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.
ag
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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