Answer to Question #109342 in Mechanics | Relativity for Joe Duplantier

Question

Block 1, of mass m1 = 5.90 kg , moves along a frictionless air track with speed v1 = 17.0 m/s . It collides with block 2, of mass m2 = 59.0 kg , which was initially at rest. The blocks stick together after the collision.

A
Find the magnitude pi of the total initial momentum of the two-block system.

B
Find vf, the magnitude of the final velocity of the two-block system.

C
What is the change ΔK=Kfinal−Kinitial in the two-block system's kinetic energy due to the collision?

Answer 1

This is a case of inelastic collision where both the blocks stick together after collision

in case of collision momentum conservation is applicable

$p_i=p_f$

$5.9\times17+59.0\times0=(5.9+59)\times v_f$

$v_f=1.54m/s$

$\Delta K=K_f-K_i=\frac12(m_1+m_2)v_f^2-\frac12m_1v_i=\frac12\times64.9\times1.54^2-\frac12\times5.9\times17^2=76.95-852.55=-775.6 J$