# How much tension should the rope be able to withstand?

1. Feb 11, 2010

### Ryuk1990

1. The problem statement, all variables and given/known data

A rope is pulling up a 1200 Kg car. The upwards acceleration is 0.8 m/s2. How much tension should the rope be able to withstand?

2. Relevant equations

Net force is equal to mass x acceleration.

3. The attempt at a solution

So would it just be 1200 Kg x 0.8 m/s2 which is 960 Newtons?

2. Feb 11, 2010

### PhanthomJay

That's the net force. The net force is the algebraic sum of all the forces acting on the car. What are the forces acting on the car?

3. Feb 11, 2010

### Ryuk1990

The normal force and gravity?

4. Feb 11, 2010

### PhanthomJay

Gravity is one force acting down on the car (it's weight). The other force is the contact force (which perhaps you are calling the normal force) which is actually the ___?____ force in the ____?___ which acts ______________(up/down, choose one).

5. Feb 11, 2010

### Ryuk1990

The net force in the system which acts up?

6. Feb 11, 2010

### PhanthomJay

You have already calculated the net (resultant) force. It is equal to 960 N. The net force always acts in the direction of the acceleration, thus, the net force of 960 N acts up. The net force on the car is comprised of 2 forces: the weight of the car, acting down, and the rope tension, which must act up (since the net force is up, the tension force must be greater than the weight force). So you have the tension force acting up, and the weight force acting down, and their net total (algebraic sum) must be 960N .. So the tension force is ????????

7. Feb 11, 2010

### Ryuk1990

960 minus the downward force?

8. Feb 11, 2010

### PhanthomJay

F_net =ma =960 N

the net force must be up (+), in the direction of the acceleration (+).

You have T (the rope tension) acting up (+), and W (the car's weight) acting down (-). T must be greater than W if the net force is up. Thus
T - W = 960. Solve for T, after first calculating W.

9. Feb 11, 2010

### Ryuk1990

Ah that makes sense. Thanks for the help. :-)