0625 · 1.8Pressure

Pressure from force and area

0:00A boot can sink into soft snow, while a snowshoe helps the same person stay near the surface. The person’s weight has not changed, but the area supporting that weight has increased. This changes the pressure on the snow. By the end of this video, you will understand pressure beneath your feet and beneath a liquid surface. We need three familiar ideas before we begin. Force is a push or pull, measured in newtons, and weight is the gravitational force on an object.

0:25Area measures the size of a surface, while density means mass per unit volume. These ideas will help us explain pressure rather than simply memorise its equations. Pressure is force per unit area. It tells us how concentrated a force is over the surface where it acts. Imagine the same downward force spread evenly over a large surface, then over a much smaller surface. Each small part of the smaller surface experiences a greater share of that force.

0:50The equation is pressure equals force divided by area. Here, we use the force acting perpendicular to the surface. This means the force pushes directly into the surface, not along it. The area is the contact area over which that force acts. It is not necessarily the total surface area of the object. Pressure is measured in pascals when force is in newtons and area is in square metres. One pascal means one newton per square metre.

1:14For the same area, doubling the force doubles the pressure. For the same force, doubling the area halves the pressure, because the force is spread more widely. Snowshoes increase the contact area between a person and the snow. The same weight produces a lower pressure, so the person is less likely to sink deeply. A sharp knife uses the opposite effect. Its narrow edge produces a high pressure for a given force, helping it cut into material.

1:39Notice that a sharp knife does not automatically produce a larger force. It concentrates the applied force over a smaller contact area. Similarly, a snowshoe does not reduce the person’s weight. It reduces the pressure by spreading that weight over a larger area.

Calculating pressure and converting areas

1:54Let us calculate the pressure beneath a person’s boots. Their weight is six hundred newtons, and the combined contact area of both boots is zero point zero three square metres. They stand still on level ground, with their weight supported by the boots. We use the combined area because the force is distributed across both contact patches. First, write the relationship as pressure equals force divided by area. Next, substitute six hundred newtons divided by zero point zero three square metres.

2:20The result is twenty thousand pascals. This means each square metre would carry twenty thousand newtons if the same average pressure extended across that area. Now suppose snowshoes increase the total contact area to zero point three square metres. Divide the same six hundred newtons by zero point three square metres. The new pressure is two thousand pascals. The area increased tenfold, so the pressure decreased to one tenth of its previous value.

2:46Before using this equation, check the area units carefully. One metre contains one hundred centimetres, so one square metre contains ten thousand square centimetres. To convert square centimetres into square metres, divide by ten thousand. Dividing by only one hundred would treat an area as though it were a length.

Liquid pressure and its equation

3:04Now let us move beneath the surface of a liquid at rest. Pressure beneath a liquid surface increases with depth. A deeper point has a taller column of liquid above it. The weight of that liquid produces a greater pressure at the deeper point. Depth means vertical distance below the liquid surface. It is not the distance measured along a sloping wall or the distance from the bottom. Two points at the same depth in the same stationary liquid have the same pressure.

3:30Moving sideways does not increase depth, so it does not increase the pressure. Pressure beneath a liquid surface also increases with the density of the liquid, when depth remains the same. A denser liquid contains more mass in the same volume. The same-sized column therefore has greater weight. This produces a greater pressure beneath it. Keep the comparison conditions clear when describing these relationships. Greater depth means greater pressure when comparing points in the same liquid.

3:56Greater density means greater pressure when comparing liquids at the same depth. If both depth and density change, we must consider both effects rather than comparing only one. We now reach the Supplement content for Extended students. The change in pressure equals density multiplied by gravitational field strength multiplied by change in depth. The change in depth is the vertical separation between the two positions. This equation calculates how much the pressure increases as we move down through a liquid.

4:24We can understand this equation by imagining a vertical column of liquid between two depths. Its volume equals its cross-sectional area multiplied by its height. Its mass equals density multiplied by that volume. Its weight equals that mass multiplied by gravitational field strength. The pressure increase between the column’s top and bottom supports its weight. Divide the column’s weight by its cross-sectional area to find that pressure increase. The area cancels, leaving density multiplied by gravitational field strength multiplied by the height difference.

4:54A wider column weighs more, but its weight is spread over a proportionally larger area. Use density in kilograms per cubic metre and change in depth in metres. Gravitational field strength is measured in newtons per kilogram. The resulting pressure change is in pascals. Use the value of gravitational field strength specified in the question.

Worked liquid-pressure calculation and recap

5:14Here is a fully worked Extended example. A sensor moves from one metre to three metres below a water surface. The water density is one thousand kilograms per cubic metre. The question gives gravitational field strength as nine point eight newtons per kilogram and asks for the increase in pressure. First, subtract one metre from three metres to find a depth increase of two metres. Next, multiply one thousand by nine point eight to obtain nine thousand eight hundred.

5:40Then multiply nine thousand eight hundred by two. The pressure increases by nineteen thousand six hundred pascals. We used two metres because the question asks for a change between two positions. Using three metres would calculate the pressure increase from the surface to the lower position instead. Pressure at the surface need not be zero, because air can press on it. The liquid equation gives the additional pressure associated with moving deeper.

6:03An examination may ask you to define pressure, calculate it, or explain a comparison. For this tank, the command word explain requires a reason, not just a statement that the lower point is deeper. A suitable answer is that the lower point has a taller column of water above it. The greater weight per unit area produces greater pressure. For a snowshoe question, connect the area change directly to the pressure change.

6:26The snowshoe increases the contact area. The person’s weight remains the same. Since pressure equals force divided by area, the pressure on the snow decreases. Let us bring the ideas together. Pressure is force per unit area, measured in pascals. Increasing force increases pressure, while increasing area reduces pressure when the force stays constant. Beneath a liquid surface, greater depth and greater density produce greater pressure. For Extended calculations, pressure change equals density multiplied by gravitational field strength multiplied by change in depth.