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A 24.5N brick slides from rest down an 11.2m, 53.0 degree ramp with a meu=0.45. At the bottom, it strikes a stationary 36.8N brick, and then the two slide on together. How far will the two slide on a level surface with a coefficient of friction of 0.080?

This problem must be done in three steps.
(1) Compute speed of the 24.5 N brick at the bottom of the ramp before it hits the 36.8 N brick. One way to do it is subtracting friction work from the potential energy loss to get the kinitic energy.
(2) The collision of the bricks is inelastic; otherwise they not stick. Use conservation of momentum to get the in initial speed of the two bricks sliding together.
(3) Use energy prinicipas again to get the didtance they slide together.
Initial kinetic energy (when they start sliding together) = (Friction force) x (distance they slide)

How would you calculate the first step though?

Part (1) goes like this:
The friction force on the brick sliding down the ramp is
(24.5 N) cos 54.3 * 0.45 = 6.43 N
Friction work = 6.43N x 11.2 m = 72.1 J
Potential energy release = (24.5)*11.2 m * sin 54.3 = 222.8 J
Kinetic energy of the sliding mass before collision = 222.8 - 72.1 = 150.7 J = (1/2) M V^2
M = 24.5/g = 2.5 kg
V(before collision) = sqrt (2*150.7/2.5) = 11.0 m/s

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