no 12 a,b,c,d,e,f 11. Mastering Michelle\'s Maniacal Mystery Machine In the scen

Question

no 12 a,b,c,d,e,f

11. Mastering Michelle's Maniacal Mystery Machine In the scenario depicted below, all surfaces are frictionless. The masses are given as Mi. M2, Ms as on the diagram. Mass Mi is free to slide on a surface at rest relative to the surface of the Earth (like a smooth table). Let the positive x-direction point to the right, and let the positive y-direction point upward. Analyze this system from a reference frame at rest relative to the surface on which block 1 is free to slide - this is an inertial frame. a. For each of the objects 1,2,3, name any other objects that are exerting a force on it. For each of these forces, if the direction of the force is known, assign a variable to the magnitude of this force. If the direction of the force is unknown, assign a variable to nonzero the component(s) of this force. 6

Explanation / Answer

for the given problem

a. M1 -> the object M2 is exterting a force on it, in addition to the floor

let force due to M2 = N2 ( downwards)

force due to floor = N ( upwards)

force due to pulley = P ( 45 deg to horizontal)

M2-> force is being exerted by object M1, magnitude = N2 ( upwards) From newtons third law

force being exerted by M3 = T ( towards the right)

M3-> force being exerted by M2 = T (upwards) from newtons third law

b. for force balance on each object

N = N2 + M1g + P/sqrt(2) ( for M1)

M2g = N2 ( for M2)

c. for each object let acceleration of each object be a1, a2, a3

M3g - T = M3a3 ( a3 is downwards)

T = M2*a2 ( a2 is rightwards)

M1*a1 = P/sqrt(2)

d. now, P/sqrt(2) = T

hence

M1*a1 = T = M3g - M3a3

a1 = (g - a3)M3/M1

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