A 100-kg, 6.0 m long beam is supported on either end by sturdy, thin legs. A stu

Question

A 100-kg, 6.0 m long beam is supported on either end by sturdy, thin legs. A student with a mass of 80. kg stands on the beam, 4.0 m to the right of the left leg. What is the upwards force exerted on the beam by each individual leg? D) This is a similar scenario to the previous problem, except that now the right leg has been moved in, such that it is 2.0 meters in from the right side of the beam, directly underneath where the student is standing. The left leg is still at the very left side of the beam. If the student begins to walk to the right, how far can he go before the beam falls over.)

Explanation / Answer

part C:

let force by left leg be F1 and force by right leg be F2.

both be in upward directions.

other forces acting on the beam area:

weight of the beam =100*9.8=980 N, acting at 3 m from the left leg.

weight of the student=80*9.8=784 N, 4 m from the left leg

balancing forces in vertical direction:

F1+F2=980+784=1764 N...(1)

balancing torque about the left leg:

F2*6=980*3+784*4

==>F2=1012.67 N

then F1=1764-F2=751.33 N

so force by the left leg is 751.33 N and force by right leg is 1012.67 N

part D:

let the student can go till distance d meters from the left leg before the beam topples

when that happens, force on the left leg=0 (as the beam is just about to lose contact)
balancing total torque about right leg:

980*(4-3)=784*(d-4)

==>d=5.25 m

so the student can go till 5.25 meters from the left leg till the beam topples.

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