Calculating the net force acting on a object from diagrams

[hg10tr]

Homework Statement

Calculate the net force acting on each object indicated in the following diagrams.
(diagrams attached)

Homework Equations

Sine Law: sin a/a = sin b/b = sin c/ c
Cosine Law: c^2 = a^2 + b^2 -2ab*cos(c)
SOHCAHTOA

The Attempt at a Solution

a) c2 = a2 + b2 – 2ab cos(c)
c2 = 222 + 382 – 2(22)(38) cos(55)
c2 = 968.980
c = 31.1 N
sin⁡A/a= sin⁡B/b= sin⁡C/c
sin A/22 N= sin⁡(55)/31.1 N
Sin A= 22 N sin⁡(55)/31.1 N
A = 35.4 º
F net = 31.1 N [W35.4ºN]

b) I'm not sure how to do this one but I tried the following...

sin45=x/75
x = 12.02 N

8 Newtons + 10 Newtons = 18 Newtons

c=√a^2+b^2
=(18)^2+(12.02)^2
=√324+144
=√468
c=21.63N

And given this I can use the sin law to find cos (a)? I'm really unsure how to approach this one.

c)
32 degrees + 24 degrees = 56 degrees

c^2=a^2+b^2-2abCosC

=(15)^2 + (12)^2 -2(15)(12)Cos56

=√369-201.3

=12.94 N

Sin A / a = sin B/b = sin c/c

Sin (b) / 12 = sin (56) / 12.94

sin B = 0.7688

B = 50.2 degrees?

F net = 12.94 N [E 50.2 degrees N]

This is a concept I am not too confident with and I would greatly appreciate it if someone can look over my attempts and point out where I'm going wrong and steer me in the right direction. Thanks

 

[darkxponent]

You don't need sine and cosine rules here. First step is to break the components in x and y direction. Then sum up the x and y component independently.
Are you familier with Vectors?

 

[hg10tr]

We have learned a little bit about vectors, unfortunately we are only shown how to solve these types of problems with the sine and cosine law.

 

[darkxponent]

Okay then i can help you through the first problem. Then you will be able to do second and third yourself, or nay other problem of this kind.

In the first problem there are two Forces acting on the object. Can you write the Vectors for the two forces?

The net Force is simply the sum of the vectors of all forces.

Fnet = F1 + F2 +...+Fn- If there are n forces acting on object. F1,F2... are vectors of Forces

 

[hg10tr]

We haven't learned much of anything about vectors, we are currently on a unit about Newton's first law. I'm doing an online course and the examples that are given me to solve these problems just show how to use the sine and cosine law.

 

[darkxponent]

The sine and cosine rules that you are using is nothing but the concept of vector addition. They should have taught you vectors first. You found the magnitude of the first problem right but the direction is not correct.

You have made mess of second problem. The sine and cosine rules you are using is converting a very simple problem into a hard one. These problems with concepts of vectors is very easy one.
Even Vectors isn't a very difficult thing to understand. It will take you less than an hour or two to understand the two dimension vectors. So if your online course includes Vectors, you should first go through it.