# Boy walking along a beam problem.?

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A 45 kg, 5.5-m-long beam is supported, but not attached to, the two posts in the figure(picture) . A 25 kg boy starts walking along the beam(shown in the picture I linked)

http://session.masteringphysics.com/problemAsset/1…

How close can he get to the right end of the beam without it falling over?

• The “fulcrum” is the support 3m. from the left end.

(45kg/5.5m) = 8.182kg/m. mass of plank.

Left, there is 3m.,= (3 x 8.182) = 24.546kg., with its CM 1.5m. left of the fulcrum.

Torque left = (1.5 x 24.546) = 36.819kg/m.

Right, there is 2.5m., with a mass of (2.5 x 8.182) = 20.455kg., with its CM at 1.25m.

Torque right = 25.569kg/m.

Torque difference = (36.819 – 25.569) = 11.25kg/m.

The boy is 25kg., so can only go right past the fulcrum (11.25/25) = 0.45m.

Distance from right end = (2.5 – .45) = 2.05m.

• let’s call the normal force of the left support Fl and the normal force of the right support, Fr

we will sum torques around the right support post; if the boy is a distance x from the left end, he

is x-3 m from the right support post

the center of mass is 2.75m from the left end, and 0.25m from the right support post

if the beam is not to rotate, the sum of torques around the right support post must be zero; this condition can be written:

Fl x 3m – 45kg x 9.8m/s/s x 0.25m + 25kg x 9.8m/s/s x (x-3) = 0

the first term is the torque due to the left support; we call that sense of rotation positive

the second term is the torque due to the weight of the beam acting at the center of gravity; its sense is counterclockwise so is negative

the final term is the torque due to the boy, it is clockwise and thus positive

the beam loses contact with the left support when Fl=0, or when

– 45kg x 9.8m/s/s x 0.25m + 25kg * 9.8m/s/s * (x-3) = 0

solve for x; I get x = 3.45 m from the left end of the beam

• You need to use moments of force:

Looks to me like he can reach the very end.

There is 45kg x 3m on one side and 2.5 x 25kg on the other – the weight of the beam at that point will always support him (I think).

• How drunk is he ?

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