Blocks connected by rope on slope

[superdave]

Homework Statement

I just want to confirm this.

A block m₁=10 kg is hanging from a rope. the rope is attached by a frictionless pulley to a block m₂=5 kg on a frictionless slope with a 40 degree angle from the ground.

Find the tension in the rope and the acceleration of the first block.

Homework Equations

So the tension is the same for both blocks, and so is the acceleration.

m₁ * a=-m₁ * g + T
m₂ * a=-m₂ *g sin(40) + T

The Attempt at a Solution

T = m₁ * a + m₁ * g
T= m₂ * a + m₂ *g sin(40)

m₁ * a + m₁ * g = m₂ * a + m₂ *g sin(40)
(m₁ - m₂) * a = m₂ *g sin(40) - m₁ * g

a = (m₂ *g sin(40) - m₁ * g) / (m₁ - m₂)
a = -13.3 m/s²

I'm not sure about the negative. Because I set up the problem so - for the first block is down and + is up. and - for the second block is downslope and + is upslope. But if a is the same for both blocks, then it doesn't make sense.

But did I do everything right?

 

[Doc Al]

If the acceleration of m1 is down, then the acceleration of m2 must be up. Fix your equations accordingly. (With your sign convention, you can't call both accelerations 'a'.)

 

[superdave]

So would I do a₁ and a₂ with a₁ = - a₂ ?

Or do I have to do all the equations over again?

 

[Doc Al]

So would I do a₁ and a₂ with a₁ = - a₂ ?

That should work.

Or do I have to do all the equations over again?

Nope.

The trick I like to use is to guess the most likely direction and call it positive. Here I'd guess that m1 goes down, so I'd say that the acceleration of m1 was 'a' downward. And thus the acceleration of m2 is fixed to be 'a' up the incline. If you guess right, 'a' will turn out to be positive; if you guessed wrong, it will be negative. No worries.

 

[superdave]

Okay, thanks