Question

Two gliders move frictionlessly towards each other. Glider A has a mass of 2.5 kg and is moving right at a speed of 3.0 m/s. Glider B has a mass of 2.1 kg and is moving left at a speed of 1.2 m/s. Glider B is cushioned by a spring with a spring constant of 1.5 × 10⁴ N/m. Determine the maximum compression of the spring during the collision.

Your Answer:

Answer 1

The law of conservation of energy gives

$$\frac{kx^2}{2}=\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}$$

$$x=\sqrt{\frac{m_1v_1^2+m_2v_2^2}{k}}$$

$$x=\sqrt{\frac{2.5*3.0^2+2.1*1.2^2}{1.5*10^4}}=0.041\:\rm m=4.1\:\rm cm$$