Pressure
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AP Physics 1 › Pressure
A sealed container holds water at rest. Point A is $0.20,\text{m}$ below the surface; point B is $0.50,\text{m}$ below the surface. Pressure is due to fluid depth. Which point has greater water pressure?
Point B, because pressure increases with depth
Point A, because it is closer to the surface
They are equal because pressure depends only on container shape
They are equal because the container is sealed
Explanation
This question assesses understanding of hydrostatic pressure in fluids, which increases with depth. In a fluid at rest, pressure at a depth h is P = ρgh + P_atm, where ρ is density, g is gravity, and h is depth, showing pressure grows linearly with depth. Point A at 0.20 m has less pressure than Point B at 0.50 m due to the greater overlying fluid weight at B. Thus, Point B experiences greater water pressure. Distractor C suggests equal pressure because the container is sealed, but sealing does not affect the depth dependence. A useful strategy is to compare depths directly, as pressure differences depend solely on Δh in the same fluid.
A $400,\text{N}$ crate rests on the floor on four identical square feet. Each foot has area $1.0\times10^{-3},\text{m}^2$. Pressure is due to contact force. What is the pressure on the floor under one foot?
$4.0\times10^2,\text{Pa}$
$1.0\times10^5,\text{Pa}$
$1.0\times10^2,\text{Pa}$
$4.0\times10^5,\text{Pa}$
Explanation
This question tests pressure due to contact force, defined as force per unit area. Pressure is P = F/A, where F is the perpendicular force on the surface. The 400 N crate is supported by four feet, so each foot bears 100 N, and with area 1.0 × $10^{-3}$ m², the pressure per foot is 100 / 0.001 = 1.0 × $10^5$ Pa. This calculation assumes even weight distribution across the feet. Distractor B (4.0 × $10^5$ Pa) might come from using the total force instead of per foot. When analyzing multi-support contacts, divide the total force equally among supports before applying P = F/A.
A lake is calm. Point C is $1.0,\text{m}$ below the surface and point D is $3.0,\text{m}$ below the surface. Pressure is due to fluid depth. How does the water pressure at D compare to at C?
Equal, because both points are in the same lake
Equal, because pressure depends on the lake’s shape, not depth
Less at D, because deeper water has less room to expand
Greater at D, because pressure increases with depth
Explanation
This question tests hydrostatic pressure, emphasizing its increase with fluid depth. Hydrostatic pressure is P = ρgh + P0, directly proportional to depth h below the surface. Point C at 1.0 m has lower pressure than Point D at 3.0 m, where the pressure is three times greater due to triple the depth. Therefore, pressure is greater at D because of the increased depth. Choice B is a distractor claiming equal pressure since both are in the same lake, ignoring depth's role. For such problems, always focus on the depth from the surface as the determining factor for pressure comparisons.
A diver is in seawater. Point G is $2.0,\text{m}$ below the surface and point H is $2.0,\text{m}$ below the surface but horizontally $10,\text{m}$ away. Pressure is due to fluid depth. Which point has greater water pressure?
They are equal, because both points are at the same depth
Point G, because it is closer to the shore
Point H, because pressure increases with horizontal distance
They are unequal, because pressure depends on the container’s shape
Explanation
This question assesses hydrostatic pressure, focusing on its dependence on vertical depth rather than horizontal position. In fluids, pressure increases with depth h as P = ρgh + P0, but is independent of horizontal distance. Points G and H are both at 2.0 m depth, so they have equal pressure despite the 10 m horizontal separation. The pressures are the same because only vertical depth matters. Choice B is a distractor that incorrectly claims pressure increases with horizontal distance, which is not true in static fluids. A transferable strategy is to ignore horizontal positions and base comparisons solely on vertical depths from the surface.
A crate exerts a $200,\text{N}$ normal force on the floor. Pressure is due to contact force. If its contact area doubles, what happens to the pressure?
It stays the same because the force is unchanged.
It is cut in half because the same force is distributed over twice the area.
It becomes zero because the force is spread out.
It doubles because pressure is proportional to area.
Explanation
This question tests understanding of the inverse relationship between pressure and area. Pressure is defined as P = F/A, so if force remains constant at 200 N while area doubles, pressure becomes half of its original value. Mathematically, if initial pressure is P₁ = F/A, then new pressure is P₂ = F/(2A) = (F/A)/2 = P₁/2. Choice B incorrectly suggests pressure remains constant, ignoring the role of area in the pressure equation. To solve pressure problems with changing conditions, apply P = F/A systematically and note which variables change.
In a column of water at rest, pressure is due to fluid depth. Point $M$ is $0.20,\text{m}$ deeper than point $N$. Which statement is correct?
