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# Free Fall – Introduction, Explanation & Case Study

Aug 24, 2022

## Key Concepts:

• Mass and Weight
• Freefall
• Weightlessness

## Introduction:

The mass of an object tells us how much matter it is composed of. It is measured in kilogram. The weight of an object is the force of gravity that acts on it and is measured in Newton.

### The formula of weight:

Force = Mass × Acceleration

F = ma

Weight = Mass × Gravitational acceleration

W = mg

Gravitational Acceleration = g

(Acceleration caused by the pull of gravitational force)

Gravitational Acceleration = g = GM / R2

Here G = Gravitational Constant

M = Mass of the planet

R = Radius of the Planet

There are two types of forces contact forces and non-contact forces. The contact forces are frictional force, tension force, and normal reaction or support force. The non-contact forces are Gravitational force, electric force, and magnetic force.

## Explanation:

### Freefall:

We can feel contact forces but not gravity because gravity is a non-contact force,

Freefall is a kind of sensation in which the object doesn’t feel the effect of gravity in absence of contact forces. When the only force acting on an object is gravity, we say that the object is falling freely.

Weight is the force with which the Earth attracts us. We are conscious of our own weight when we are standing on a surface since the surface applies a force opposite to our weight to keep us at rest.

A man standing on floor is in equilibrium under the action of two forces : weight w and normal reaction N.

ΣF = N – W = 0

Or

N = W

The same principle holds good when we measure the weight of an object by a spring balance hung from a fixed point like a ceiling. When we hang an object to a spring balance, the spring is pulled down a little by the gravitational pull of the object and in turn, the spring exerts a force on the object vertically upwards.

Now imagine the top end of the spring balance is no longer fixed to the ceiling both ends of the spring as well as the object move with the same acceleration g. The spring is not stretched and does not exert any upward force on the object which is moving down with acceleration g due to gravity. The reading recorded in the spring balance will be zero.

If the object were a human being, he or she will not feel his weight since there is no upward force on him. Thus, when an object is in free fall it is weightless.

In an elevator, the forces acting on an object with a mass m are:

The gravitational force (mg) in the downward direction

The reaction force N or push of the elevator floor on the object (N) in the upward direction.

Acceleration of Lift = a.

### Case 1:

When the lift is at rest or in uniform motion

Acceleration = a = 0

Net force on lift = F = N – mg = 0

N = mg

But N = reading of the weighting scale = W

W = mg

### Case 2:

When the lift is moving downwards with acceleration = a

Then mg – N will provide downward acceleration

Net force on lift = F = mg – N = ma

N = mg – ma

But N = reading of the weighting scale = W

W = mg – ma

### Case 3:

When the lift is moving upwards with acceleration = a

Then N – mg will provide upward acceleration

Net force on lift = F = N – mg = ma

N = mg + ma

But N = reading of the weighting scale = W

W = mg + ma

### Case 4:

When the lift is under freefall

moving downwards with acceleration = g

Then N – mg will provide downward acceleration g

Net force on lift = F = N – mg = mg

N = 0

But N = rearing of the weighting scale = W

W = 0

Weightlessness: A freely falling object experiences weightlessness as the only force acting on it is the force of gravity which acts downwards. The object’s acceleration is equal to the acceleration due to gravity. Hence, the net force acting on the object is zero.

The apparent weight we feel while riding a roller coaster along a curved path arises from the support we get from the floor and seat. When we ride a roller coaster towards the top, the downward acceleration of our seats is equal to the acceleration due to gravity. As a result, we experience weightlessness since there is no net force acting on us during free-fall.

Another situation when we feel weightless is during the take-off and landing of an airplane. When the airplane accelerates or decelerates at a rate equal to the acceleration due to gravity, we experience weightlessness.

Weightlessness time duration:

During High Jump or Long Jump: 1 Sec

Jumping from a Tower: 1-2 Sec

Freefall ride: 2-3 sec

During Airplane landing or take-off (Or Sky Diving): 10-30sec

## Summary:

• The difference between Weight and Mass s that the mass of an object tells us how much matter it is composed of whereas the weight of an object is the force of gravity that acts on it. Mass is measured in kilogram and weight is measured in Newton.
• We can feel contact forces but not gravity because gravity is a non-contact force.
• Free fall is a kind of sensation in which the object doesn’t feel the effect of gravity in absence of contact forces.
• In an elevator, the forces acting on an object with a mass m are the gravitational force(mg) in the downward direction and the reaction force or push of the elevator floor on the object (N = ma) in the upward direction. Acceleration of Lift = a.

Case 1:  When the lift is at rest or in uniform motion Acceleration = a =0, W = mg,

Case 2: When the lift is moving down with acceleration a. (a – acting downward) W = mg – ma Lightweight

Case 3: When the lf is moving upward with acceleration a. (a – acting upward) W = mg + ma Heavy Weight

Case 4: When the lift is falling freely a= g (Free Fall) W = 0 Weightlessness

• Weightlessness: A freely falling object experiences weightlessness as the only force acting on it is the force of gravity which acts downwards. The object’s acceleration is equal to the acceleration due to gravity. Hence, the net force acting on the object s zero.
• A freely falling object experiences weightlessness as the only force acting on it is the force of gravity which acts downwards. The object’s acceleration is equal to the acceleration due to gravity. Hence, the net force acting on the object is zero.

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