If F2 = 150 and θ = 55°, determine the magnitude and direction, measured clockwise from the positive x axis, of the resultant force of the three forces acting on the bracket.

Question

If [latex]F_{2} [/latex] = 150 and θ = 55°, determine the magnitude and direction, measured clockwise from the positive x axis, of the resultant force of the three forces acting on the bracket.

Accepted Answer

Scalar Notation: Summing the force components algebraically, we have

[latex]\overset{+}{\longrightarrow } F_{R_{x} } = \sum{F_{x}; F_{R_{x}}=80+52\left(\frac{15}{3} \right) } +150 cos 80^{°}[/latex]

= 126.05 lb →

[latex] +\uparrow F_{R_{y} } = \sum{F_{y}; F_{R_{y} }=52\left(\frac{12}{13} \right) } -150 sin 80^{°} [/latex]

= -99.72 lb = 99.72 lb ↓

The magnitude of the resultant force [latex] F_{R} [/latex] is:

[latex] F_{R} = \sqrt{F^{2}_{R_{x} } + F^{2}_{R_{y} }} =\sqrt{126.05^{2}+99.72^{2} } =161 [/latex] lb

The direction angle θ measured clockwise from positive x axis is

[latex]θ = tan^{-1} \frac{F_{R_{y} }}{F_{R_{x} }} =tan^{-1}\left(\frac{99.72}{126.05} \right) =38.3° [/latex]

Question 2.57: If F2 = 150 and θ = 55°, determine the magnitude and directi...

Related Answered Questions

Determine the magnitude and coordinate direction angles of the resultant force. Set FB = 630 N, FC = 520 N and FD = 750 N, and x = 3 m and z = 3.5 m. ...

Verified Answer:

If FB = 560 N and FC = 700 N, determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole. ...

Verified Answer:

Determine the components of F that act along rod AC and perpendicular to it. Point B is located at the midpoint of the rod. ...

Verified Answer:

Determine the components of F that act along rod AC and perpendicular to it. Point B is located 3 m along the rod from end C . ...

Verified Answer:

Determine the angle Φ between cable AC and strut AO. ...

Verified Answer:

Determine the angle θ between cables AB and AC . ...

Verified Answer:

Determine the magnitude of the projection of force F = 600 N along the u axis. ...

Verified Answer:

Determine the magnitudes of the components of F = 600 N acting along and perpendicular to segment DE of the pipe assembly. ...

Verified Answer:

Solve Prob. 2-7 with F=350 Ib. ...

Verified Answer:

Two cables exert forces on the pipe. Determine the magnitude of the projected component of F1 along the line of action of F2. ...

Verified Answer: