Comparing Pressure Exerted by the Same Force on Different Areas

The same force of 1 N is applied across two surfaces of different areas, a larger one of 1 m{eq}^2 {/eq}, and a smaller one of 0.5 m{eq}^2 {/eq}. Compare the pressures experienced by the two surfaces.

Two pistons, one with an area of 0.1 m{eq}^2 {/eq} and another with an area of 1.0 m{eq}^2 {/eq} are used to apply an identical force of 2 newtons onto a piece of wood. How do you compare the pressure values experienced by the pistons?

A boy applies a force of 10 newtons onto a wall by pressing, first with his thumb of surface area 2 cm{eq}^2 {/eq}, and then with his whole palm of surface area 100 cm{eq}^2 {/eq}. In which case is he applying greater pressure, thumb or palm?

A girl of weight 40 kg walks on tiptoe across a room, while her friend of identical weight plants her size-10 shoes squarely on the floor while walking alongside. Assuming the total area of the toe-tips is only 10 cm{eq}^2 {/eq}, while that of both shoes is 200 cm{eq}^2 {/eq}, in which case is the pressure exerted on the floor greater?

A circus elephant has a mass of about 2000 kg. Each of its feet has a cross-sectional area of, say, 400 square inches. During an act, this elephant is required to pick itself up onto one foot, with the other three feet poised in mid-air. In which case is the pressure on the floor greater, when the elephant is standing on all four feet, or when it stands on one foot?

A hydraulically driven piston is able to exert a total force of 100 newtons. Its default design gives it a cross-sectional surface area of 1 square centimeter, but a special contraption may be fitted on such that the area on which the same force is applied increases to 2 square centimeters. How do you compare the pressure values in the two cases, with and without the contraption?

Two cups of the same capacity of 100 cm{eq}^3 {/eq} are crafted with different base areas, the broad one with 30 cm{eq}^2 {/eq}, and a narrower one with 25 cm{eq}^2 {/eq}. Assuming both cups are filled with the same amount of water, which one exerts a smaller pressure on the table?

A champion gymnast does a handstand during which his entire bodyweight of 60 kg is supported on an area of 100 cm{eq}^2 {/eq}. His rival, of identical bodyweight, is still standing on his two feet, of combined surface area 500 cm{eq}^2 {/eq}. Who applies greater pressure on the gymnasium floorboards?

A brand-new knife has a cutting area of approximately 10 mm{eq}^2 {/eq}, while an old blunt knife has a cutting area of 15 mm{eq}^2 {/eq}. A butcher is able to apply a constant force of 100 newtons on both knives. In which case is the pressure on the meat greater?

A woman of mass 50 kg stands on her two feet which have a total area of 100 cm{eq}^2 {/eq}. While walking, she picks up one foot, leaving her entire weight to rest on the other foot. In which case is the pressure on the ground greater?

A boy of mass 18 kg is standing barefoot on snow. The surface area on which he rests his entire weight is 80 cm{eq}^2 {/eq}. Later, he dons his ice-skating shoes, which causes the area of contact between his feet and the snow to increase to 200 cm{eq}^2 {/eq}. Compare the pressure exerted in the two cases.

When lying on one's back, the bodyweight of an average human is distributed over a surface area of 20 square feet, whereas when lying on one's side, the same body weight is spread over 10 square feet. In which case is the pressure on the mattress less?

A sharp pencil has a tip area of a mere 0.1 mm{eq}^2 {/eq}, while a blunt pencil has a tip area of up to 1 mm{eq}^2 {/eq}. Suppose a writer exerts a downward force on the pen of 10 newtons. In which case is the pencil lead more likely to break off? Note that the lead breaks off when the pressure on it exceeds a critical value.

A cord is used to suspend a heavy container of cement during the construction of a house. When starting a lifting operation, the cross-sectional area of the cord is 3 square inches, but during the operation, the cord frays and the area decreases to 1 square inch. Assuming the mass of the cement container is 10 kg, in which case is the pressure on the threads in the cord greater?

A carpenter is capable of exerting a total force of 130 N. He first presses down on a plank of wood with his bare palm of area 16 square inches, and then on a nail of tip area 0.001 square inches. In which case is the plank of wood experiencing smaller pressure?

