Sam Joe 1.00 m 2.00 m- A uniform beam of length 8.70 m and weight 1.28 X 10 N is

Question

Sam Joe 1.00 m 2.00 m- A uniform beam of length 8.70 m and weight 1.28 X 10 N is carried by two workers, Sam and Joe, as shown above. a) What is the first condition for equilibrium? b) What is the second condition for equilibrium? c) Write the equation showing all the forces acting on the beam in this problem. d) What point on the beam will you choose to be the axis of rotation? e) Write the equation showing all the torques acting on the beam in this problem. f) Determine the force that Sam exerts on the beam. g) Determine the force that Joe exerts on the beam.

Explanation / Answer

let forces on the beam are:

force by sam , in vertically upward direction=Fs

force by joe, in vertically upward direction=Fj

part a:

first condition of equilibrium:

sum total of all the forces on the beam =0

part b:

second condition of equilibrium:

total torque about any point on the beam =0

part c:

balancing all the forces:

Fs+Fj=weight of the beam=1.28*10^2 N

part d:

let axis of rotation be passing through the point where sam is holding the beam

part e:

balancing all the torque:

weight*((8.7/2)-1)=Fj*(L-1-2)

==>1.28*100*3.35=Fj*5.7

part f:

Fj=1.28*100*3.35/5.7=75.228 N

thn Fs=1.28*10^2-Fj=52.772 N

hence force exerted by sam is 52.772 N in upward direction

part g:

force exerted by joe is 75.228 N, in upward direction.

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