Net force of object indicated in following diagram

In summary, the homework statement is to calculate the net force acting on an object indicated in the diagrams.
  • #1
Evangeline101
112
5

Homework Statement


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

1)
upload_2016-5-4_15-20-43.png


2)
upload_2016-5-4_15-21-18.png

Homework Equations


upload_2016-5-4_15-22-33.png

[/B]
upload_2016-5-4_15-22-57.png


The Attempt at a Solution



1)
8.0 N (north) + 10.0 N (south)
- 8.0 N (south) + 10.0 N (south)
= 2.0 N (south)

c= [ (2.0 N) 2 + (17.0 N) 2 - 2 (2.0 N) x (17.0 N) cos 45° ] 1/2
c= 15.6 N

sinA/2.0N = sin45°/15.6N

A= 5.2°
A= 45° - 5.2° = 39.8°

Fnet = 15.6 N [N 39.8° W]

2)
c= [ (12 N) 2 + (15 N)2 - 2 (12 N) x (15 N) cos124°]
c= 23.9 N

sinA/15N = sin124°/ 23.9 N

A = 31°

Fnet = 23.9 N [ N 31° E]

is this correct?
 
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  • #2
I agree with both magnitudes.

In 1, you do not show a diagram for the triangle of forces, so I'm not sure what your angle A is. You seem to have used it inconsistently, leading to the wrong answer for direction of force.

In 2, the angle you found is not the one you want. It seems to be the angle between the resultant and the 12N force.

Can you post your force triangle diagrams?
 
  • #3
haruspex said:
In 1, you do not show a diagram for the triangle of forces, so I'm not sure what your angle A is. You seem to have used it inconsistently, leading to the wrong answer for direction of force.

1)
Here is the diagram for 1) :

upload_2016-5-6_20-13-21.png

I corrected my answer for 1) :

8.0 N (north) + 10.0 N (south)

-8.0 N (south) + 10.0 N (south)

= 2.0 N (south)

c = [(2.0 N)2 + (17.0 N)2- 2 (2.0 N) x (17.0 N) cos 45°]1/2

c = 15.6 N

sinA/a = sinB/b = sinC/c

sinA/2.0 N = sin 45°/15.6 N

A = 5.2°

45° - 5.2° = 39.8°

Fnet = 16 N [ W 40° N]

is this better?
 
Last edited:
  • #4
haruspex said:
In 2, the angle you found is not the one you want. It seems to be the angle between the resultant and the 12N force.

2)
Here is the diagram for 2):
upload_2016-5-6_20-26-14.png


I also corrected my answer for 2) :

c2 = a2 + b2 - 2abcosC

c = (a2 + b2 - 2abcosC)1/2

c = [(12 N)2 + (15 N)2- 2 (12 N) x (15 N) cos 124°]1/2

c = 23.9 N

sinA/a = sinB/b = sinC/c

sinA/15 N = sin 124°/ 23.9 N

A = 31°

32° - 31° = 1°

90° - 1° = 89°

Fnet = 24.0 N [N 89° E] or 24.0 N [E 1° N]

better?
 
Last edited:
  • #5
Evangeline101 said:
1)
Here is the diagram for 1) :

View attachment 100369
I corrected my answer for 1) :

8.0 N (north) + 10.0 N (south)

-8.0 N (south) + 10.0 N (south)

= 2.0 N (south)

c = [(2.0 N)2 + (17.0 N)2- 2 (2.0 N) x (17.0 N) cos 45°]1/2

c = 15.6 N

sinA/a = sinB/b = sinC/c

sinA/2.0 N = sin 45°/15.6 N

A = 5.2°

45° - 5.2° = 39.8°

Fnet = 16 N [ W 40° N]

is this better?
Looks right.

Edit: the angle might be a bit inaccurate. Retry it keeping more significant digits at each step.
Doing it a slightly different way (using arctan) I got about 42 degrees.
 
Last edited:
  • #6
Evangeline101 said:
2)
Here is the diagram for 2):
View attachment 100371

I also corrected my answer for 2) :

c2 = a2 + b2 - 2abcosC

c = (a2 + b2 - 2abcosC)1/2

c = [(12 N)2 + (15 N)2- 2 (12 N) x (15 N) cos 124°]1/2

c = 23.9 N

sinA/a = sinB/b = sinC/c

sinA/15 N = sin 124°/ 23.9 N

A = 31°

32° - 31° = 1°

90° - 1° = 89°

Fnet = 24.0 N [N 89° E] or 24.0 N [E 1° N]

better?
yes, but again the angle could be a touch more accurate.
 
  • #7
haruspex said:
Edit: the angle might be a bit inaccurate. Retry it keeping more significant digits at each step.
Doing it a slightly different way (using arctan) I got about 42 degrees.

Ok, I will keep a few more significant digits to make the angle more accurate. Anyway, thanks for the help :)
 

1. What is the net force of the object in the diagram?

The net force of the object in the diagram is the overall or total force acting on the object. It is the sum of all the individual forces acting on the object in a specific direction.

2. How is the net force calculated for the object in the diagram?

The net force is calculated by adding all the forces acting on the object in a specific direction. If the forces are acting in the same direction, they are added together. If they are acting in opposite directions, they are subtracted from each other.

3. What happens if the net force is zero?

If the net force is zero, it means that all the forces acting on the object are balanced and there is no overall force acting on the object. The object will either remain at rest or continue moving at a constant velocity.

4. What does a positive net force mean?

A positive net force means that the forces acting on the object are unbalanced and there is a greater force acting in one direction. This will cause the object to accelerate in that direction.

5. How does the net force affect the motion of the object?

The net force determines the acceleration of the object. If the net force is greater than zero, the object will accelerate in the direction of the net force. If the net force is zero, the object will either stay at rest or continue moving at a constant velocity.

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