# Calculate Tension of Wire with 6kg Mass on 3.5m Rod

• Chica1975
In summary: I calculated mg as 58.8. I also tried to find the angle using trigonometry until I was able to find the tension of the wire. My answer was way off.The correct answer is 177.8.
Chica1975
A light rod of length 3.5m was pivoted at one end and was horizontal. On the end away from the pivot was a mass of 6kg. In addition to the pivot, a vertical wire supported the rod. The wire was attached at a point 1.16m from the pivoted end. Calculate the tension in the wire

## Homework Equations

Force by gravity = mg
sintheta = opp/hyp

## The Attempt at a Solution

I drew a diagram relating to all the info given above. I have attempted to find the angle using mg and 3.5m i get something ridiculous like 1 degree. I know there are 180 degrees in a triangle and tried to find the other angle and follow this pattern using trigonometry until I was able to find the tension of the wire. My answer was way off.

apparently the correct answer is 177.

Thanks a mil.

Can you create an image of the free body diagram you used? What are the actual calculations you did?

Unfortunately, I am traveling and do not have a scanner at all. However, I drew as best I could I also calculated mg = 58.8

I even tried to draw a right angled triangle using mg as one of the sides, this did not work.

The forces working on this are vertical (the wire), mg (gravitational).

Thanks

Okay, I'll try and work you through the first bit of setting this problem up. From the looks if this the problem ignores the mass of the arm.

The thing with this problem is that it's not your straight up force problem, it requires you deal with torques. Never fear though, because they're incredibly simple to work with at this level. Just in case you've forgotten, all you need to calculate a torque is the force, and the distance from the pivot. So your torque is applied like this: Torque=(force in Newtons)(distance in metres), with your units being Newton metres (N*m).

Now as always with a free body diagram label all the forces acting on the object. I'm going to try and approximate the drawing here:

(pivot)====(support)=========(weight)

I'm going to define up, right, and counter-clockwise as positive. Imagine the support arrow going up, and the weight arrow going down.
Now when dealing with torques, a handy technique for eliminating unknowns is placing your pivot point on those unknowns. In this case you're given the pivot point, and the distances of each force applied from that pivot. So you don't need to worry about that.

Now use your standard net force equation, since the arm is stationary you have no net force. Therefore your torque forces must cancel out:
(the standard symbol for torques is a lowercase Tau)
$$F_{net}=0=\tau_{support}+\tau_{weight}$$

Try and move on from there.

Last edited:

I would approach this problem by first identifying the forces acting on the system. In this case, we have the force of gravity acting on the mass (6kg) and the tension force in the wire. We can use Newton's Second Law (F=ma) to determine the magnitude of the tension force.

First, we need to find the acceleration of the mass. Since the rod is horizontal and the mass is not moving, we can assume that the acceleration is 0. Therefore, the net force acting on the mass must also be 0. This means that the tension force in the wire must be equal and opposite to the force of gravity acting on the mass.

We can calculate the force of gravity using the equation F=mg, where m is the mass (6kg) and g is the acceleration due to gravity (9.8 m/s^2). So the force of gravity on the mass is 6kg x 9.8 m/s^2 = 58.8 N.

Since the tension force in the wire is equal and opposite to the force of gravity, the magnitude of the tension force is also 58.8 N.

To find the angle of the wire, we can use trigonometry. Since the wire is attached at a point 1.16m from the pivoted end and the rod is 3.5m long, we can use the tangent function to find the angle. tan(theta) = 1.16m/3.5m = 0.3314. Taking the inverse tangent, we get theta = 18.4 degrees.

However, this angle does not match the given answer of 177 degrees. This may be a typo or mistake in the given information. If we assume that the wire is attached at a point 1.16m from the non-pivoted end instead, the angle would be 177 degrees. In this case, the tension force in the wire would be in the opposite direction, but the magnitude would still be the same (58.8 N).

In conclusion, the tension force in the wire is 58.8 N and the angle of the wire is either 18.4 degrees or 177 degrees, depending on the point of attachment.

## What is the formula for calculating tension in a wire?

The formula for calculating tension in a wire is T = mg, where T is the tension in the wire, m is the mass of the object attached to the wire, and g is the acceleration due to gravity (9.8 m/s^2).

## How do I calculate the tension in a wire with a 6kg mass on a 3.5m rod?

To calculate the tension in a wire with a 6kg mass on a 3.5m rod, you would use the formula T = mg. In this case, the mass (m) is 6kg and the acceleration due to gravity (g) is 9.8 m/s^2. Plugging these values into the formula, we get T = (6kg)(9.8 m/s^2) = 58.8 N. Therefore, the tension in the wire would be 58.8 Newtons.

## What units should I use when calculating tension in a wire?

When calculating tension in a wire, you should use standard units such as kilograms (kg) for mass, meters (m) for length, and Newtons (N) for force. It is important to use consistent units throughout the calculation to ensure accurate results.

## Can the mass of the object on the wire affect the tension?

Yes, the mass of the object on the wire can affect the tension. As the mass increases, the tension in the wire will also increase. This is because the force of gravity acting on the mass will pull down on the wire, causing it to stretch and increase the tension.

## Are there any other factors that can affect the tension in a wire?

Yes, besides the mass of the object, there are other factors that can affect the tension in a wire. These include the length and thickness of the wire, the material it is made of, and any external forces or loads acting on the wire. These factors should be taken into consideration when calculating the tension in a wire.

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