Question

A 5.8 kg box is on a frictionless 37 ∘ slope and is connected via a massless string over a massless, frictionless pulley to a hanging 1.7 kg weight.What is the tension in the string once the box begins to move?

Answer 1

Answer:T=20.62 N

Explanation:

Given

`m_1=5.8 kg`

`m_2=1.7 kg`

inclination
`\theta =37^(\circ)`

Let T be the tension

From diagram

`5.8 g\sin\theta -T=5.8 a`

`5.8 g\sin\theta -5.8 a=T`---1

For
`m_2` block

`T-1.7 g=1.7 a`

`T=1.7(g+a)`--2

from 1 & 2 we get

`1.7(g+a)=5.8 g\sin\theta -5.8 a`

`7.5 a=5.8g\sin \theta -1.7g`

`7.5 a=1.79 g`

`a=(1.79 g)/(7.5)=0.238 g=2.33 m/s^2`

`T=1.7(9.8+2.33)=1.7* 12.132`

`T=20.62 N`