View source for Exercises on Conservation of Momentum

''Helena Dedic''

<span style="color:Red"><u>'''Beware:</u></span> Many of the solutions to these exercises use <math>g = 10 m/s^2</math> !'''
<br>

==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 <math>K_B \over K_A</math>?

(b) If they have the same kinetic energy, what is the ratio of their momenta <math>p_B \over p_A</math>?<br><br>

*[[Conservation of Momentum EX 1|SOLUTION EX 1]]<br><br>

==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?<br><br>

*[[Conservation of Momentum EX 2|SOLUTION EX 2]]<br><br>

==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 <math>\tfrac{kg m}{s}</math> and points in the direction of 60° East of South. The momentum of the second particle has a magnitude of 167 <math>\tfrac{kg m}{s}</math> 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.<br><br>

*[[Conservation of Momentum EX 3|SOLUTION EX 3]]<br><br>

==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?<br><br>

*[[Conservation of Momentum EX 4|SOLUTION EX 4]]<br><br>

==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.<br><br>

*[[Conservation of Momentum EX 5|SOLUTION EX 5]]<br><br>

==Exercise 6==

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

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

(b) Determine its kinetic energy.<br><br>

*[[Conservation of Momentum EX 6|SOLUTION EX 6]]<br><br>