Some insects can walk below a thin rod (such as a twig) by hanging from it. Suppose that such an insect has mass m and hangs from a horizontal rod as shown in Figure, with angle its six legs are all under the same tension, and the leg sections nearest the body are horizontal. (a) What is the ratio of the tension in each tibia (forepart of a leg) to the insect’s weight? (b) If the insect straightens out its legs somewhat, does the tension in each tibia increase, decrease, or stay the same?
(a) Ratio of the tension in each tibia to the insect’s weight is 0.26 .
(b) Tension will decrease in each tibia when the insect straightens out its legs.
The angle of the leg joint,
From the free-body diagram of the insect, we can calculate the tension in both cases. According to the conservation law, all forces acting on the body are to be balanced for the body to be at equilibrium. So, the total force in a given direction is zero.
Since, the total forces acting on the body are balanced in the given direction,
We take the summation of all forces in y direction to be zero, so from equation (i), we get
As there are 6 legs of the insect, we get the force from 6 sine components. Hence, we get,
Hence, the value of the required ratio is 0.26.
As the insect straightens out its legs, the value of anglewould increase. Since the is inversely proportional to the tension, as value ofincreases, the tension would decrease.
Holding on to a towrope moving parallel to a frictionless ski slope, a skier is pulled up the slope, which is at an angle of with the horizontal. What is the magnitude of the force on the skier from the rope when (a) the magnitude v of the skier’s velocity is constant at localid="1657161930942" and (b) as v increases at a rate oflocalid="1657161837037" ?
July 17, 1981, Kansas City: The newly opened Hyatt Regency is packed with people listening and dancing to a band playing favorites from the 1940s. Many of the people are crowded onto the walkways that hang like bridges across the wide atrium. Suddenly two of the walkways collapse, falling onto the merrymakers on the main floor.
The walkways were suspended one above another on vertical rods and held in place by nuts threaded onto the rods. In the original design, only two long rods were to be used, each extending through all three walkways (Fig. 5-24a). If each walkway and the merrymakers on it have a combined mass of M, what is the total mass supported by the threads and two nuts on (a) the lowest walkway and (b) the highest walkway?
Apparently, someone responsible for the actual construction realized that threading nuts on a rod is impossible except at the ends, so the design was changed: Instead, six rods were used, each connecting two walkways (Fig. 5-24b). What now is the total mass supported by the threads and two nuts on (c) the lowest walkway, (d) the upper side of the highest walkway, and (e) the lower side of the highest walkway? It was this design that failed on that tragic
night—a simple engineering error.
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