100A QUIZ 4

1. A 2-kg ball with speed of 35m/s collides with a 15-kg ball with speed of 2m/s as shown. Find the system’s energy after a perfect inelastic collision.

Solution. Because this is a perfect inelastic collision two balls stick together after the collision,                From conservation of momentum we have                          m1v1 + m2v2 = (m1 +m2)V;                         (2kg)(35m/s) + (15kg)(-2m/s) = (2kg + 15kg)V, which gives V = 2.35m/s.               We find the energy of the system after the collision from                         KE = 1/2(m1 +m2)V2 = 1/2(2kg + 15kg)(2.35m/s)2 = 47.1J

2. A submarine dives into 100m deep sea. Find the pressure (in k pa) on top of the submarine. Take the density of the seawater as 1.025 x10³kg/m³, and the atmospheric pressure as 101.3kpa. 

   Solution. We find the pressure due to the seawater from

                    P_sea = r_seawatergh = (1.025 x10³kg/m³)(9.80m/s²)(100m) = 1.0045 x10⁶N/m² = 1.0045 x10⁶pa 

                 Thus the total pressure on the top of the submarine is

                  P_air + P_sea = 101.3kpa + 1.0045 x10⁶pa = 1.106 x10⁶pa.