A uniform beam 4.00 m long and weighing 2250 Ncarries a 3350 N weight 1.50 m fro

Question

A uniform beam 4.00 m long and weighing 2250 Ncarries a 3350 N weight 1.50 m from the far end, as shown in the figure below (Figure 1) . It is supported horizontally by a hinge at the wall and a metal wire at the far end.

a.) How strong does the wire have to be? That is, what is the minimum tension it must be able to support without breaking

b.) What are the horizontal component of the force that the hinge exerts on the beam?

c.) What are the vertical component of the force that the hinge exerts on the beam?

Explanation / Answer

let the minimum tension be T...

take the moment about the hinge point...

2250*4/2 + 3350*(4-1.5) = T*4

so T = 3218.75 N

Also the forces should be balanced....

there is no horizontal force at all... so horizontal componet at hinge is zero.

In vertical direction...... Fv + T = 2250+3350

Fv = 2250+3350-3128.75 = 2381.25 N

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