Pulley System: A block of mass m1 = 7.60 kg is connected by

[soccerball3211]

A block of mass m1 = 7.60 kg on a frictionless plane inclined at angle theta = 33.9° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.44 kg hanging vertically. (a) What is the acceleration of the hanging block (choose the positive direction up)? (b) What is the tension in the cord?

First I found the weight of both blocks using the equation W=mg

W of m1 = 74.48N
W of m2 = 23.91N

After I found the weight of each I calculated the tension in each section of rope

T1 = Wsin(theta) T2 = 23.91N
T1 = 41.54N

Then to figure out acceleration I said that a = (T1 - T2)/(m1 + m2), this gave me an acceleration of 1.76m/s^2

Then from my acceleration calculation I found the tension in the cord to be 54.9N

My acceleration is correct but I can't figure out why my tension calculation is incorrect?

Can someone point me in the right direction?

Thanks again

 

[skeeter]

force of the hanging block's weight = 2.44g

force of the block's weight on the incline parallel to the incline surface = 7.60g*sin(33.9)

from my calculations, the force of the block's weight component parallel to the incline wins.

since the pulley's mass & friction are negligible, the tension in the cord, T, connecting the two blocks is the same.

so ... let M = mass of the larger block
m = mass of the smaller block

setting up a pair of scalar net force equations (larger force - smaller force) ...

Ma = Mgsin(33.9) - T
ma = T - mg (add these together, note that the T's cancel)
-------------------------------
Ma + Ma = Mgsin(33.9) - mg

a(M + m) = Mgsin(33.9) - mg

a = [Mgsin(33.9) - mg]/(M + m)

this last equation gives you the magnitude of acceleration for both masses ... deal with the directions (+ or -) as your directions indicate.