Question

Two forces are of magnitude 450N and 240N respectively . Determine
{a} the maximum magnitude of the resultant force
{b} the minimum magnitude of the resultant
{c}the resultant force when the forces act at right angles to each other.
{d} Use scaled vector diagram to determine the resultant of [c] above and compare your results

Answer 1

Answer on Question #47017, Physics, Mechanics | Kinematics | Dynamics

Question:

Dear expert, please provide an answer to the question below within 12 hours.

Two forces are of magnitude 450N and 240N respectively. Determine

(a) the maximum magnitude of the resultant force

(b) the minimum magnitude of the resultant

(c) the resultant force when the forces act at right angles to each other.

(d) Use scaled vector diagram to determine the resultant of [c] above and compare your results

Answer:

We have 2 vectors $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ and their resultant force $\vec{F}$. Magnitude of $\vec{F}$ equals:

$$c = \sqrt{a^2 + b^2 + 2ab \cos \alpha}$$

where $\alpha$ – angle between $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$.

a) F is maximum if $\cos \alpha = 1$:

$$F = F_1 + F_2 = 450 + 240 = 690\,N$$

b) F is maximum if $\cos \alpha = -1$:

$$F = F_1 - F_2 = 450 - 240 = 210\,N$$

c) when the forces act at right angles to each other $\cos \alpha = 0$:

$$F = \sqrt{F_1^2 + F_2^2} = \sqrt{450^2 + 240^2} = 510\,N$$

d)

Length of $F_{1} + F_{2}$ around 51 units, therefore:

$$F _ {1} + F _ {2} \cong 5 1 0 N$$

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