontal plane.

SOLUTION EX 5

Exercise 6

A nucleus of radioactive radium ( $^{226}Ra$ ), initially at rest, decays into a radon nucleus ( $^{222}Rn$ ) and an $\alpha$ particle (a $^{4}He$ ). The kinetic energy of the $\alpha$ particle is $6.72\times 10^{-13}J$ after the decay. The mass of $^{226}Ra$ is 226 $u$ ; the mass of radon is 222 $u$ and the mass of $^{4}He$ is 4 $u$ . You may recall from chemistry that a unified mass unit $u=1.66\times 10^{-27}kg$ .