Solving a Mass-Pulley System: m1 & m2

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The discussion revolves around solving a mass-pulley system involving two blocks, m1 and m2, with specific masses and an inclined angle. The participant initially calculated the acceleration of the hanging block and the tension in the cord but found their answers to be incorrect. They used the equations of motion, including the sine function to resolve forces, but sought clarification on the application of the sine in their calculations. The sine function is derived from the free body diagram, where it helps determine the x-component of gravitational force acting on the inclined block. The conversation emphasizes the importance of correctly applying physics principles to solve for acceleration and tension in such systems.
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Homework Statement


A block of mass m1 = 6.75 kg on a frictionless plane inclined at angle = 30.3° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.07 kg hanging vertically (Fig. 5-54). (a) What is the acceleration of the hanging block (choose the positive direction up)? (b) What is the tension in the cord?


Homework Equations


Fynet= T-m2g= m2a aka T=m2g+m2a
Fxnet=m1g(sin)-T=m1a

when these two are put together it is, a=(m1g sin - m2g)/(m1+m2)



The Attempt at a Solution


So I used the equations above and first found acceleration to be -1.914m/s squared and then I used the acceleration and plugged it back into the problem to find T and I got it to be 16.32 N, these answers are wrong and I don't know what I did wrong. Can someone help me please?
 
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Last edited:
tabchouri said:
Can you tell where the (sin) came from ?

From the free body diagram... when you extend out the normal force and make a triangle with the force of gravity, the sin is to find the x-component of the triangle
 
shell4987 said:
From the free body diagram... when you extend out the normal force and make a triangle with the force of gravity, the sin is to find the x-component of the triangle

the normal force counter acts only the gravity ?

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