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. The force on the mass is found from F = ma (action). This gravitational force is F = -mg. Kinematic view 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. Downward acceleration reduces weight Upward acceleration increases weight Mass is unchanged. Newton’s law of acceleration F = ma net force, F = -mg + FN. 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. Pearson Education

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 NASA studies weightlessness here on the Earth. Use free fall Microgravity research at NASA Demonstration: link to NASA