What is the resultant force and what is its consequent acceleration?

[looi76]

[SOLVED] What is the resultant force and what is its consequent acceleration?

Homework Statement

http://img48.imageshack.us/img48/4810/assignment503ij5.png
What is the resultant force acting on the object in the figure, and what is its consequent acceleration?

Homework Equations

F = m.a
Vertical component = F\sin\theta
Horizontal component = F\cos\theta

The Attempt at a Solution

http://img153.imageshack.us/img153/4963/assignment50301fq6.png

Horizontal Component = \cos{45} \times 60 = 42.4N
Vertical Component = \sin{45} \times 60 = 42.4N

http://img81.imageshack.us/img81/1580/assignment50302ns9.png

Horizontal Component = \cos{30} \times 60 = 52.0N
Vertical Component = \sin{30} \times 60 = 30N

Total Horizontal Component = 52 - 42 = 10N
Total Vertical Component = 42 - (30 + 5) = 7N

c^2 = a^2 + b^2
x^2 = 7^2 + 10^2
x = \sqrt{7^2 + 10^2}
x = 12.2N

F = m.a

a = \frac{F}{m} = \frac{12.2}{5.0} = 2.4ms^{-2}

Is my answer correct?

 

[Hootenanny]

Vertical component = F\sin\theta
Horizontal component = F\cos\theta

You should be careful when applying these formulae, they are not universally valid. To use these formulae the angle must be measured from the horizontal. For example,

http://img153.imageshack.us/img153/4963/assignment50301fq6.png

Horizontal Component = \cos{45} \times 60 = 42.4N
Vertical Component = \sin{45} \times 60 = 42.4N

This is not correct, since the angle is measured from the vertical.

http://img81.imageshack.us/img81/1580/assignment50302ns9.png

Horizontal Component = \cos{30} \times 60 = 52.0N
Vertical Component = \sin{30} \times 60 = 30N

However, this solution is correct.

In general, it is better to understand how to resolve vectors rather than remembering specific formulae.

 

[looi76]

Thnx Hootenanny, but if I measure it from the horizontal its the same because the angle is 45^o and is the final answer wrong?

 

[Hootenanny]

Thnx Hootenanny, but if I measure it from the horizontal its the same because the angle is 45^o and is the final answer wrong?

Your final answers look okay to me (but I haven't checked your arithmetic), just be careful of rounding errors since you round off early in your calculations. I just wanted to emphasise that it is better to know how to result vectors rather than remembering formulae.

Secondly, remember than force and acceleration are vectors. Therefore, you need to quote the direction is which they act.