Chapter 12: Q66P (page 352)

A uniform beam is $5 .0 m$ long and has a mass of $53 kg$ . In Fig. 12-74, the beam is supported in a horizontal position by a hinge and a cable, with angle $θ = 60 °$ . In unit-vector notation, what is the force on the beam rom the hinge?

Short Answer

Expert verified

The force on the beam in unit vector notation, $F_{P} = (- 150 N) \hat{i} + (260 N) \hat{j}$ .

Step by step solution

Understanding the given information

Mass, $m = 53 kg$

Length of the beam, $L = 5.0 m$

$θ = 60 °$

Concept and formula used in the given question

Using the condition for the static equilibrium, you can write the equation for forces for the given figure. In addition, the equation for the torque can be written about a pivot point. The equations are given below and can be solved for the unknown forces.

Condition of equilibrium,

$\begin{array}{l} τ = 0 \\ Momentofforce=perpendiculardistance×Force \end{array}$

Calculation for theforce on the beam from the hinge

As we see the diagram, we can say that

$\begin{array}{l} T s i n 60 ° \times L - m g \times (\frac{L}{2}) = 0 \\ T s i n 60 ° = m g \times \frac{(\frac{L}{2})}{L} \\ T s i n 60 ° = \frac{m g}{2 s i n 60} \\ T s i n 60 ° = 300 N \end{array}$

As the system is in equilibrium, we can say

$\begin{array}{l} \sum F_{x} = 0 \\ \sum F_{y} = 0 \end{array}$

So,

$\begin{matrix} F_{P x} = - T c o s θ \\ = - (300 N) (0.5) \\ = - 150 N \\ F_{P y} = M g - T s i n 60 ° \\ = (519.4 N) - (300 N \times 0.8660) \\ = 260 N \end{matrix}$

So, we get

$F_{P} = (- 150 N) \hat{i} + (260 N) \hat{j}$

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A uniform beam is $5 .0 m$ long and has a mass of $53 kg$ . In Fig. 12-74, the beam is supported in a horizontal position by a hinge and a cable, with angle $θ = 60 °$ . In unit-vector notation, what is the force on the beam rom the hinge?

Short Answer

Step by step solution

Understanding the given information

Concept and formula used in the given question

Calculation for theforce on the beam from the hinge

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A uniform beam is 5.0 mlong and has a mass of 53 kg. In Fig. 12-74, the beam is supported in a horizontal position by a hinge and a cable, with angleθ=60°. In unit-vector notation, what is the force on the beam rom the hinge?

Short Answer

Step by step solution

Understanding the given information

Concept and formula used in the given question

Calculation for theforce on the beam from the hinge

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Dynamics

Engineering Physics

Linear Momentum

Radiation

Astrophysics

Study anywhere. Anytime. Across all devices.

A uniform beam is $5 .0 m$ long and has a mass of $53 kg$ . In Fig. 12-74, the beam is supported in a horizontal position by a hinge and a cable, with angle $θ = 60 °$ . In unit-vector notation, what is the force on the beam rom the hinge?