$p_M=p_N$ because the water’s density is the same at both points.
$p_N>p_M$ because pressure decreases as you go down.
The pressures depend on the container’s shape, not depth.
$p_M>p_N$ because deeper points have more fluid above them.
Explanation
This question tests understanding of pressure variation with depth in fluids. In any static fluid, pressure increases with depth following P = P₀ + ρgh. Since point M is 0.20 m deeper than point N, M experiences greater pressure due to the additional weight of water above it. The pressure difference equals ρg(0.20 m), where ρ is water density and g is gravitational acceleration. Choice B incorrectly suggests pressure decreases with depth, which violates basic fluid statics principles. When analyzing fluid pressure, remember that pressure always increases as you go deeper, regardless of the fluid type or container.
Two points are in the same still water column open to the atmosphere. Point A is $0.30,\text{m}$ below the surface and point B is $0.30,\text{m}$ below the surface but at a different horizontal location. Pressure is due to fluid depth. How do the pressures compare?
Cannot be determined without the container’s shape
$P_A>P_B$, because A is directly under the surface
$P_A<P_B$, because B is farther from the container wall
$P_A=P_B$, because pressure depends only on depth in a static fluid
Explanation
This question tests understanding that pressure depends only on depth in a static fluid. In any static fluid, pressure at a given depth is P = P₀ + ρgh, which depends only on the vertical depth h below the surface, not on horizontal position. Since both points A and B are at the same 0.30 m depth, they experience identical pressure regardless of their horizontal separation or position relative to container walls. This principle allows pressure to be transmitted equally throughout a fluid at the same depth. Choice A incorrectly suggests that being "directly under" matters, confusing vertical depth with horizontal position. When analyzing fluid pressure, only the vertical depth below the surface determines the pressure value.
A $40,\text{N}$ book rests on a table. Pressure is due to contact force. It can rest on Area $A_1=0.020,\text{m}^2$ or $A_2=0.010,\text{m}^2$. Which is true?
Pressure is greater for $A_1$ because the book is more stable.
Pressure depends on the table material, so it cannot be compared.
Pressure is greater for $A_2$ because the same force acts on smaller area.
Pressures are equal because the weight is the same.
Explanation
This question tests understanding of pressure as force per unit area. With the same 40 N weight but different contact areas, pressure varies inversely with area according to P = F/A. For area A₁ = 0.020 m², pressure is P₁ = 40/0.020 = 2000 Pa. For smaller area A₂ = 0.010 m², pressure is P₂ = 40/0.010 = 4000 Pa, which is greater. Choice C incorrectly assumes equal pressures because weight is constant, missing that pressure depends on both force and area. To compare pressures with constant force, remember that smaller contact area always produces greater pressure.
In a lake, pressure is due to fluid depth. At points $P$ and $Q$, $Q$ is $2.0,\text{m}$ deeper than $P$. Which is true?
$p_P>p_Q$ because the water above $P$ has less area to push on.
$p_Q>p_P$ because pressure increases with depth in a fluid at rest.
$p_Q=p_P$ because water pushes equally in all directions.
The deeper point has lower pressure because its volume is smaller.
Explanation
This question tests understanding of pressure variation with depth in fluids. In a static fluid, pressure increases linearly with depth according to P = P₀ + ρgh, where ρ is fluid density, g is gravitational acceleration, and h is depth below the surface. Since point Q is 2.0 m deeper than point P, the pressure at Q must be greater than at P due to the additional weight of water above it. Choice B incorrectly suggests equal pressures, confusing the fact that pressure acts in all directions with pressure magnitude. When comparing pressures in fluids, always consider the depth difference and remember that deeper points have higher pressure.
A crate is pulled across a floor, but only the downward normal force contributes to pressure. In case A the crate’s contact area is $0.50,\text{m}^2$; in case B it is $0.25,\text{m}^2$. The normal force is the same. Pressure is due to contact force. Which case has greater pressure?
Case A, because the area is larger
Case B, because the same normal force is distributed over less area
They are equal, because the crate’s weight is unchanged
Case A, because friction increases pressure
Explanation
This question tests understanding of pressure as force per unit area. Pressure is calculated as P = F/A, where F is specifically the normal force (perpendicular to the surface) and A is the contact area. Since the normal force is the same in both cases but Case B has half the contact area (0.25 m²) compared to Case A (0.50 m²), Case B produces twice the pressure. The horizontal friction force from pulling does not contribute to vertical pressure. Choice D incorrectly suggests friction affects pressure, when only the perpendicular normal force matters. For pressure calculations, always identify which force component is perpendicular to the surface.