Pressure: Physics 0625 (Cambridge O Level / IGCSE)

A concrete paving block rests on flat ground. The block exerts a force of $900\text{ N}$ on the ground through its base, which has an area of $300\text{ cm}^2$. What pressure does the block exert on the ground?

A woodworker is comparing a sharp chisel with a blunt one.

(a) State the equation linking pressure, force and area, and give the SI unit of pressure. [2]

(b) The woodworker presses the sharpened edge of the chisel onto a block of wood with a force of $45\text{ N}$. The very thin cutting edge has a contact area of only $0.03\text{ cm}^2$. Calculate the pressure exerted by the edge on the wood, in $\text{Pa}$. [3]

(c) Explain, using the idea of pressure, why sharpening the chisel makes it easier to cut into the wood, even though the force pressing down has not changed. [2]

A dairy processing plant stores fresh milk in a tall, cylindrical stainless-steel tank. Set into the curved side of the tank are two identical circular inspection hatches, each held shut by a ring of bolts: one hatch is near the top of the tank, and the other is near the base. When the tank is full of milk, maintenance engineers tighten far more bolts on the base hatch than on the top hatch to keep it sealed.

(a) State how the pressure due to the milk compares at the top hatch and at the base hatch when the tank is full. [1]

(b) Explain, in terms of the weight of milk above a point, why the pressure at the base hatch is greater than the pressure at the top hatch. [2]

(c) Explain, in terms of pressure and force, why the base hatch needs more bolts than the top hatch to stay sealed. [2]

(d) The plant considers replacing the milk with a cream product that is denser than milk, filled to the same maximum depth in the tank. State and explain how the pressure at the base hatch would compare with the pressure when the tank holds milk. [2]

Two swimmers dive into different pools. Take the density of the fresh water in the first pool as $1000\text{ kg/m}^3$, the density of the salt water in the second pool as $1030\text{ kg/m}^3$, the gravitational field strength as $g = 10\text{ N/kg}$, and atmospheric pressure at the surface of both pools as $1.0\times10^{5}\text{ Pa}$.

(a) The first swimmer dives to a depth of $2.5\text{ m}$ below the surface of the fresh-water pool. Calculate the increase in pressure, due to the water alone, at this depth. [3]

(b) Calculate the total pressure (due to the water and the atmosphere together) acting on the first swimmer at this depth. [2]

(c) The second swimmer dives to a depth of only $1.0\text{ m}$, but in the salt-water pool. Calculate the increase in pressure, due to the water alone, at this depth. [2]

(d) Using your answers to (a) and (c), state which swimmer experiences the greater increase in pressure due to the water above them. [1]

A research submarine is cruising at a depth of $150\text{ m}$ below the surface of the sea. Take the density of sea water as $1030\text{ kg/m}^3$, the gravitational field strength as $g = 10\text{ N/kg}$, and atmospheric pressure at the sea surface as $1.0\times10^{5}\text{ Pa}$.

(a) Calculate the increase in pressure, due to the sea water alone, at this depth. [2]

(b) Calculate the total pressure acting on the outside of the submarine's hull at this depth, including the atmosphere. [2]

(c) The submarine has a circular observation window of radius $0.20\text{ m}$. Calculate the area of this window. [2]

(d) Calculate the total force exerted on the outside of the window by the water and the atmosphere. [3]

(e) Inside the submarine, the air is kept at close to normal atmospheric pressure at all times, regardless of depth. Explain, in terms of the pressure difference across the window, why this window must be far stronger than a window of the same size in a building at the surface. [2]

A ballet dancer balances en pointe, with her full weight of $480\text{ N}$ passing through the tip of one pointe shoe. The tip is in contact with the floor over an area of $50\text{ mm}^2$. What pressure does the dancer exert on the floor?

A removable floor safe stands on four identical rectangular feet, resting on a wooden floor tile in an office. The safe has a total weight of $6000\text{ N}$, shared equally between the four feet. Each foot has a rectangular base measuring $40\text{ mm}$ by $50\text{ mm}$. The manufacturer states that the floor tile will crack if the pressure on it ever exceeds $5.0\times10^{5}\text{ Pa}$.

(a) Calculate the total area of the four feet in contact with the floor, in $\text{m}^2$. [2]

(b) Calculate the pressure the safe exerts on the floor through its feet. [2]

(c) By comparing your answer to (b) with the maximum pressure the tile can withstand, state whether the floor tile will crack. [2]

(d) To move the safe without damaging the floor, workers place it on a rigid wooden board with an area of $0.50\text{ m}^2$, so its weight is spread evenly over the whole area of the board. Calculate the new pressure on the floor, and explain why this prevents the tile from cracking. [3]

A technician sets up a simple mercury barometer: a long glass tube is filled completely with mercury, sealed at one end, then inverted (open end down) into a dish of mercury that is open to the atmosphere. The mercury in the tube falls slightly until it settles with a vertical column height of $760\text{ mm}$ above the mercury level in the dish, leaving a vacuum in the sealed space at the top of the tube.

(a) State what supports the column of mercury inside the tube at this height. [1]

(b) The technician tilts the tube slightly away from the vertical, without lifting its open end out of the mercury in the dish. The length of mercury inside the tube increases, but the vertical height of the column stays at $760\text{ mm}$. Explain why the vertical height does not change. [2]

(c) Explain why mercury, rather than water, is used to fill the tube of a laboratory barometer. [2]

(d) A small amount of air leaks into the sealed space at the top of the tube. State and explain the effect this has on the height of mercury in the tube. [2]

A U-tube manometer contains water of density $1000\text{ kg/m}^3$. One arm is connected to a laboratory gas supply pipe; the other arm is open to the atmosphere, where the pressure is $1.0\times10^{5}\text{ Pa}$. Take $g = 10\text{ N/kg}$.

With the gas supply turned on, the water level in the arm connected to the gas supply is pushed down, and the level in the open arm rises, until there is a vertical difference of $12\text{ cm}$ between the two water levels.

(a) Explain, using the difference in the two water levels, why the gas pressure must be greater than atmospheric pressure. [2]

(b) Calculate the pressure due to this $12\text{ cm}$ difference in water levels, using $\Delta p = \rho g \Delta h$. [3]

(c) Calculate the pressure of the gas supply. [2]

(d) The technician repeats the experiment with the manometer filled with mercury (density $13\,600\text{ kg/m}^3$) instead of water, connected to the same gas supply. State and explain how the height difference between the two mercury levels would compare with the $12\text{ cm}$ found using water. [2]

A student builds a mercury barometer, using mercury of density $13\,600\text{ kg/m}^3$, and takes $g = 10\text{ N/kg}$.

(a) At sea level, the vertical height of the mercury column is $760\text{ mm}$. Calculate the atmospheric pressure at sea level, using $\Delta p = \rho g \Delta h$. [3]

(b) The student then carries the barometer to the top of a mountain, where the column height falls to $700\text{ mm}$. Calculate the atmospheric pressure at the top of the mountain. [2]

(c) Calculate the decrease in atmospheric pressure between sea level and the top of the mountain. [1]

(d) Explain, in terms of the air above the barometer, why atmospheric pressure is lower at the top of the mountain than at sea level. [2]