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A 10.0-cm diameter suction cup is pushed against a smooth ceiling. Assuming that the mass of the cup is negligible, the maximum mass of an object that can be suspended from the suction cup without pulling it off is closest to:

(a)81kg
(b)42kg
(c)20kg
(d)323kg
(e)7kg

User Mr Morgan
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1 Answer

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Final answer:

The maximum mass that can be suspended from the suction cup without pulling it off is approximately 8.12 kg.

Step-by-step explanation:

To determine the maximum mass that can be suspended from the suction cup without pulling it off, we need to consider the maximum force it can withstand. The force holding the cup against the ceiling is the atmospheric pressure acting on the upper surface of the cup, and it can be calculated using the formula:

Force = Pressure x Area

The atmospheric pressure at sea level is approximately 101,325 Pa. We also need to convert the diameter of the suction cup to radius by dividing it by 2. The radius is then 5.0 cm = 0.05 m.

Substituting these values into the formula, we get:

Force = 101325 Pa x π(0.05 m)^2

Simplifying the equation, the force is approximately 79.6 N (Newton).

The maximum mass that the suction cup can suspend without pulling it off is equal to the weight of the object. Using the formula:

Weight = Mass x Acceleration due to gravity

Assuming the acceleration due to gravity is 9.8 m/s², we can rearrange the equation to solve for mass:

Mass = Weight / Acceleration due to gravity

Substituting the value of the force, we get:

Mass = 79.6 N / 9.8 m/s²

The mass is therefore approximately 8.12 kg.

User Jamie Ronin
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