Question

A car and a truck have the same kinetic energies at a certain instant while they are moving along two parallel roads. (Assume that the truck is heavier than the car)

1. Which one will have greater momentum?

2. Write the relationship between kinetic energy and linear momentum.

3. If the mass of truck is 100 times greater than that of the car, find the ratio between their velocities.

Answer 1

1. Kinetic energy, of car, K.E_c = \(\frac{P^2_c}{2m_c}\)

Kinetic energy of truck,

Since m_c < m_t

Hence P_t > P_c

∴ momentum of truck is greater than car.

2. KE = P²/2m.

3. KE_c = KE_t

1/2m_c V_c² = 1/2 x m_tV_t²

But m_t = 100m_c

V²_t= \(\frac{V^2_c}{100}\)

Velocity of truck, V_t =\(\frac{V_c}{10}\)

ratio of velocity, 10V_t = V_c

10:1.