The drawing shows a uniform horizontal beam attached to a vertical wall by a fri

Question

The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle ? = 45degrees by a brace that is attached to a pin. The beam has a weight of 340 N. Three additional forces keep the beam in equilibrium. The brace applies a force P to the right end of the beam that is directed upward at the angle with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component H and a vertical component V. Find the magnitudes of these three forces.

Explanation / Answer

Horizontal force = Pcos - H = 0 -(1)

Vertical force = Psin + V - W = 0 - (2)

Torques = W(0.5*L) - VL = 0 -(3)

From equation 3,

VL = W(0.5*L)

V = 0.5W

= 0.5(340) = 170 N

sub the value into equation 2,

Pin + 0.5 W - W = 0

Psin = 0.5(340)

P = 170 / sin45 = 240.16 N

sub the value into equation 1,

Pcos - H = 0

H = 240.16cos45 = 170 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.