Question: Mass one is 15.0 kg and mass 2 is 9.0 kg. They are connected by a massless rope which passes over a frictionless pulley. The pulley has a shape of a solid disk. They pulley mass is 8.0 kg and the pulley radius (R) is 0.20 meter.(adsbygoogle = window.adsbygoogle || []).push({});

What is the speed of the falling body?

Solution:

I think my issue is determining if the forces in my equations are either positive or negative...

In my diagrams I forgot to label the the direction of my force vectors...

Body 1 and Body 2: Both T1 and T2 point up towards top of page and w1 and w2 point down towards bottom of page.

Equations:

1. Ʃ (torque) = T1(R) - T2(R) = (I)(a/R) = (MR^2/2)(a/R) = M*a*R/2

2. Ʃ(F1) = T1 - w1 = (m1)(a) .... T1 = m1*a + w1

3. Ʃ(F2) = w2 - T2 = (m2)(a) .... -T2 = m2*a - w2

4. T1 - T2 = m1*a + w1 + m2*a - w2

* Substitute eq. 4. into eq. 1.

(m1*a + w1 + m2*a - w2) = M*a*/2

a = (w1 - w2)/(M/2 - m1 - m2) = -2.94 m/s^2

V = (2*-2*-2.94)^(1/2) = 3.42 m/s

The answer is 2.9 m/s

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# Velocity Of pulley

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