Question

Problem 3: An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.45 m2, and you may assume that his back is essentially flat. The gauge pressure of the water at the depth of the otter is P = 10500 Pa.

Part (a) Enter an expression for the magnitude of the force F on the back of the otter in terms of the gauge pressure P and the atmospheric pressure P0.

Part (b) Solve for the magnitude of the force F, in newtons.

Part (c) The direction of the force F is always ________ to the surface the water is in contact with (in this case, the back of the otter).

Answer 1

The magnitude of the force F on the back of the otter can be determined using the equation F = A(P - P0), where A is the surface area of the otter's back, P is the gauge pressure of the water, and P0 is the atmospheric pressure. The direction of the force F is always perpendicular to the surface the water is in contact with, in this case, the back of the otter.

Step-by-step explanation:

To determine the magnitude of the force F on the back of the otter, we can use the equation F = A(P - P0), where A is the surface area of the otter's back, P is the gauge pressure of the water, and P0 is the atmospheric pressure. So the expression for the magnitude of the force F is F = 0.45(P - P0).

To solve for the magnitude of the force F, we need to know the value of the atmospheric pressure P0. Once we have that value, we can plug it into the expression F = 0.45(P - P0) to calculate the force.

The direction of the force F is always perpendicular to the surface the water is in contact with, in this case, the back of the otter. This is because pressure is exerted perpendicular to all surfaces it contacts, as shown in the diagrams provided.

Answer 2

The magnitude of the force F on the otter's back is given by F = A(P - P₀), where A is the surface area (0.45 m²), P is the gauge pressure (10500 Pa), and P₀ is atmospheric pressure (101325 Pa). Substituting the values yields F ≈ -2541 N. The force F acts perpendicular to the otter's back.

Part (a) Expression for the magnitude of the force F

The magnitude of the force F on the back of the otter can be expressed as:

F = A(P - P₀)

where:

F is the force on the back of the otter (in newtons, N)

A is the surface area of the otter's back (0.45 m²)

P is the gauge pressure of the water at the depth of the otter (10500 Pa)

P₀ is the atmospheric pressure (approximately 101325 Pa)

Part (b) Solving for the magnitude of the force F

Plugging in the given values:

F = (0.45 m²)(10500 Pa - 101325 Pa)

F ≈ -2541 N

Part (c) Direction of the force F

The direction of the force F is always perpendicular to the surface the water is in contact with (in this case, the back of the otter).