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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

In most species of clingfish (family Gobiesocidae), pelvic and pectoral fins converge to form a suction cup edged by hairy structures that allow a good seal even on rough surfaces. Experiments have shown dial a clingfish’s suction cup can support up to 230 times the fish’s body weight. Suppose a 30.0-g northern clingfish has a suction cup disk area of 15.0 cm2 and the ambient water pressure is 1.10 × 105 Pa. What ratio Pcop/Pambient of the pressure inside the suction cup to the ambient pressure allows the fish to support 230 times its body weight?

To determine
The ratio Pcup/Pambient of the pressure inside the suction cup to the ambient pressure allows the fish to support 230times its body weight.

Explanation

Given info: The mass of the fish is 30.0kg , area of the suction cup is 15.0cm2 , the ambient pressure is 1.10×105N/m2 , and acceleration due gravity is 9.80m/s2 .

Explanation: There are three kinds of forces involved in the suction cup. They are a force due to its 230 times weight and a force due to the pressure created inside the cup and both these two forces act along downward direction. Another force on the cup that be directed upward due to outside pressure. By applying Newton’s equations of motion at its static equilibrium condition Fy=0=(230mfish)gPcupAcup+PambientAcup and this expression is rearranged for the pressure ratio.

The formula for the pressure inside the suction cup to the ambient pressure is,

PcupPambient=1230mgPambientAcup

m is mass of the fish.

g is acceleration due to gravity.

Pambient is ambient pressure.

Acup is area of the cup.

Substitute 30.0kg for m , 9.80m/s2 for g , 1.10×105N/m2 for Pambient , and 15

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