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).