What equations should be used to calculate the tension in a rope?

[deezy]

Homework Statement

A block is pulled up by a rope. The block has an acceleration of 5 \;m/s^2. The mass of the block is 5 kg. What is the tension in the rope?

Homework Equations

T = mg
a = \frac {F_{net}}{m}

The Attempt at a Solution

Not sure which equation I should use in this problem, don't know if I have the right relevant equations. Not sure where to get started.

 

[xhhux]

Tension is equal to mass time acceleration(g in the first equation). So:

T=(5m/s/s)(5Kg) = 25N

Tension is a force; you could use the other eq just the same.

 

[mateomy]

Separate the forces into their x and y components, I find that always makes it easier. So do free body diagrams.

 

[deezy]

How do I separate the forces into x, y components?

 

[mateomy]

Well you don't really have an x component for this problem but it's basically an extension of drawing a free body diagram. Say you have a block on an incline plane. There will be a force in the x direction and a force in the y direction, some of them, like gravity for instance will have a component in each direction. In that case you would use trig functions to get their values. But enough of the confusion….

In your problem you only have a mass on a rope, that is accelerating upward. You should immediately realize that there will be two forces at work here, the tension in the rope and the force of gravity working against it. These forces only work in the y direction and they are opposite of each other.

This is where Newton's equations come in…

F=ma

You have forces, and accelerations….now you need to figure out how to put everything together.