Rotation about a fixed axis problem

[Rob K]

Hi guys I was trying not to post this as it is difficult to understand without the diagram, but I will try and give you a visual. Basically there are 2 pulleys attached together on the one pivot, the larger one is driven by a belt that is driven by a motor. The inner pulley is used to hoist the weight.

Homework Statement

Figure 3 shows a block A attached to a hoisting mechanism which consists of two
drums of radii r1 = 0:4 m, r2 = 0:8 m, ¯xed at O and which have a combined mass
of m1 = 100 kg and a radius of gyration about O of kO = 0:5 m. If a constant force
P = 1:5 kN is applied by the power unit, which consists of a pulley of radius r3
attached to a motor, determine the vertical acceleration of block A. The cord from
the motor to the drum is at an angle 40± to the horizontal. Block A has a mass
m2 = 300kg.

Homework Equations

I = mk²

+CCW $\Sigma$M_o = I_o$\alpha$

+$\uparrow$$\Sigma$F_y = m(a_g)_x

+CCW a = $\alpha$r

a = $\alpha$r

The Attempt at a Solution

I = 100kg * (0.5m)$^{2}$ = 25kg.m²

$\Sigma$M_o
T(0.4m) = (25 kg.m²$\alpha$

+$\uparrow$$\Sigma$F_y = m(a_g)_x
-300(9.81)N + 1500sin40N + T = - 300a

a = $\alpha$0.4

I worked out $\alpha$ to be 5.56, or 24. something. Basically after 20 odd hours, I have given up, there is something clearly very wrong and missing, and between me and 2 other people we don't know where to go from here.

The answers are as follows
[$\alpha$ = 0:312 rads/s2CW, T = 2980:5 N, a = 0:125 m/s2.]

Please help.

Kind Regards

Rob K

 

[Rob K]

Can anyone help with this?

Do I need to provide some more information?

 

[ehild]

Try to attach a picture. And explain your notations. What do you mean by ":"? Is it for decimal point? ehild