Apparent Weight (College Board AP® Physics 1: Algebra-Based): Study Guide

Apparent weight

Apparent weight and normal force

• The magnitude of the apparent weight of a system is the magnitude of the normal force exerted on the system

  • The apparent weight of an object is the weight it appears to be and not the weight it actually is

• The normal force is the perpendicular component of the force exerted on an object by the surface with which it is in contact

  • The normal force is a contact force acting against the weight of an object

Normal contact force

• Apparent weight can be observed when an object is immersed in a fluid (liquid or gas)

  • The magnitude of the normal force is equal to the buoyant force acting upwards on the object

  • The buoyant force is equal to the weight of the fluid displaced by the object

Buoyant force

Apparent weight and gravitational force

Apparent weight for a system not accelerating

• Recall that an object's apparent weight is equal to the normal force exerted on it

• When the system is stationary or at constant speed, the apparent weight is equal to actual weight

• If an object is placed on a scale, the scale will read the object's actual weight

Apparent weight for an accelerating system

• When a system has a non-zero acceleration in the direction of its weight:

  • the apparent weight of the system can be greater than or less than the actual weight, depending on the direction of acceleration

• If an object is placed on a scale, the scale will not read the object's actual weight

• The scale will read the object's apparent weight

Acceleration in the same direction as weight

• Consider an object in an elevator

• When the elevator accelerates downwards it may be either:

  • moving upwards and decelerating

  • moving downwards and accelerating

• Apply Newton's second law to the vertical forces on the object to find apparent weight

  • Define downwards as the positive direction

  • This means the downwards acceleration is positive

• Therefore, when acceleration is in the same direction as weight, apparent weight is less than actual weight

Acceleration in the opposite direction to weight

• When the elevator accelerates upwards it may be either:

  • moving upwards and accelerating

  • moving downwards and decelerating

• Apply Newton's second law to the vertical forces on the object to find apparent weight

  • Define downwards as the positive direction

  • This means the upwards acceleration is negative

• Therefore, when acceleration is in the opposite direction to weight, apparent weight is more than actual weight

Apparent weight of an object accelerating in different directions

Gravitational force equivalence principle

• The equivalence principle states that an observer in a non-inertial reference frame is unable to distinguish between an object’s apparent weight and the gravitational force exerted on the object by a gravitational field

  • A non-inertial reference frame is a reference frame that is accelerating with respect to an inertial reference frame

Moving in a non-inertial reference frame

• An example of an object moving in a non-inertial reference frame is when an external net force is applied to accelerate or decelerate a vehicle

  • The passengers and the car no longer move together

  • The inertia of the passengers causes them to resist a change in motion as the car accelerates and moves differently to them

• When a vehicle accelerates, an object inside will initially move backwards as it resists the change in motion

• When a vehicle decelerates, an object in the vehicle will continue to move forward as it resists the change in motion

Resisting the change in motion of a moving vehicle

• The equivalence principle implies that experiencing a constant acceleration, , not in a gravitational field is equivalent to being at rest in a uniform gravitational field with gravitational field strength, where

• For example, if an elevator is in space beyond the reach of a gravitational field and the elevator experiences a constant acceleration of then:

  • objects in the elevator fall with the same magnitude of constant acceleration of

  • a person inside the elevator can not tell the difference between being accelerated inside the elevator and being stationary on Earth where

An elevator accelerating in space

An elevator stationary on Earth

• It can be shown algebraically in a non-inertial reference frame that an object’s apparent weight and the gravitational force exerted upon it by a gravitational field appear equal to an observer also in the non-inertial reference frame

• From the reference frame of the accelerating elevator, the apparent weight of the person is

• From the reference frame of the stationary person in the stationary elevator on Earth, their apparent weight is equal to their actual weight

• The two scenarios are equivalent

  • The laws of Physics will work in exactly the same way for both