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Motion and Wedge Reaction

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A particle of mass m slides down a smooth circular wedge (radius = R) of mass M (see fig). The wedge rests on a smooth horizontal table.

a) Find the equation of motion of m and M
b) The reaction of the wedge on m

See attached file for full problem description.

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Set of three problems on Newton's laws of motion

1) A window washer of mass M is sitting on a platform suspended by a system of cables and pulleys as shown (see attachment). He is pulling on the cable with a force of magnitude F . The cables and pulleys are ideal (massless and frictionless), and the platform has negligible mass.
Find the magnitude of the minimum force that allows the window washer to move upward. Express your answer in terms of the mass and the magnitude of the acceleration due to gravity .

2) Two blocks with masses M1 and M2 hang one under the other. For this problem, take the positive direction to be upward, and use g for the magnitude of the acceleration due to gravity.
A) Find T2, the tension in the lower rope. Express your answer in terms of some or all of the variables M1, M2 ,and g.
B) Find T1, the tension in the lower rope. Express your answer in terms of some or all of the variables M1, M2 ,and g.
C) Find T2, the tension in the lower rope. Express your answer in terms of some or all of the variables M1, M2 ,a, and g.
D) Find T1 , the tension in the upper rope. Express your answer in terms of some or all of the variables

3) A wedge with an inclination of angle rests next to a wall. A block of mass m is sliding down the plane, as shown (see attachment). There is no friction between the wedge and the block or between the wedge and the horizontal surface.

A) Find the magnitude, Fnet , of the sum of all forces acting on the block. Express Fnet in terms of theta and m along with any necessary constants.
B) Find the magnitude, Fww , of the force that the wall exerts on the wedge. Express in terms of theta and m along with any necessary constants

See attached file for full problem description.

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