University of Wisconsin Green Bay

a.) Estimate how much pressure a cat puts exerts on you if it stands on you with all four paws. Give your answer in English units.

b.) How much more pressure do you feel at the bottom of a 6.0 m deep diving pool compared to the pressure you feel on land?
Give your answer in MKS units.

  • In part a) of this problem, you are asked to estimate the pressure exerted by a cat. The definition of pressure involves force and area; both are numbers that you can estimate for a cat. Therefore, you don’t need to do anything more complicated than work with the definition of pressure.

    In part b) of this problem, you are asked for the pressure exerted by a fluid at a given depth. Pressure and depth of a fluid are directly related through the definition of pressure of a fluid. Therefore, part b) is also a definition problem using the expression for pressure exerted by a fluid.

  • There is no need for a picture in most definition problems, and this is one of them.

    In part a), you can estimate force (weight) and area information and are asked for the closely-related pressure. A picture of a cat will not provide any additional insight or organization beyond what is already present in the problem.

    In part b), you are given information about depth of a fluid and are asked for the closely-related pressure due to that fluid. You may certainly draw a picture of a swimming pool if it helps to visualize the problem, but a drawing will not provide any organization beyond what is already present in the problem.

  • In equation form, pressure is defined as

    P = F/A

    This is the only relation you need for part a) of this problem.

    The pressure exerted by a fluid is given by

    Pfluid = ρfluidgh

    This is the only relation you need for part b) of this problem.

  • -- --

    a) P = F/A
    The force exerted by a cat is equal to the weight of a cat. I personally know house cats that weigh as little as 5 lb. and as much as 18 lb. so I will estimate the weight of a cat to be 12 lb. Any reasonable value that you select is fine.

    The area over which a cat exerts pressure is the area of its paws. Each paw has an area of around 1 square inch, so

    P 12 lb/ 4 sq. in.
    P 3 lb/sq. in.

    b) Pfluid = ρfluidgh
    Pwater = ρwatergh
    Pwater = (1000 kg/m3)(9.8 m/s2)(6.0 m)
    Pwater = 59,000 Pa

  • Each part of this problem is merely a definition problem. Pressure is defined as force/area, regardless of the cause of the force. In the particular case of a fluid, force is the weight of the fluid above you:

    Pfluid = (mg)fluid above you/A = (ρVg)fluid above you/A
    = ρfluidg(V/A) = ρfluidg(A h/A) = ρfluidgh

    and so in the case of a fluid the definition of pressure can be rewritten as ρfluidgh.

    Both parts of the problem are straightforward, single step, calculations once the correct version of the definition is identified. Because the unit Pascal is probably not a familiar one, you can see if you answer to part b) makes sense by comparing your answer to a known pressure. In this case, the pressure due to 6.0 m of water is a little over half atmospheric pressure (101,000 Pa) so it is reasonable.