Pressure
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Chapter – 2
Pressure
Exercise
2. Differentiate between:
(a) Pressure and Upthrust
| Pressure | Upthrust |
|---|---|
| The thrust or force acting per unit area of an object is called pressure. | The net upward force by which water pushes the object in it is called upthrust. |
| It’s SI unit is pascal i.e. Newton per square meter (N/m2). | It’s SI unit is Newton (N). |
(b) The reason for a steel pin sinking in water and a steel plate floating on water
| The reason for a steel pin sinking in water | A steel plate floating on water |
|---|---|
| It cannot displace water equal to its mass. | It can displace water equal to its mass. |
| It has low surface area. | It has high surface area. |
| Upthrust is less. | Upthrust is more. |
(c) The process of a hot air balloon sinking in air and rising in air
| The process of a hot air balloon sinking in air | The process of a hot air balloon rising in air |
|---|---|
| Air is more dense than outside air. | Air is less dense than outside air. |
| It moves downward. | It moves upward. |
| Cool air sinks. | Warm air rises. |
3. Give a reason for:
(a) A special type of oil is used in hydraulic brakes.
→ Because it is non-compressible and can withstand high temperatures, ensuring effective braking.
(b) A wooden cork dipped below the surface of the water by applying force with a finger comes to the surface when the finger is removed.
→ Because as the force applied by the finger is removed the upthrust of water acts on the wooden cork and comes to the surface and the density of water is higher than the wooden cork.
(c) We feel lighter while floating on water.
→ Because upthrust acts on our body. In water any object that is immersed in liquid feels a force called upward thrust which makes the mass of the object less on water.
(d) On lifting a stone submerged in water it feels heavier when it comes out of the water.
→ Because, the upthrust is pushing the stone upward which makes it feels lighter inside the water and it feels heavier outside because there is no upthrust without water.
(e) It is easier to float in the Dead sea than in a swimming pool. (the density of water in dead sea is 1240 kg/m3).
→ Because the density of dead sea is heavier than normal water which increases upthrust where as swimming pool has low density and it’s difficult to float in it.
(f) If more passengers climb a boat than its maximum capacity, the boat is likely to sink.
→ Because, if the boat reaches more than its maximum capacity of passengers then the boat is unable to displace the same amount of water as its mass, which leads the boat to sink.
4. Answer the following questions:
(a) State Pascal’s law.
→ Pascal law states that, when pressure is applied on a vessel inclosed with liquid then the pressure is equal in all direction.
(b) Write any two applications of Pascal’s law in daily life.
→ The two applications of Pascal’s law in daily life are:
- hydraulic lift
- hydraulic brakes
(c) What is hydraulic machine?
→ A machine that uses the principle of Pascal law to generate, control or transmit forces using confined fluid is known as hydraulic machine.
(d) State Archimedes principle.
→ It states that that when a body is fully or partially immersed in a liquid it experiences an up thrust equal to weight of displaced water.
(e) What is upthrust?
→ When an object is partially or completely immersed in a gas or liquid (fluid), the upward force acting on the object is called upthrust.
(f) Mention the forces acting on a floating objects and their directions.
→ The forces acting on a floating object and their directions is upthrust.
(g) State the law of floatation.
→ It states that for a floating body, weight of body = weight of displaced liquid.
(h) Write any two applications of Archimedes principle.
→ Applications of Archimedes principle:
- Lactometer. (purity of milk).
- Barometer. (Atmospheric pressure).
- Hydrometer. (density of water).
- Hygrometer. (humidity in air).
(i) Explain with a figure, the cause of the production of upthrust.
→ The liquid exerts normal pressure on the object immersed in it from all side. The pressure increases as the depth of the object increases. Since the lower surface of the object is at a greater depth, the pressure and force on the upper surface of the object is subtracted from the force on the lower surface. The resultant force has an upward direction.
(j) When a stone is dropped into the water it sinks. Does it happen because of the absence of upthrust?
→ No, it doesn’t happen because of the absence of upthrust, it is happened because the stone is not able to displace the water equal or more than its weight.
(k) A person is trying to lift a stone of 500N keeping it on the smaller piston of a hydraulic machine by applying a force on the large piston. What suggestion would you give him/her so that he/she can lift the load easily?
Explain, with an appropriate figure, the process of increasing the force in the hydraulic machine.
→ I will suggest him to keep the stone of 500N in the larger piston and apply force from small piston so that it can multiply the applied force by small piston.
(l) Substance with a density greater than the density of the liquid sink in it. Is this statement always true? Justify with example.
→ No, this statement is not always true because, mainly the object need to displace the water according to its weight. For example, the iron nail sinks in water whereas iron plate floats.
(m) Two balloons, one filled with air and the other with hydrogen look identical. What differences can be noticed when they are released into the air? Explain with reasons.
→ Two balloons, filled with hydrogen and air may look identical but, if they are released into the air, the balloon filled with hydrogen goes up where as balloon filled with air goes downward. It is because, the hydrogen is lighter gas as compared to air.
(n) An object is suspending/floating just below the surface of the water. If the amount of salt dissolving in the water goes on increasing what change will occur in the position of the balloon? Explain with reason.
