M2 Question Help Watch

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jakegreen
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#1
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A Semicircular Metal Plate Of Radius 1m Is Freely Hinged At A So That It Can Move In A Vetical Plane. The Plane Is Of Mass 5kg And Is Maintained In Equilibrium, With The Boundary Diameter Ab Vertical And B Above A, By A Horizontal Cable Attached At B And In The Vertical Plane Of The Plate. By Modelling The Plate By A Uniform Semicircular Lamina, Find:

A) Tenstion T In Cable
B) The Horizontal And Vertical Components Of Force Exerted By Hinge On The Plate.

Also,

A Uniform Rod Ab Of Length 4m And Mass 4kg Is Freely Hinged At A To A Vertical Wall. A Force P Is Applied At B At Right Angles To The Rod In Order To Keep The Rod In Equilibrium At An Angle Of 30 Degrees To Horizontal.

Find:
A) Magnitude Of R, The Reaction At The Hinge.

Thanks For Your Help.
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JamesF
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Can you draw a picture please.
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jakegreen
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heres the diagram
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jakegreen
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heres the diagram
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Fermat
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Position of c.o.g of a semi-circular plate is,

b=4r/(3pi)

Take moments about A

5gb=2rT
5x9.81x4x2/(3xpi)=2x2xT
T=10.408 N

Resolving horizontal and vertical components

Rsin(t)=T
Rcos(t)=5g
tan(t)=T/5g=10.408/5x9.81
tan(t)=0.2122
t=11.98 deg

Rcos(t)=5g
R=5g/cos(11.98)

R=50.14 N
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Fermat
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(Original post by jakegreen)
...
A Uniform Rod Ab Of Length 4m And Mass 4kg Is Freely Hinged At A To A Vertical Wall. A Force P Is Applied At B At Right Angles To The Rod In Order To Keep The Rod In Equilibrium At An Angle Of 30 Degrees To Horizontal.

Find:
A) Magnitude Of R, The Reaction At The Hinge.

Thanks For Your Help.
Resolve the weight into components along and perpindicular to the rod.
Component along the rod = 4sin 30 =2kg

Therefore Reaction at hinge is 2g N in direction of rod
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