# Confirmation of a net force calculation from a diagram

• Humbleness
In summary, the net force acting on the object in the given diagram was calculated using the tip-to-tail method and the cosine/sine law. The resultant magnitude was determined to be 15.65N (N 50.2 W). The diagram used was correct and the angle was corrected from the original answer.
Humbleness

## Homework Statement

Calculate the net force acting on the object indicated in the following diagram. Show your work.

cosine/sine law

## The Attempt at a Solution

First I subtracted 10N and 8N (since they are forces acting in different directions):
-8.0N (S) + 10.0N (S) = 2.0 (S)

Then I used the tip-to-tail method:

First using cosine law to find magnitude of the net force:
c2 = a2 + b2 - 2abcosC
c2 = 4 + 289 - 2 x 2 x 17 (cos45)
c2 = 293 - 48
c = 15.6N

Now angle using sine law:
sina/2.0N = sinb/17N = sin45/15.6N
b = sin-1 (sin45/15.6 x 17)
b = 50.4

Therefore, the net force is 15.6N (S 50.4 W) West of South

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Your resultant magnitude looks right, but your angle (as reported: "S 50.4 W") does not. The angles are close, so if you want to go with "S <angle> W" notation, then then your B vector would have an angle of "S 135 W". Think about it.

Humbleness
lewando said:
The angles are close, so if you want to go with "S <angle> W" notation, then then your B vector would have an angle of "S 135 W". Think about it.
I think I understand what I did wrong regarding the angle. As far as I can tell based on the original diagram, 17N is (N 45 W), therefore, the angle of the net force should be (N 50.4 W). Does this look right?

Looks much better, except I got a slightly different value because I held on to an extra digit in the magnitude result (15.65), when doing the sin rule calculation.

Humbleness
I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm on my phone at the moment but will try and post again later.

lewando said:
Looks much better, except I got a slightly different value because I held on to an extra digit in the magnitude result (15.65), when doing the sin rule calculation.
After re-doing the calculations, I got the same result (15.65).
So it would actually end up being: 15.65N (N 50.2 W).
Is this what you got?

Yes. 15.65 is over-precise, given the digit-significance of the values in the problem statement. It is good to be overprecise during intermediate calculations.

Humbleness
CWatters said:
I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm pretty sure I used head-to-tail in my diagram, I don't think I got that part wrong.

CWatters said:
I haven't had time to check your working but your diagram looked wrong to me. You appear to be doing tail to tail rather than head to tail if you see what I mean.

I'm on my phone at the moment but will try and post again later.

Humbleness
Okay, thank you though as well for checking out, I always like to receive confirmations of whether my work is correct, since I am doing this course online, and it's difficult with no teacher present or class peers with whom I can verify my work, hence why it is good that forums such as these exist.

## 1. How do you calculate net force from a diagram?

To calculate net force from a diagram, you first need to identify all the forces acting on the object. Then, using the appropriate mathematical equations, you can find the magnitude and direction of each force. Finally, add all the forces together to find the net force on the object.

## 2. What is the significance of confirming a net force calculation from a diagram?

Confirming a net force calculation from a diagram is important because it ensures that all the forces acting on an object have been accurately identified and taken into consideration. This helps to accurately predict the motion of the object and make informed decisions about any necessary adjustments.

## 3. Can a net force calculation from a diagram be incorrect?

Yes, a net force calculation from a diagram can be incorrect if any forces have been left out or if the mathematical equations have been used incorrectly. It is important to double check all calculations and ensure that all forces have been accurately represented in the diagram.

## 4. How do you know if a net force calculation from a diagram is correct?

A net force calculation from a diagram is considered correct if it follows the laws of motion and accurately predicts the motion of the object. Additionally, it should take into account all the forces acting on the object and use correct mathematical equations and values.

## 5. Are there any common mistakes when calculating net force from a diagram?

Yes, some common mistakes when calculating net force from a diagram include forgetting to include all the forces, using incorrect mathematical equations, and miscalculating the magnitude or direction of a force. It is important to carefully check all steps and calculations to avoid these mistakes.

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