Supposedly Simple Tension Problem

[coconut7]

Q: You are pulling your younger sister along in a small wheeled cart. You weigh 65.0 kg and the combined mass of your sister and the cart is 35.0 kg. You are pulling the cart via a short rope which you pull horizontally. You hold one end of the rope and your sister holds the other end. If you are accelerating at a rate of 0.10 m/s-2, the rope is inelastic, and the frictional force acting on the cart is 30 N: what is the tension on the rope?

Now, I've tried to search for this online, and all answers I've found go something like this:
F = MA = Tension - friction
Thus MA = Tension - friction
T = MA + F = 35*.1 + 30 = 33.5 N

Is this correct? Assuming from the equation above (Tension - friction), tension would be in the opposite direction of the friction (which I assume would be opposite the direction of motion). I'm a bit confused by this, as I thought tension was supposed to be opposite of the applied force.

Please explain how to do this problem clearly :) Thanks!

 

[Simon Bridge]

Welcome to PF;
It is not a good idea to just use equations from online or other sources unless you understand them.

The trick with these questions is to draw a free-body diagram.
You should draw one for you and one for your sister+the cart - then you'll see how the tension works out.

Or you can just think about the last time you hauled on a rope attached to something.
Didn't the rope pull on the thing in the same direction as you pulled on the rope?
Didn't the rope also pull back on you?

 

[ehild]

Q: You are pulling your younger sister along in a small wheeled cart. You weigh 65.0 kg and the combined mass of your sister and the cart is 35.0 kg. You are pulling the cart via a short rope which you pull horizontally. You hold one end of the rope and your sister holds the other end. If you are accelerating at a rate of 0.10 m/s-2, the rope is inelastic, and the frictional force acting on the cart is 30 N: what is the tension on the rope?

Now, I've tried to search for this online, and all answers I've found go something like this:
F = MA = Tension - friction
Thus MA = Tension - friction
T = MA + F = 35*.1 + 30 = 33.5 N

Is this correct? Assuming from the equation above (Tension - friction), tension would be in the opposite direction of the friction (which I assume would be opposite the direction of motion). I'm a bit confused by this, as I thought tension was supposed to be opposite of the applied force.

Please explain how to do this problem clearly :) Thanks!

Welcome to PF!

The boy applies force on the rope, but the girl is is accelerated by the force of tension. The friction opposes her motion, so the net force accelerating the girl and the cart is T-F.



ehild

 

[coconut7]

Thanks for the replies! :) How exactly do you find the direction of a tension force?

 

[ehild]

Think: a rope can only pull. What is the direction of the force it exerts on something connected to one end? What is the direction of force the rope exerts on the other end?

Try to pull something with a string attached to it. In principle, Physics is about reality... Do experiments.

ehild