Object A and B has mass of 2 kg Object A start to slide on i

Object A and B has mass of 2 kg. Object A start to slide on inclined planes as shown. Blue parts have no friction. Find the velocity of object A just before it enters a surface with friction coefficient of 0.2? K = 1/2 m middot V^2 Assume that it takes 2 second to travel friction surface. Find the velocity of object A after friction surface and length of the friction surface? Suppose that object A collides with object B on a frictionless surface. After colliding, they move together. Find the final velocity of two masses moving together. K E_i_a + m_i_b = KE F_a + m_f_b

Solution

a. mgh = 1/2mv^2 (Conservation of Energy)
sqrt(9.8*6.4*sin(30)*2)=v =7.919595949 m/s

b. deacceleration = .2*9.8 = 1.96 m/s2
v = 7.91 - 1.96*2 = 3.99 m/s (v = u +at)
s = 7.91*2 -.5*1.96*2*2 = 11.9 m (s = ut + .5at^2)

c. conservation of momentum
mv = 2mv\'
v\' = v/2
v\' = 3.99/2 = 1.995