A 12.0 kg block (m1) is on a 40.0 degree incline. It is attached to a 17.0 kg bl
ID: 1502506 • Letter: A
Question
A 12.0 kg block (m1) is on a 40.0 degree incline. It is attached to a 17.0 kg block (m2) by a massless cable stretched over a massless, frictionless pulley. Block m2 is at a height of 3.00 m when released. The static friction coefficient of the ramp is 0.400 and the kinetic friction is 0.275. The spring constant is 50.0 N/m.
a) Find the total initial mechanical energy of the system.
b) Find the position x_H when block m1 stops going up the ramp.
c) Find the mechanical energy of the system at this point.
d) Find the position of max velocity (x_M, v_M)
e) Find the return position x_L when the cycle is complete.
f) Find the mechanical energy of the system at this point.
g) Where is the end of the motion?
Explanation / Answer
a) Find the total initial mechanical energy of the system = 17 * 9.8 * 3
= 499.8 J
b) Here, 1/2 * 50 * x2 = 17 * 9.8 * x - 0.4 * 12 * 9.8 * cos40 * x - 12 * 9.8 * sin40 * x
=> 1/2 * 50 * x = 54.97
=> x = 2.2 m -------------------> position x_H when block m1 stops
c) mechanical energy of the system at this point = (1/2 * 50 * 2.2 * 2.2) + (17 * 9.8 * 0.8)
= 254.28 J
d) position of max velocity = x = 0 m
e) return position x_L = (54.97 - 0.275 * 12 * 9.8 * cos40) * 2/50
= - 1.207 m
f) mechanical energy of the system at this point = (1/2 * 50 * 1.207 * 1.207) + (17 * 9.8 * 4.207)
= 737.307 J
g) end of the motion is after infinite time .
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