State the relation between the (i) volume of an object in (m) and its volume in (cm)
(ii) density of a substance in (kg/m”) and its density in (g/cm?) and (iii) speed of an object in
(km/hour) and its speed in (cm/s).
plz answer fast it's urgent
Subject- Physics
Answers
Answer:
University Physics Volume 1
6 Applications of Newton’s Laws
6.4 Drag Force and Terminal Speed
LEARNING OBJECTIVES
By the end of the section, you will be able to:
Express the drag force mathematically
Describe applications of the drag force
Define terminal velocity
Determine an object’s terminal velocity given its mass
Another interesting force in everyday life is the force of drag on an object when it is moving in a fluid (either a gas or a liquid). You feel the drag force when you move your hand through water. You might also feel it if you move your hand during a strong wind. The faster you move your hand, the harder it is to move. You feel a smaller drag force when you tilt your hand so only the side goes through the air—you have decreased the area of your hand that faces the direction of motion.
Drag Forces
Like friction, the drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as cyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force
F
D
is proportional to the square of the speed of the object. We can write this relationship mathematically as
F
D
∝
v
2
.
When taking into account other factors, this relationship becomes
F
D
=
1
2
C
ρ
A
v
2
,
where C is the drag coefficient, A is the area of the object facing the fluid, and
ρ
is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as
F
D
=
b
v
2
,
where b is a constant equivalent to
0.5
C
ρ
A
.
We have set the exponent n for these equations as 2 because when an object is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. As we shall see in Fluid Mechanics, for small particles moving at low speeds in a fluid, the exponent n is equal to 1.
Drag Force
Drag force
F
D
is proportional to the square of the speed of the object. Mathematically,
F
D
=
1
2
C
ρ
A
v
2
,
where C is the drag coefficient, A is the area of the object facing the fluid, and
ρ
is the density of the fluid.
Athletes as well as car designers seek to reduce the drag force to lower their race times ((Figure)). Aerodynamic shaping of an automobile can reduce the drag force and thus increase a car’s gas mileage.
A photograph of a bobsled on a track at the Olympics.