answers should be: a) 1.24 m. b) 3.49 m. please show all steps A wooden block (A

Question

answers should be: a) 1.24 m. b) 3.49 m. please show all steps

A wooden block (A) is released from rest at the top of a frictionless ramp, as shown here. The block slides down the ramp, collides with block B, and they stick together and slide across a rough patch, whose coefficient of kinetic friction is 0 130. After crossing the rough patch, the combined mass encounters a spring whose force constant is 210.0 N/m. (There is no friction when they are in contact with the spring.) Find the maximum compression of the spring. Find the position (x=?) where the two blocks finally come to rest.

Explanation / Answer

part a )

before collision block a velocity = sqrt(2gh) =

here momentum remain conserve

velocity of both block = m1v1 / (m1+m2) = 10 * 10.84 / 15 = 7.23 m/s

kinetic energy after rough patch

KEf = 1/2 * mv^2 - mu*m*g*d

KEf = 162.73 J

now apply energy conservation

KEf = KEspring

KEf = 1/2 * kx^2

x = 1.24 m

part b )

after just loosing the contact from spring , kinetic energy of both block

162.73

162.73 = mu*m*g*x

x = 8.51 m

this is from right to left side ( means from x = 12 to x = 0 )

x = 12 - 8.51 = 3.49 m

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