* need solutions to answers marked in red Conservation of Mechanical Energy A sm

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* need solutions to answers marked in red

Conservation of Mechanical Energy A small mass m = 1 kg is released from rest on a frictionless track at a height H = 5 m, as shown. The mass slides on the track following the path shown and eventually strikes a spring, compressing it by an amount, d. . k = 1175 N/m (See Fig. below) What is the mechanical energy of the mass at the release point? 49. 0 J What is the gravitational potential energy of the mass when it is at point B as shown? 112. 25 J What is the kinetic energy of the mass just before it strikes the spring? 36. 75 J By how much is the spring compressed at point B? 0. 25 m Work-Energy Theorem A 20-kg block is given an initial velocity v_0 = 5. 0 m/s and slides onto a horizontal, frictional surface (muk = 0. 40) which is 2. 5 m long, and then back onto a frictionless surface. The initial kinetic energy of the block is 1250 J The net force on the block while sliding over the frictional surface is 78. 4 N The work done by this net force is 196 J The final speed of the block as it leaves the frictional surface is 2. 32 m/s

Explanation / Answer

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Q4.

a) KE = 1/2 (mv^2) = 250 Joules.
b) (20 x g) x 0.4 = 78.4N. friction.
c) Work = (fd) = 78.4 x 2.5 = 196 Joules. the DIRECTION is negative, not the work.
d) (250 - 196) = 54 Joules kinetic energy remaining.
V = sqrt.(2KE/m) = 2.32 m/sec.

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