block a is released from a position. it has a velocity of 6m/s when it strikes a

Question

block a is released from a position. it has a velocity of 6m/s when it strikes and sticks to block b. if the coefficient of friction is 0.3, how long does it take the blocks to come to rest? what is the maximum velocity of B? A's mass of 50 kg and B mass of 30kg

Explanation / Answer

A--->B Max velocity of B is when they stick together 50*6=80*v====> v=3.75 m/s Then after some time it stops then total energy is drawn by friction and work done by friction= mu*M*g*x x= distance travelled but x=0.5*a*t^2 Here a = decceleration by friction=mu*g ===> distance travelled x=0.5*0.3*10*t^2=1.5*t^2 ===> total work done by friction=0.3*80*10*1.5*t^2=360*t^2 But work done = change inKE=0.5*80*3.75^2=562.5 J ==> 562.5=360*t^2===> t=1.25 seconds

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