Solving Force Problems: Finding F with Trig and Components

[rt525600]

I'm having a lot of trouble solving force problems even though I understand the concepts (or, at least I think I do). This is a specific example:

A sphere of mass 3.0 x E-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 34 degrees with the vertical when at rest.

Find the a) magnitude of that push and b) the tension in the cord.


The only equation that I know of to solve force problems is F=ma. We have m.


I think that I can use trig to find F, but I can't figure out how.
I tried to solve for F by using components: I found the downward force by finding mg (= -2.94 E-3). I'm kind of stuck now. Any suggestions?

 

[learningphysics]

Divide the tension in the cord into 2 compoennts... horizontal and vertical. If T is the tension, what is the horizontal component of tension? what is the vertical component of tension?

net force in x direction = max... however ax = 0

net force in the x direction = 0

same way

net force in the y direction = 0

What are the forces acting vertically... what are the forces acting horizontally?

 

[ogb p]

First of all, it is important to note that in order to solve force problems, you need to consider all the forces acting on an object and their respective directions. In this specific example, the forces acting on the sphere are the weight (mg) and the horizontal push from the breeze (F).

To find the magnitude of the push (F), you can use trigonometry to solve for the horizontal component of this force. Since the cord makes an angle of 34 degrees with the vertical, the horizontal component of the force (Fcos34) will be equal to the magnitude of the push. You can then use this value in the equation F=ma, where m is the mass of the sphere and a is the acceleration in the horizontal direction (which is 0 since the sphere is at rest).

To find the tension in the cord, you need to consider the vertical forces acting on the sphere. The tension in the cord (T) will be equal to the vertical component of the weight (mgcos34) plus the vertical component of the push (Fsin34). You can then use this value in the equation T=ma, where m is the mass of the sphere and a is the acceleration in the vertical direction (which is also 0 since the sphere is at rest).

It is important to carefully consider all the forces and their respective components in order to solve force problems accurately. I would suggest practicing with different examples and seeking help from a teacher or tutor if necessary. Good luck!