- #1

Adriano25

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1. Homework Statement

1. Homework Statement

Pulley is mass less accelerating downward at 2.0 m/s

^{2}.

M1 = 4.0 kg

M2 = 2.0 kg

M3 = 3.0 kg

Find the acceleration of M2 & M3.

## Homework Equations

I made up the slope positive pointing up.

Since M2 and M3 have the same acceleration, a2=a3 ⇒ a

Since it's accelerating downwards, Apy = -2.0 m/s

^{2}

Mass 1:

ΣF1y = m1a1y

T-m1g = m1a1y

T = m1a1y + m1g

**(1)**

Mass 2:

ΣF2y = m1ay

T-T1 = m2ay

**(2)**

Mass 3:

ΣF3y = m3ay

T1-m3g = m3ay

**(3)**

Pulley:

apy = (a1y+ay) / 2

**(4)**

## The Attempt at a Solution

I added eq. (2) & (3) to get rid of T1

T-m3g = m2ay+m3ay

**(5)**

I plugged eq

**. (1)**into

**(5)**

m1a1y + m1g - m3g = ay(m2+m3)

Solve for a1y:

a1y = (ay(m2+m3) - m1g + m3g) / m1

**(6)**

Plug

**(6)**into

**(4)**

apy = [ (ay(m2+m3) - m1g + m3g) / m1) + ay ] / 2

Solve for ay:

ay = (m1g-m3g+2m1apy) / m2+m3+m1) = 2.87 m/s

^{2}

By the answer key, the acceleration for m2 and m3 is -2.87 m/2

^{2}. How do I know that is negative and not positive? Is it because m2 + m3 have a higher mass than m1, thus when the pulley is accelerating downwards, m1's acceleration points up and m2 & m3's acceleration point down?

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