A block of mass m1 on a frictionless plane inclined at an angle ? is connected b

Question

A block of mass m1 on a frictionless plane inclined at an angle ? is connected by a cord over a massless, frictionless pulley to a second block of mass m2. Our goal is to find the acceleration of the blocks and the tension in the cord.

a) Draw a free-body diagram for mass m1. Define your coordinate system so that positive x is parallel to the incline plane and points up and to the right. Define positive y to be perpendicular to the incline plane and point up and to the left.

b) Draw a free-body diagram for mass m2. Define positive y to be downward.

c) Find expressions for the net force on m1 (both x and y direction) and m2 (y direction only). Your expressions for the net force should be in terms of m1, m2, T, theta, the normal force FN exerted on mass m1, and physical constants.

d) Using your expressions from part c, determine the normal force that the incline plane exerts on m1. Put your answer in terms of m1, theta, and physical constants

eUsing your expressions from part c, show that the tension T in the cable and the acceleration a of the blocks are

T=(m1m2/m1+m2)(1+sin(theta))

a=(m2-m1sin(theta))/m1+m2

Explanation / Answer

the force acting on mass m1 is

Fx = m1g x cosA - m2g

or m1a = m1g x cosA - m2g

or a = (1/m1) x g x (m1 x cosA - m2)

where a is acceleration of system,g = 9.8 m/s^2 and A is the angle of inclined plane

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