# Supposedly Simple Tension Problem

• coconut7
In summary, the tension on the rope is 33.5 N and it is in the same direction as the applied force, opposite the direction of friction. This can be understood by drawing a free-body diagram or by thinking about a real-life example of pulling on a rope.
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!

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?

coconut7 said:
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

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

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

## 1. What is the "Supposedly Simple Tension Problem"?

The "Supposedly Simple Tension Problem" is a physics problem that involves calculating the tension force in a rope or cable that is being pulled at both ends. It is a common problem in introductory physics courses and is used to demonstrate concepts such as Newton's Laws of Motion and free body diagrams.

## 2. Why is the "Supposedly Simple Tension Problem" considered difficult?

The "Supposedly Simple Tension Problem" is often considered difficult because it requires a good understanding of Newton's Laws of Motion and the ability to set up and solve a complex system of equations. It also involves multiple variables and forces acting on the same object, which can be challenging for some students.

## 3. Can you provide an example of the "Supposedly Simple Tension Problem"?

Yes, an example of the "Supposedly Simple Tension Problem" would be a rope being pulled at both ends with a force of 50 N and 30 N respectively. The rope has a mass of 2 kg and is at rest. What is the tension force in the rope?

## 4. How do you solve the "Supposedly Simple Tension Problem"?

To solve the "Supposedly Simple Tension Problem", you need to draw a free body diagram of the object in question and identify all the forces acting on it, including the tension force. Then, you can use Newton's Second Law (F=ma) to set up and solve equations for the unknown variables. It is important to carefully consider the direction and magnitude of each force in order to get an accurate solution.

## 5. What are some tips for solving the "Supposedly Simple Tension Problem"?

Some tips for solving the "Supposedly Simple Tension Problem" include carefully labeling all forces on your free body diagram, breaking the problem down into smaller, more manageable parts, and checking your final solution for reasonableness. It can also be helpful to practice similar problems and seek help from a teacher or tutor if needed.

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