Question

a group of particles has a net momentum equal to zero. which of the following must be true?
i. the speed of each particle is zero.
ii. the velocity of each particle is zero.
iii. the mass of each particle must be equal.
iv. the kinetic energy of each particle must be zero.
none of the above is true.
ii only
iii only
i only
i and iv
i and iii
iv only

Explanation:

• Statement I: Just because the net momentum is zero doesn't mean each particle's speed is zero. For example, two particles of equal mass moving in opposite directions with the same speed have a net momentum of zero, but their speeds are non - zero.
• Statement II: Similar to speed, velocity of each particle isn't necessarily zero. The vector sum (net momentum) being zero doesn't imply individual velocity vectors are zero (as in the two - particle opposite - motion example).
• Statement III: Masses of particles don't have to be equal. Consider three particles: \(m_1 = 1\space kg\), \(v_1= 2\space m/s\); \(m_2 = 2\space kg\), \(v_2=- 1\space m/s\); \(m_3\) (any mass), \(v_3 = 0\space m/s\). The net momentum \(p_{net}=m_1v_1 + m_2v_2+m_3v_3=(1\times2)+(2\times(- 1))+(m_3\times0)=0\), and masses are not all equal.
• Statement IV: Kinetic energy \(K=\frac{1}{2}mv^{2}\). Using the two - particle opposite - motion example (non - zero speeds), kinetic energy of each particle is non - zero.

Answer:

None of the above is true.