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

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

## Homework Statement

http://img48.imageshack.us/img48/4810/assignment503ij5.png [Broken]
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 [Broken]

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

http://img81.imageshack.us/img81/1580/assignment50302ns9.png [Broken]

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

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

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

$$F = m.a$$

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

Last edited by a moderator:

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Hootenanny
Staff Emeritus
Gold Member
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 [Broken]

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 [Broken]

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.

Last edited by a moderator:
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
Staff Emeritus
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?