When driving over sandy areas in desert countries, drivers often release some air from the tyres of the car. The surface area of contact between tyre and road before releasing air is known to be 3 square inches, and after releasing air, it increases to 4 square inches. The weight of the car is constant, at 1 ton. In which case is the car applying greater pressure on the sand?

Consider a camel and a horse, both of identical mass of 400 kilograms. The foot of a camel is designed such that during gait, the contact area with the ground is approximately 36 square inches, while in the case of the hoof of the horse, the area of contact is only about 10 square inches. Which footprint in damp soil is likely to be deeper? Hint: the greater the pressure, the deeper the footprint.

When trying to cross a frozen lake, it is advisable to crawl on all fours, rather than to walk right across. The typical body mass of a human male is about 65 kilograms. When crawling, the total surface area over which the weight is spread is about 100 square inches, whereas when walking on two feet, the surface area is about 15 square inches. In which case is the pressure smaller?

Gardeners regularly sharpen their hoes when they feel that they are not able to break soil easily. The maximum force an average gardener can exert is 100 N. With a sharp hoe, the force is applied across an area of 5 square mm, but with a blunt hoe, the force is spread over a larger area of 8 square mm. In which case is the pressure on the soil greater?

When a teacher presses on a thumbtack (of tip area 0.01 square milimeter) with a force of 20 newtons, she is able to drive it into the noticeboard easily. However, when she tries to press with the same force using the tip of her forefinger, of area 100 square milimeters, there is no noticeable effect on the noticeboard. Compare the pressure exerted in both scenarios, with thumbtack versus with forefinger.

A mason uses two drilling bits, one with cross-sectional area 1 square millimeter, and a bigger one with area 1.5 square millimeter. He pushes down on the handle of the drill with the same force of 10 newtons. In which case is he more likely to make a hole in the masonry? Hint: The greater the pressure at the tip of the drill bit, the more likely he is to succeed in making the hole.

A mechanic has resorted to a self-tapping screw to drill a hole through a piece of metal. He applies a force of 26 N on the screw, which is later measured to have a tip area of 0.01 square mm. His colleague applies the same force, onto a bolt which is documented to have a tip area of 100 square mm. Who exerts a smaller pressure on the metal?

A speeding truck hurtles into a wall with a force of 2000 Newtons during an airbag test. The surface area over which the impact is spread is documented to be 10 square meters. During the second run of the same test, the same force of impact is achieved, but the area of impact is only 5 square meters. How do you compare the pressure on the wall?

In a biomechanical laboratory, indentation tests are frequently performed to assess the quality of bone. A consistent force of 5 Newtons is applied by a particular indentation machine, first using a tip of area 0.1 square millimeters, and then using a tip of area 0.2 square millimeters. In which case is the pressure on the bone greater?

A piece of wood of mass 2 kg lies on its broadside of surface area 50 square centimeters. It is picked up by a passer-by and placed on its narrower face, of area 40 square centimeters. In which orientation is it applying greater pressure on the ground?

A coin is placed on its face of area 3 square centimeters, and later picked up and balanced on its thin side, where the contact area is only 0.01 square centimeters. The mass of the coin is about 5 grams. In which orientation is the pressure on the surface greater?

A ceiling fan of mass 8 kg is suspended by four bolts, of total cross-sectional area 12.5 cm{eq}^2 {/eq}. After a year of use, one of the bolts breaks, leaving the entire mass to be spread across 9.4 cm{eq}^2 {/eq}. What effect does this rupture have on the pressure in the bolts?

Calligraphers use pens attached with nibs of various shapes and sizes. Let's assume that a broad nib has a surface area of 1 square milimeter of contact with the paper, while a narrow nib has a surface area of 0.5 square milimeter. Assuming that the calligrapher applies a constant force of 10 newtons in both cases, how do you compare the pressure on the paper?

Crates of cement of mass 5 kg are being stacked up in various orientations. Sometimes they lie on their broad side, such that a total area of 0.4 square meters is in contact with the ground, and at other times, they are placed on their narrow side, such that a total area of 0.2 square meters is in contact with the ground. How does the pressure applied by the crate on the ground compare in the two cases?

A lunar rover is being designed such that it can land on either three wheels or four. Its mass is 1000 kg, and the area of contact of each wheel with the ground is 20 square centimeters. In which design is the pressure on the landing apparatus greater?