Apparent Weight
Acceleration of Gravity

Objects that fall to the Earth all experience an
acceleration.

The acceleration due to gravity is g = 9.8 m/s2.

This acceleration must be due to a force.
Force of Gravity

The acceleration of a falling
mass m is -g.


 
ag
Kinematic view
The force on the mass is
found from F = ma (action).
This gravitational force is
F = -mg.


Fgrav  mg
Dynamic view
Normal Weight

We measure weight with a scale
that measures normal force.
• W = mg

Weight is related to mass by the
gravitational field g.
False Weight


A vertical acceleration can
change the weight.
The normal force on the floor
is our sense of weight.

 F = ma
 net force, F = -mg + FN.

• Downward acceleration
reduces weight
• Upward acceleration
increases weight

Mass is unchanged.
Newton’s law of acceleration
Solve for the normal force
 -mg + FN = ma
 FN = ma + mg
 FN = m (a + g)

Apparent mass based on g
 mapp = FN / g
Accelerated Weight

An elevator is accelerating
downward at 2.0 m/s2.
The person has a mass of
70 kg.
What mass is on the scale?

Add all the forces, but the
net force is – ma = FN – mg.
Solve for FN = m (g – a)
Convert to mass mapp = FN /g
The scale shows 56 kg.



Weightlessness

If the elevator accelerated downward at g, the normal
force would become 0.
• FN = m (g – a) = m (g – g) = 0

The person would feel weightless.

An object in free fall is weightless, but not massless.
Microgravity
research at NASA
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