Calculating the tension in a rope

In summary, the problem involves a very heavy sack being hung from a rope and pushed sideways with a force of 220N. The rope supporting the sack is inclined at 18 degrees to the vertical. The task is to calculate the tension in the rope and find the mass of the sack. To solve this, a Free Body Diagram should be drawn and the angle should be adjusted to 18 degrees away from 90 degrees. Trigonometry can also be used to find the tension in the rope.
  • #1
Otolith
1
0

Homework Statement



A very heavy sack is hung from a rope and pushed sideways. When the sideways push is 220N the rope supporting the sack is inclined 18 degrees to the vertical.

A) Calculate the tension in the rope
B) Hence find the mass of the stack

Homework Equations





The Attempt at a Solution


I'm really cluesless as to what to do on this question. For part A I figured I would try trig and did 220Sin(18) = 67.98. I have no idea if I did that right though, as for part B I thought it would be either splitting the answer I got for tension into it's components and and using the downward force or it would just be the same as the answer to A.
 
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  • #2
First off, draw a Free Body Diagram. It will help you visualize all the forces involved. Make sure you include everything you know.

Secondly, notice that the angle is not 18 degrees, but 18 degrees to the vertical. That means is 18 degrees away from being 90 degrees.

If those don't help enough, come back and let us know where you're still stuck at.
 

FAQ: Calculating the tension in a rope

1. How do you calculate the tension in a rope?

To calculate the tension in a rope, you need to know the mass of the object hanging from the rope, the acceleration due to gravity, and the angle at which the rope is suspended. You can then use the formula T = mgcosθ, where T is the tension, m is the mass, g is the acceleration due to gravity, and θ is the angle.

2. What is the unit of measurement for tension?

The unit of measurement for tension is Newtons (N). This is a unit of force, which is the product of mass and acceleration.

3. How does the angle affect the tension in a rope?

The angle at which the rope is suspended affects the tension because it changes the direction of the force acting on the rope. The greater the angle, the greater the component of the force acting against the rope, resulting in a higher tension.

4. Does the weight of the rope itself affect the tension?

Yes, the weight of the rope itself does affect the tension. The weight of the rope is considered part of the mass in the tension formula, so a heavier rope will result in a higher tension.

5. Can the tension in a rope be negative?

No, the tension in a rope cannot be negative. Tension is a force, and negative forces do not exist. If the calculated tension is negative, it means that the rope is not under tension, but rather under compression.

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