Inertia is the reluctance of a body to change its state of rest or uniform motion in a straight line. The more massive a body is, the greater the force required to change its state of rest or of uniform motion and give acceleration to the body, hence the greater the inertia. Inertia is determined by the quantity of matterScience meaning: Matter is any substance (often a particle) that has mass, and also volume (occupies space). Matter exists in three states, solid, liquid and gas and is made up of... More contained in a body.

Since F = ma.

### Objects in a Lift:

When an object is in a lift or elevator, there are two forces act on the object.

The forces are:**i.** The true weight of the object which acts vertically downward (W = mg)**ii.** The reaction force T of the floor of the lift on the man, which acts upward.

We are going to take a close look at different cases when an object is in a lift.

### When the lift is ascending with acceleration, a:

In this case, when the lift is ascending with an acceleration, there is an unbalanced force acting on the object in the lift. The upward reaction force of the floor, T, is greater than the downward force of the object’s weight on the floor of the lift, W. (T > W)

From Newton’s second law of motion,

Force F = ma

In this case the effective force, F = T – W

Therefore T – W = ma (Since F = ma)

T – mg = ma

T = ma + mg

Factorize m: T = m (a + g)

T = m (a + g)

T = m (a + g) is also regarded as the apparent weight of the object when the lift is accelerating upward. The scale will record a value that is greater than the object’s true weight.

### When the lift is descending, a is less than g:

If the lift accelerates downwards with acceleration a, It means that the downward force due to the object’s weight is greater than the upward reaction force of the lift floor. (W > T)

From Newton’s second law of motion,

Force F = ma

In this case the effective force, F = W – T

Therefore W – T = ma (Since F = ma)

mg – T = ma

-T = ma – mg, Therefore T = mg – ma

Factorize m: T = m (g – a)

T = m(g – a)

T = m(g – a) can also be called apparent weight of the object. The object will fill lighter in weight. The scale will record a value that is smaller than the true weight of the object.

### When the lift is stationary or moving up with uniform acceleration or constant velocity:

In this case, the downward force due to the weight of the object is equal to the upward reaction force of the floor of the lift. Therefore the lift is stationary or moving with constant velocity. Its acceleration is zero.

a = 0 m/s^{2},

T = m(g + 0)

T = mg.

Weight of object = Reaction force of the floor = mg

It means that there is no unbalanced force acting on the object because the object’s weight is canceled by the upward reaction force of the floor of the lift. If the object is measured on a spring scale, the scale will record the object’s true weight.

### When the lift is falling under gravity or falling freely, g = a, T = 0:

This situation happens when the cable of the lift cuts and the lift is moving downwards with an acceleration that is equal to the acceleration due to gravity.

From Newton’s second law of motion,

Force F = m*a

W > T ( the lift is falling )

Effective force F = W – T

Then. W – T = ma

mg – T = ma

mg – ma = T

Factorize m: m( g – a ) = T

Recall that the lift is falling freely, then a = g .

T = m ( g – g) = ( 0 ) = 0 N

We can see that T = 0. The object appears to have no weight (weightless). The object and the floor of the lift are not exerting force on each other. The scale of the weighing instrument reads zero.

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