Question

Determine the magnitude of the component of F directed along the axis of AB. Set F = 520 N .

Answer 1

Answer:

The component of F along AB is equal to Fcos45

F = 520N

Component along AB = 520cos45

= 367.7N

This is done by rotating the diamonds such that AB is now taken as the x-axis. Then the force F is resolved along AB.

Explanation:

Answer 2

Answer:

Force AB = 466.2N

Force AC = 380.7N

Complete Question:

The vertical force F acts downward at A on the two membered frame. Determine the magnitude of the component of F directed along the axis of AB . Set F=520 N

Determine the magnitude of the component of F directed along the axis of AC.

Attached is the image of the question.

Explanation:

Given the force distribution in the image attached:

Let X represent force AB and Y represent force AC

F = 520N

Resolving the force distribution to the vertical and horizontal components.

For vertical component (x axis)

F = Xcos45 + Ycos60 .....1

For horizontal component ( y axis)

Xsin45 = Ysin60 .....2

From equation 2

Y = Xsin45/sin60 ....3

Substituting equation 3 into equation 1

F = Xcos45 + (Xsin45/sin60)cos60

F = X ( cos45 + (sin45/sin60)cos60)

X = F/ ( cos45 + (sin45/sin60)cos60)

Substituting F = 520N and solving for X

X = 520/ ( cos45 + (sin45/sin60)cos60)

X = 466.2N

From equation 3.

Y = Xsin45/sin60

Y = 466.2sin45/sin60

Y = 380.7N

Therefore,

Force AB = 466.2N

Force AC = 380.7N