The retardation of the object projected vertically upwards is how much? Does it depends on mass or all objects have same velocity while coming down?
The retardation of the object projected vertically upwards is how much? Does it depends on mass or all objects have same velocity while coming down?
The force of gravity pulls objects toward the Earth. The resistance to the pull of gravity consists of inertia from the object's acceleration and air resistance from the object's velocity.
Total force According to Newton's Law of Action-Reaction, the force of gravity equals the resistive forces for a freely falling object.
Fg = Fi + Fa
where
- Fg is the force of gravity
- Fi is the resistance from inertia
- Fa is the air resistance force
Force of gravity The force of gravity to accelerate an an object is constant:
Fg = mg
where
- Fg is the force of gravity in newtons (N) or pound-force (lbs)
- m is the mass of the object in kilograms (kg) or pound-mass (lbs)
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
Note: Pounds are typically considered units of force or weight. However, some people also use the expression “pound” when referring to mass. Thus, the unit of pound-force is used to distinguish it from pound-mass. Also, since F = mg, 1 pound-mass equals 32 pound-force.
Resistance from inertia As an object accelerates during a free fall, the resistance of inertia increases, according to Newton's Law of Inertia. The resistive force of inertia is:
Fi = ma
where
- Fi is the force of inertia resisting acceleration
- a is the rate of acceleration
Air resistance or drag The air resistance force or drag is:
Fa = kv2
where
- Fa is the air resistance or drag force
- k is a constant dependent on density and shape of the object
- v is the velocity of the object
Negligible air resistance For large masses or at low velocities, air resistance can be considered negligible. This is the usual assumption in equations for falling objects. In such a case:
Fg = Fi
and
mg = ma
For example, the experiment of dropping an object in the lab or even dropping two lead balls from the Leaning Tower of Pisa, the effect of air resistance can be ignored.
Terminal velocity However, at some velocity, air resistance can equal the force of gravity, resulting in zero resistance from inertia.
kv2 = mg = Fg
Fg = Fi + Fg
Fi = 0
No acceleration means the velocity is constant.
For example, when dropping a coin from a tall building, the air resistance will cause the coin to reach a terminal velocity, when it no longer accelerates while falling.
In either case, the force of gravity—and thus the work done by gravity—is the same.
The force of gravity pulls objects toward the Earth. The resistance to the pull of gravity consists of inertia from the object's acceleration and air resistance from the object's velocity.
Total forceAccording to Newton's Law of Action-Reaction, the force of gravity equals the resistive forces for a freely falling object.
Fg = Fi + Fa
where
- Fg is the force of gravity
- Fi is the resistance from inertia
- Fa is the air resistance force
The force of gravity to accelerate an an object is constant:
Fg = mg
where
- Fg is the force of gravity in newtons (N) or pound-force (lbs)
- m is the mass of the object in kilograms (kg) or pound-mass (lbs)
- g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2)
Note: Pounds are typically considered units of force or weight. However, some people also use the expression “pound” when referring to mass. Thus, the unit of pound-force is used to distinguish it from pound-mass. Also, since F = mg, 1 pound-mass equals 32 pound-force.
Resistance from inertiaAs an object accelerates during a free fall, the resistance of inertia increases, according to Newton's Law of Inertia. The resistive force of inertia is:
Fi = ma
where
- Fi is the force of inertia resisting acceleration
- a is the rate of acceleration
The air resistance force or drag is:
Fa = kv2
where
- Fa is the air resistance or drag force
- k is a constant dependent on density and shape of the object
- v is the velocity of the object
For large masses or at low velocities, air resistance can be considered negligible. This is the usual assumption in equations for falling objects. In such a case:
Fg = Fi
and
mg = ma
For example, the experiment of dropping an object in the lab or even dropping two lead balls from the Leaning Tower of Pisa, the effect of air resistance can be ignored.
Terminal velocityHowever, at some velocity, air resistance can equal the force of gravity, resulting in zero resistance from inertia.
kv2 = mg = Fg
Fg = Fi + Fg
Fi = 0
No acceleration means the velocity is constant.
For example, when dropping a coin from a tall building, the air resistance will cause the coin to reach a terminal velocity, when it no longer accelerates while falling.
In either case, the force of gravity—and thus the work done by gravity—is the same.
