A plant hangs from a 1.9 cm diameter suction cup affixed to a smooth horizontal surface (there's a figure but it's pretty simple, a plant in a plant pot hanging from a couple wires, but what seems to matter is the suction cup part).
(a) What is the maximum weight that can be suspended at sea level?
(b) What is the maximum weight that can be suspended in Denver, where atmospheric pressure is about 0.80 atm?
To find the maximum weight that can be suspended by a suction cup, we need to consider the maximum force it can generate. The maximum force is determined by the pressure difference between the inside and outside of the suction cup.
(a) To calculate the maximum weight that can be suspended at sea level, let's assume that the inside of the suction cup is fully evacuated (i.e., a perfect vacuum). At sea level, atmospheric pressure is around 1 atm.
We can use the following formula to calculate the force exerted by the suction cup:
Force = Pressure difference × Area
The pressure difference is the difference between the atmospheric pressure (outside the suction cup) and the pressure inside, which is zero in this case.
Area is the cross-sectional area of the suction cup, which can be calculated using the formula for the area of a circle:
Area = π × (radius)^2
Given that the diameter is 1.9 cm, the radius (r) is half of the diameter, which will be 0.95 cm or 0.0095 m.
Substituting these values into the formulas:
Pressure difference = (1 atm - 0 atm) = 1 atm
Area = π × (0.0095 m)^2
Now, let's plug the values into the force equation:
Force = (1 atm) × π × (0.0095 m)^2
Calculating this expression will give us the maximum force that the suction cup can generate. To convert this force into weight, we need to use the equation:
Weight = Force × gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
(b) To find the maximum weight that can be suspended in Denver, where atmospheric pressure is about 0.80 atm, we will follow the same steps as in part (a), but use a different pressure difference in the force equation.
Pressure difference = (0.80 atm - 0 atm) = 0.80 atm
Again, we will use the same formula to calculate the maximum force and then convert it to weight using the gravitational acceleration.