→ If the amount of salt dissolving in the water goes on increasing then, the object floating below the surface of water slowly started to come upward this happens because the
salt increases the density of water which automatically increases the upthrust which pushes the object upward to the surface.
(o) What are the readings shown by the weighing machine given in figure (a) and (b)? Explain with reason.
→ The reading shown by weighing machine in figure (a) are 25N and 28N.
The reading shown by weighing machine in figure (b) are 35N and 38N.
(p) When a person puts a lactometer into the milk, the whole part of the narrow stem sinks into the milk. What conclusions can be drawn from this event?
→ A lactometer sinks into the milk completely, this concludes that a large amount of water is mixed into the milk and the milk is impure.
5. Solve the numericals.
(a) In the figure, a sample of a hydraulic machine constructed by syringe is shown. How much force is to be applied through syringe B to balance the force on piston A?
Here,
F1 = 20N
A1 = 0.5cm2
A2 = 5cm2
F2 = ?
we k it,
F1/A1 = F2/A2
20 × 5 = F2 × 0.5
100 / 0.5 = F
∴ F = 200N.
(b)
[No question statement is written on this page in the supplied source.]
Solution for (b)
P1 = 30,000.
P1 = P2
P1 = F2/A2
30,000 = F2/0.1
F2 = 30000 × 0.1
∴ F2 = 3000N.
(c)
[Question text is not written/readable in the supplied source.]
For (b)
Weight of an object in air = 20N.
Weight of an object in water = 14N.
upthrust = ?
we k it,
upthrust = wt. in air − wt. in water
= 20 − 14
= 6N.
For (c)
weight in air = 20N.
weight in water = 10N.
upthrust = ?
we k it,
upthrust = wt. in air − wt. in water.
= 20 − 10
= 10N.
Notes
Force acting perpendicular per unit area is called pressure. It is given by p = F/A. Its SI unit is N/m2 or pascal and CGS unit is dyne/cm2.
Liquid pressure
The pressure exerted by liquid on a vessel on which it is placed in, is called liquid pressure.
Where
- h = depth of liquid
- δ = density of liquid (i.e. water = 1)
- g = acceleration due to gravity.
Proof
∴ Let us consider a vessel of surface area (A) having liquid of density (δ) up to the depth (h).
Now, pressure acting on the vessel due to liquid is given by,
p = mg/A (F = mg)
p = δ × V × g / A (m = δ × V)
p = δ × l × b × h × g / A (V = l × b × h)
p = δ × A × h × g / A (A = l × b)
∴ p = hδg proved.
Upthrust or Buoyant force
The upward pulling force in any liquid is called upthrust or Buoyant force. It is calculated by using formula.
- U = wt. in air − weight in liquid.
- U = Vδg.
- Again, U = m × g (∵ m = V × δ).
U = weight of displaced liquid.
Pascal’s Law
Statement: It states, “when pressure is applied on a liquid enclosed in a vessel then it is transmitted equally in all direction.”
Explanation: “Let us consider a liquid is enclosed on a vessel having 4 pistons,” then according to Pascal’s law:
where from fig:
so, “pressure = constant” said pascal.
Instruments like hydraulic press, hydraulic jack, lift, brake etc use Pascal’s law.
1) Hydraulic lift
It is a device which is used to lift heavy loads by using small amount of force. It works as a force multiplier. It works on a principle of Pascal’s law.
Explanation: “Let’s consider a hydraulic lift having 2 pistons:”
- small piston where force is to be applied.
- large piston where load is placed.
Archimedes principle
Statement: It states, “when a body is wholly or partially immerse in a liquid it experience an upthrust equal to weight of displaced liquid.”
OR
“It states, upthrust equals to weight of displaced liquid,” i.e.:-
Proof
Let us consider a vessel containing liquid of density (δ). Let us place an object of height (h) and surface area (A) so that the bottom portion of the object is at depth (h2) and upper portion is at depth (h1).
Now, Force acting on the object at lower portion (F2):
F2 = p × A
F2 = h2 × δg × A — (i)
Force acting on the object at upper portion:
F1 = p × A
F1 = h1 × δg × A — (ii)
Now, Net force acting the object = F2 − F1
U = h2δgA − h1δgA
U = δgA (h2 − h1)
U = hδgA
U = Vδg (∵ V = A × h)
Again,
U = m × g (∵ m = V × δ)
U = mg
U = weight of displaced liquid.
Law of Floatation
Statement: It states “For a floating body, weight of a body = weight of displaced water.”
∴ Instruments like lactometer, barometer, hygrometer etc work on this principle of floatation.
Atmospheric pressure
The pressure exerted by different layers of air on an object is called atmospheric pressure. For eg:- kite flying, use of parachute etc.
Para for flying body.
Chapter – 3
Exercise:
5. Solve the [Unreadable in source]
(a) [Unreadable in source]
Soln, mass (m) = [Unreadable in source]
T1 = [Unreadable in source]
T2 = [Unreadable in source]
specific heat [Unreadable in source]
Discussion
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