1. Apparent Weight

2. Acceleration of Gravity  Objects that fall to the Earth all experience an acceleration.  The acceleration due to gravity is g = 9.8 m/s 2.  This acceleration must be due to a force.

3. 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 viewDynamic view

4. Normal Weight  We measure weight with a scale that measures normal force. W = mgW = mg  Weight is related to mass by the gravitational field g.

5. False Weight  A vertical acceleration can change the weight.  The normal force on the floor is our sense of weight. Downward acceleration reduces weightDownward acceleration reduces weight Upward acceleration increases weightUpward acceleration increases weight  Mass is unchanged.  Newton’s law of acceleration  F = ma  net force, F = -mg + F N.  Solve for the normal force  -mg + F N = ma  F N = ma + mg  F N = m (a + g)  Apparent mass based on g  m app = F N / g

6. Accelerated Weight  An elevator is accelerating downward at 2.0 m/s 2.  The person has a mass of 70 kg.  What mass is on the scale?  Add all the forces, but the net force is –  ma = F N – mg.  Solve for F N = m ( g – a )  Convert to mass m app = F N / g  The scale shows 56 kg.

7. Weightlessness  If the elevator accelerated downward at g, the normal force would become 0. F N = m (g – a) = m (g – g) = 0F N = m (g – a) = m (g – g) = 0  The person would feel weightless.  An object in free fall is weightless, but not massless. next Microgravity research at NASA