TERMINAL VELOCITY
TERMINAL VELOCITY – DEFINITION
The terminal velocity is the constant speed accomplished by the falling item through a viscous liquid or the environment with no speed increase as portrayed by Newton’s first law.
The viscous force/drag experienced by the falling article adjusts the power because of speed increase.
EXPRESSION FOR TERMINAL VELOCITY
FALLING THROUGH THE ENVIRONMENT
Two outside(external) forces are impacting the article that is falling through the atmosphere.
One is the gravitational force, also called the heaviness of the falling item, and the other one is the air opposition or the drag of the article.
For this situation, the net outer(external) forces are equivalent to the distinction of weight W and the drag D. F = W – D
At the point when the drag on the article is equivalent to the heaviness of the item then there is no net power following up on the article.
F = W – D = 0
At terminal velocity D = W
FALLING THROUGH THE VISCOUS LIQUID
The outer(external) forces that are impacting the item that is falling through the thick fluid are, one is the gravitational force, also called the heaviness of the falling article, and the other two forces are upthrust and the viscous force.
At the point when the descending power of gravity approaches the viscous force plus buoyant force then the net power on the article becomes zero.
The speed of the item stays consistent. mg = F + B
EXPRESSION FOR TERMINAL VELOCITY
SURFACE TENSION – EXAMPLES
A parachute with an enormous projected region comparative ith its mass has a lower max speed than one with little projected region comparative with its mass
A downpour drop arriving at the ground with a max speed is likewise a model.
Question & Answers
Questions:
1. Terminal velocity is reached when weight=
2. The terminal velocity of a sphere in a fluid is proportional to the square of its:
3. If the viscosity of a fluid is tripled, the terminal velocity of a falling sphere becomes:
4. Two spheres of same material but radii r and 2r fall through same fluid. Ratio of terminal velocities is:
5. An air bubble of radius 1 mm rises through water (η = 0.001 Pa·s, ρw = 1000 kg/m³, ρair ≈ 0). Terminal velocity (g=10) is:
6. Terminal velocity of a raindrop of radius 0.2 mm falling through air (η=1.8×10⁻⁵ Pa·s, ρair=1.2 kg/m³, ρwater=1000 kg/m³, g=10) is:
7. The time to reach terminal velocity in a viscous medium is:
8. A body falling through a viscous medium eventually attains constant velocity because:
9. If two identical spheres fall through different liquids A and B and have terminal velocities 10 cm/s and 5 cm/s, the ratio of viscosities ηA : ηB is:
10 For a sphere in free fall through air, terminal velocity is attained when acceleration=
11 A lead sphere and a wooden sphere of same radius fall through water. Which has larger terminal velocity?
12 The terminal velocity of a body in a viscous medium is independent of:
13 If g is doubled, terminal velocity becomes:
14 A sphere of density 5000 kg/m³ and radius 1 mm has terminal velocity 0.1 m/s in a fluid. The viscosity of fluid is (g=10): (ρf=1000)
15 For small particles, terminal velocity increases with:
16 The ratio of terminal velocities of two spheres of same material but radii R and R/2 in same fluid is:
17 Terminal velocity of a small steel ball in a jar of honey is measured. If the jar is taken to Moon (g/6), terminal velocity becomes:
18 The expression for terminal velocity (from Stoke’s law) is valid if:
19 A 0.5 mm radius water droplet falls in air (η=1.8×10⁻⁵). Its approximate terminal velocity (g=10, ρwater=1000, ρair=1.2) is:
20 In Millikan’s oil drop experiment, terminal velocity is used to find:
Answers:
1. Weight = Buoyant force + Drag force
2. Radius
3. 1/3
4. 1 : 4
5. 2.22 m/s
6. 4.9 m/s
7. Finite theoretically infinite (approaches asymptotically)
8. Drag force balances net gravity
9. 1 : 2
10 zero
11 Lead
12 Initial velocity
13 Double
14 0.89 Pa·s
15 Square of radius
16 4 : 1
17 1/6
18 Laminar flow
19 30 m/s
20 Charge of electron
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