- #1

danut

- 7

- 2

- Homework Statement
- In the system bellow, there are 3 ideal pulleys. m₁ = 1.00 kg, m₂ = 1.00 kg, m₃ = 2.00 kg.

Find the tension in the string/wire that connects said pulleys.

- Relevant Equations
- -

The pulleys are ideal, so I figured that

**m₁**and

**m₂**will both move upwards (towards the ceiling?) with the acceleration

**a,**while

**m₃**will move downwards with the acceleration

**-a.**

Let

**T**be the tension in the string which connects the 3 pulleys, and

**T'**the tension of the string that holds the object

**m₃.**Using the law of cosines,

**T' = 2T.**

T - m₁g = m₁a (1)

T - m₂g = m₂a (2)

m₃g - 2T = m₃a (3)

adding up the first 2 equations, I got that

a = [g(m₁ + m₂) - 2T]/(m₁+m₂)

and replacing a in the 3rd equation, I finally got that T = [gm₃(m₁ + m₂)]/(m₁ + m₂ + m₃) which does (I think) coincidentally get me to 9,81 N.

Please help a girl out!!