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 $\frac{K_B}{K_A}$?

(b) If they have the same kinetic energy, what is the ratio of their momenta $\frac{p_B}{p_A}$?

• 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 $\frac{kgm}{s}$ and points in the direction of 60° East of South. The momentum of the second particle has a magnitude of 167 $\frac{kgm}{s}$ 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 $u=1.66\times 10^{-27}kg$.

(a) Determine the recoil speed of the radon nucleus.

(b) Determine its kinetic energy.

• SOLUTION EX 6