As shown in the diagram, a crate (mc = 25 kg) on a ramp (? = 30.0o ) is attached
ID: 1393654 • Letter: A
Question
As shown in the diagram, a crate (mc = 25 kg) on a ramp (? = 30.0o ) is attached on one side to a spring (initially unstretched) with spring constant k = 15 N/m and on the other side to a rope which is strung over a pulley and attached to a hanging mass (mh = 50 kg). The hanging mass is initially a height h = 0.80 m above the ground. If released from rest, will the hanging mass hit the ground? If so, with what velocity? The force of kinetic friction between the crate and the ramp is Fk = 10 N. Be careful! Acceleration is NOT constant in this problem.
Explanation / Answer
Here we use energy conservation
Workdone by gravity on two bodies = -mc*g*h*sin(30) + mh*g*h
= -25*9.8*0.8*sin(30) + 50*9.8*0.8
= 294 J
Workdone by spring = -0.5*k*(h)^2
= -0.5*15*(0.8)^2
= -4.8 J
Workdone by friction = -Fk*h
= -14*10
= -140 J
Net workdone = 294 - 4.8 - 140
= 149.2 J
Now Apply Work-Enrgy theorem
Wnet = 0.5*(mc+mh)*v^2
==> v = sqrt(2*Wnet/(mc+mh))
= sqrt(2*149.2/(25+50))
= 2 m/s <<<<<<<<<<<<<-------------------Answer
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