Need help in physics finding magnitude in word problem

Physics
Tutor: None Selected Time limit: 1 Day

The 4.9 N weight is in equilibrium under the influence of the three forces acting on it. The F force acts from above on the left at an angle of α with the horizontal. The 5.9 N force acts from above on the right at an angle of 48◦ with the horizontal. The force 4.9 N acts straight down.

What is the magnitude of force F

Jun 2nd, 2015

Thank you for the opportunity to help you with your question!

5.9 N ......... 4.9 N
...┌...... ......┐
.....\..... ...../
.....α\... .../ ß
-------- \ . /---------
...........◙
............|
............|
...........V 4.9 N 

(It wasn't clear from your description whether the two angled forces act upward or downward, but if they're going to be in equilibrium with the weight, they should be upward.) 

So, we're in static equilibrium - the body is not accelerating. From the vector version of F = ma, that means that the net vector force is zero. If the vector force is zero, that means that orthogonal components of the net vector force are zero. So, we take the horizontal and vertical directions (which are orthogonal), find the net force components in those directions, and set them equal to zero. We need to define the positive and negative directions for those components, so let's say that the positive x direction is to the right, and the positive y direction is up.

In the x direction, the weight has no component. The 5.9 N force component acts in the -x direction, with magnitude -5.9 N * cos α. The 4.9 N force component acts in the +x direction, with magnitude +4.9 * cos ß. So, the sum of forces in the x direction (which is equal to zero) is 

ΣFx = -5.9 N * cos α + 4.9 N * cos ß = 0

In the y direction, the weight acts in the negative direction, with magnitude -9.6 N. The other forces act in the +y direction, with magnitude 5.5 N * sin α and 6.4 N * sin ß. So, the sum of forces in the y direction (which is equal to zero) is

ΣFy = -4.9 N + 4.9 N * sin α + 4.9 N * sin ß = 0

So, we have 2 equations, and 2 unknowns, and we can solve. Let's start with the first equation.

-5.9 N * cos α + 4.9 N * cos ß = 0
5.9 * cos α = 4.9 * cos ß
cos α = (4.9 / 5.9) * cos ß 


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 2nd, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jun 2nd, 2015
...
Jun 2nd, 2015
Feb 23rd, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer