- #1
Adriano25
- 40
- 4
1. Homework Statement
Pulley is mass less accelerating downward at 2.0 m/s2.
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/s2
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/s2
By the answer key, the acceleration for m2 and m3 is -2.87 m/22. 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?
Last edited: