- #1

Asterast

- 13

- 3

**Summary::**I have solved the question but I'm getting answers wrong, some reaction equations seems to have trouble.

Question: Let m

_{1}= 1 kg, m

_{2}= 2 kg and m

_{3}= 3 kg in figure. Find the accelerations of m

_{1}, m

_{2}and m

_{3}. The string from the upper pulley to m

_{1}is 20 cm when the system is released from rest. How long will it take before m

_{1}strikes the pulley?

here's what I did:

Assuming acceleration of m

_{1}be a

Assuming acceleration of m

_{2}and m

_{3}be a'

Tension in string between mSUB]2[/SUB] and m

_{3}be T

so tension in upper string connected to m

_{1}is 2T

So equations I made for the bodies:

**equation for m**

_{1}2T-m

_{1}g = m

_{1}a

**2T-g=a ...**

equation for m

equation 1

equation for m

_{2}T-m

_{2}g = m

_{2}(a'-a)

Since m

_{2}will be going up because of weight of m

_{3}and system of mm

_{2}and m

_{3}will be going downwards.

**T-2g=2(a-a') ...**

equation for m

equation 2

equation for m

_{3}m

_{3}g-T = m

_{3}(a'+a)

since m

_{3}will be going down simultaneously with m

_{2}and m

_{3}

**3g-T=3(a'+a) ...**_________

equation 3

Eliminating T from equation 1 and 2

**3g = -3a+4a' ...**_________

equation 4

Eliminating T from equation 2 and 3

g = 5a+a' ...

g = 5a+a' ...

equation 5

Solving equation 4 and 5 I get a' = 18g/23

Which is wrong.. please help. :3