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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 2: Force & Translational DynamicsGravitational ForceApparent Weight

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

Study Guide

Ann Howell

Written by: Ann Howell

Reviewed by: Caroline Carroll

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

apparent space weight space equals space open vertical bar stack F subscript n with rightwards arrow on top close vertical bar

  • 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

An object with mass "m" has an upward reaction force and downward weight. Caption reads "Reaction forces support an object by balancing its weight."
An object resting on another in contact has a normal reaction force acting in the opposite direction to its weight

  • 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

apparent space weight space equals space open vertical bar F with italic rightwards arrow on top subscript n close vertical bar space equals space buoyant space force space equals space weight space of space fluid space displaced

Buoyant force

Diagram showing a soccer ball being immersed in water and displacing it, resulting in the ball floating due to buoyant force Fb equalling gravitational force Fg.
The buoyant force on an object immersed in water is equal to the weight of the water displaced

Apparent weight and gravitational force

  • If a system is accelerating:

    • the apparent weight of the system is not equal to the magnitude of the gravitational force exerted on the system

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

  • When the system is stationary:

    • for example, an object placed on a bathroom scale

    • the reading on the scale will equal the object's actual weight

apparent space weight space equals space open vertical bar stack F subscript n with rightwards arrow on top close vertical bar space equals space actual space weight space equals space m g

  • When the system is accelerating:

    • for example, if the scale is placed in an elevator that is accelerating

    • the reading on the scale will be equal to the object's apparent weight

  • When the elevator is accelerating positively (speeding up):

    • the normal force exerted by the scale on the object is greater than object's actual weight

    • the scale exerts an upward force equal to the object's actual weight plus the additional force producing the acceleration

apparent space weight space equals space open vertical bar stack F subscript n with rightwards arrow on top close vertical bar space equals space m g space plus space m a

  • When the elevator is accelerating negatively (slowing down):

    • the normal force exerted by the scale on the object is less than the object's actual weight

    • the scale exerts an upward force equal to the object's actual weight minus the additional force producing the acceleration

apparent space weight space equals space open vertical bar stack F subscript n with rightwards arrow on top close vertical bar space equals space m g space minus space m a

Apparent weight of an object accelerating in different directions

Three diagrams show the normal force on an object: stationary (Fn=mg), positive acceleration (Fn=mg+ma), and negative acceleration (Fn=mg-ma).
The magnitude of the apparent weight of a person in an elevator changes depending on the direction of the acceleration

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

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

Two images depict a car with a box on its roof. As the car moves forward, the box moves backward. When the car stops, the box moves forward and falls off.
When a car starts to move a box on the top resists the change in motion and moves backwards in the opposite direction.

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

  • For example, if an elevator is in space beyond the reach of a gravitational field and the elevator experiences a constant acceleration of 10 space straight m divided by straight s squared then:

    • objects in the elevator fall with the same magnitude of constant acceleration of a space equals space 10 space straight m divided by straight s squared

    • a person inside the elevator can not tell the difference between being accelerated inside the elevator and being stationary on Earth where g space equals space 10 space straight m divided by straight s squared

An elevator accelerating in space

Elevator accelerating upwards at 10 m/s². A ball inside is dropped, also accelerating at 10 m/s² downwards, meeting the elevator. Text explains the scenario.
An object dropped in an elevator that is accelerating at 10 m/s^2 away from any gravitational field will also drop at 10 m/s^2

An elevator stationary on Earth

A stick figure holding a purple ball in a stationary elevator on Earth is shown above an illustration of the Earth. Text reads, "a = g = 10 m/s²."
The person in the elevator cannot tell the difference between being stationary on Earth and accelerating at 10 m/s^2 far away from any gravitational field

  • 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

open vertical bar F with rightwards arrow on top subscript n close vertical bar space equals space m a

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

open vertical bar F with rightwards arrow on top subscript n close vertical bar space equals space open vertical bar F with rightwards arrow on top subscript g close vertical bar space equals space m g

  • The two scenarios are equivalent

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

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    Author
    Reviewer
    Ann Howell

    Author: Ann Howell

    Expertise: Physics Content Creator

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.