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End A of the bar AB in the fig rests on a frictionless horizontal surface, and end B is hinged. A horizontal force Fof magnitude 220 N is exerted on end A. Ignore the weight of the bar. What are the horizontal and vertical components of the force exerted by the bar on the hinge at B?

Short Answer

Expert verified

Horizontal component is 220 N to the right and vertical component is 293 N upward.

Step by step solution

01

The given data

Given that end A of the bar AB rests on a frictionless horizontal surface, and end B is hinged.

A horizontal force Fof magnitude 220 N is exerted on end A.

So horizontal forceF=220N

Weight of the bar is negligible.

02

Formula used

Torque=Fl

Where Fis force exerted and l is distance.

03

Find the horizontal and vertical component of force.

Let HvandHhare vertical and horizontal components of force exerted on the bar by the hinge.

Let nis the normal force exerted on the bar by the surface.

The components of force of the bar on the hinge will be equal in magnitude but opposite in direction.

Force of bar on hinge in horizontal direction Fx=Hh=220N

Force of bar on hinge in vertical directionFy=n-Hv

Now, applying the condition of equilibrium,

Net torque is zero.

This implies

F4m-n3m=0400N4m-n3m=0n=293N

ThusHv=293N

04

Conclusion

Hence, horizontal component of force exerted on the bar by the hinge is 220 N to the right and vertical component is 293 N upward.

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