Picture two masses, M and m, connected by a frictionless pulley. M is sliding al

Question

Picture two masses, M and m, connected by a frictionless pulley.  M is sliding along a frictionless ramp that makes an angle with the horizontal of theta, and m hangs vertically from the other side of the pulley.  Let M= 14 kg, m=6kg, and theta=33 degrees.

a) Does the mass m go up or down (assume the system is released from rest)

b) what is the magnitude of the acceleration of m?

What did I do wrong?  I'm pretty sure it's in the signs that I chose for the variables.  Please look at MY two coordinate systems before answering the questions.  The answers are: m goes up, |a|=0.79 m/s2

I need to know what I did wrong!  Thank you!

T + Mgsintheta - Mgcostheta + N = T = -mg + ma T = Mgsintheta + ma T = 14(9.8)sin(33) + 14(a) T = 74.7 + 14(a) T = (6)(9.8) + 6a T = -58.8 + 6a 74.7 + 14(a) = -58.8 + 6(a) 74.7 = -58.8 - 8a 133.5 = -8a -8 = -8 -16.7 = a

Explanation / Answer

a) mass m go up

b) on m

T - 6g = 6a

om M

14gsin33 - T = 14a

add

14gsin33 - 6g   = 20a

a = 0.797 m/s2

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