A cook holds a 2.59-kg carton of milk at arm's length (see the figure below). What force vector F B

Physics
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A cook holds a 2.59-kg carton of milk at arm's length (see the figure below). What force vector F B must be exerted by the biceps muscle? (Ignore the weight of the forearm. State the magnitude of the force vector F B.) N

Jun 11th, 2015

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Jun 11th, 2015


Jun 11th, 2015

The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium (netτ=0) becomes

r2wa+r3wb=r1FB.

Note that sinθ=1 for all forces, since θ=90º for all forces. This equation can easily be solved for FB in terms of known quantities, yielding

FB=r2wa+r3wbr1.

Entering the known values gives

FB=(0.160m)(2.50kg)(9.80m/s2)+(0.380m)(4.00kg)(9.80m/s2)0.0400m

which yields

FB=470 N.

Now, the combined weight of the arm and its load is (6.50 kg)(9.80m/s2)=63.7 N, so that the ratio of the force exerted by the biceps to the total weight is

FBwa+wb=47063.7=7.38.


Jun 11th, 2015

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