Calculating Net Force Using Vector Addition

In summary, the conversation involved solving a vector addition problem using the tip-to-tail method and trigonometric functions. The final answer was 15.6 N with a direction of North 39.8 degrees West. The person asking for verification redid the problem and arrived at the same answer, with a small typo in their post.
  • #1
alexandria
169
2

Homework Statement


upload_2016-3-15_1-26-57.png


Homework Equations


upload_2016-3-15_1-27-24.png

upload_2016-3-15_1-27-48.png


The Attempt at a Solution



8.0 N (north) + 10.0 N (south) = 2.0 N (south)
upload_2016-3-15_1-38-38.png

i used the tip-to-tail method to add the vectors
c = ([2.0 N]^2 + [17.0 N]^2 - 2 (2.0 N) (17.0 N) cos45°)1/2
c = 15.6 N

SinA/17.0 N = Sin45°/15.6 N
A = 40°

Net force = 15.6 N (S 40° W)

can someone please verify if my answer is correct! thanks in advance :)

 
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  • #2
alexandria said:
SinA/17.0 N = Sin45°/15.6 N
A = 40°
I don't get 40 degrees from that, but also you have fallen into a trap.
sin(x) increases as x goes from 0 to 90 degrees, but then decreases to 0 at 180 degrees.
sin(x) and sin(180-x) produce the same number. So when you know the sine and want to find the angle, you have to decide whether it is the angle returned by the arcsin function, or 180 degrees minus that angle.
There are deterministic processes for ensuring the right answer, but in this case just look at your triangle diagram. If you draw the 2N to scale it will be much shorter.
Like I said, it's always worth checking whether the answer looks sensible.
 
  • #3
SinA/17.0 N = Sin45°/15.6 N
how do i solve this to determine SinA?
 
  • #4
and does my answer look 'sensible' so far? i feel like I am doing something wrong
 
  • #5
alexandria said:
SinA/17.0 N = Sin45°/15.6 N
how do i solve this to determine SinA?
What did you do to get 40 degrees? Please show your working.
 
  • #6
sorry to bring back this forum again, but i re-did this question, can anyone tell me if this is correct.
39.

8.0 N (north) + 10.0 N (south) = 2.0 N (south)
upload_2016-3-31_16-34-24.png
c = ([17.0 N]2 + [2.0 N]2 - 2 (17.0 N) (2.0 N) cos45°) ½

c = 15.6 N

SinA/a = SinB/b = SinC/c

SinA/2.0 N = Sin45 degrees/15.6 N

SinA = (2.0 N) Sin45° / 15.6 N

A = sin^-1 (0.091)

A = 5.2 degrees

90 degrees – 5.2 degrees = 39.8 degrees

Fnet = 15.6 N [North 39.8 degrees West]
?
 
  • #7
alexandria said:
sorry to bring back this forum again, but i re-did this question, can anyone tell me if this is correct.
39.

8.0 N (north) + 10.0 N (south) = 2.0 N (south)
View attachment 98274c = ([17.0 N]2 + [2.0 N]2 - 2 (17.0 N) (2.0 N) cos45°) ½

c = 15.6 N

SinA/a = SinB/b = SinC/c

SinA/2.0 N = Sin45 degrees/15.6 N

SinA = (2.0 N) Sin45° / 15.6 N

A = sin^-1 (0.091)

A = 5.2 degrees

90 degrees – 5.2 degrees = 39.8 degrees

Fnet = 15.6 N [North 39.8 degrees West]
?
That all looks right except for a typo in making the post. You wrote 90- instead of 45- near the end.
 
  • #8
so then, its 45 - 5.2 = 39.8
thanks for the help.
 

1. What is net force?

Net force is the overall force acting on an object, taking into account the magnitude and direction of all individual forces acting on that object.

2. How do you calculate net force?

To calculate net force, you need to add up all the individual forces acting on an object. If the forces are acting in the same direction, you simply add them together. If the forces are acting in opposite directions, you subtract the smaller force from the larger force to find the net force.

3. What is the formula for calculating net force?

The formula for calculating net force is Fnet = ΣF, where Fnet represents the net force and ΣF represents the sum of all individual forces acting on the object.

4. What units are used to measure net force?

The units used to measure net force are Newtons (N). This is a unit of force in the metric system, which is equivalent to 1 kg*m/s².

5. How does net force affect an object's motion?

According to Newton's second law of motion, the net force acting on an object will cause it to accelerate in the direction of the force. If the net force is zero, the object will remain at rest or continue moving at a constant speed in a straight line.

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