Question

1. How fast is the collision crash of 5,000kg car moving with a velocity of 5.2m/s that hits a stationary 8000kg truck on a frictionless track?

2. A bullet with 2.0 g mass and 300 m/s velocity hits a wooden trolley with 1.5 kg mass which is at rest on a frictionless track. Determine the final velocity of the wooden trolley.

Answer 1

1) Let's assume that the car and truck hook together in the collision. Then, applying the law of conservation of energy, we get:

$$m_1v_1=(m_1+m_2)v_c,$$ $$v_c=\dfrac{mv_1}{m_1+m_2}=\dfrac{5000\ kg\times5.2\ \dfrac{m}{s}}{5000\ kg+8000\ kg}=2\ \dfrac{m}{s}.$$

2) Let's assume that the bullet becomes embedded in the wood block. Then, applying the law of conservation of energy, we can find the common velocity of the bullet and wooden block:

$$m_1v_1=(m_1+m_2)v_c,$$ $$v_c=\dfrac{mv_1}{m_1+m_2}=\dfrac{0.002\ kg\times300\ \dfrac{m}{s}}{0.002\ kg+1.5\ kg}=0.4\ \dfrac{m}{s}.$$