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

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

Study Guide

Ann Howell

Written by: Ann Howell

Reviewed by: Caroline Carroll

Calculating weight

  • The gravitational force exerted by an astronomical body on a relatively small nearby object is called weight

    • For example, the Earth is the astronomical body that exerts a gravitational force on a person, a relatively small object standing on the surface nearby

  • An object with mass has the same mass everywhere in the Universe

    • Mass is a measure of the amount of matter a body or substance is composed of

    • Mass is a measure of an object's inertia

  • The weight of an object is determined by the magnitude of the gravitational field at the object's position

    • A person of mass 70 kg has a greater weight force on Earth than on the Moon because the gravitational field strength on the Earth is greater

Comparing weight on the Earth and Moon

Comparison of weight on Earth and the Moon. A person weighs 700 N on Earth and 114 N on the Moon despite having the same mass of 70 kg in both places.
A mass in a stronger gravitational field will have a larger weight

Derived equation

  • The gravitational force exerted by an astronomical body on a relatively small nearby object is called weight

Weight space equals space stack F subscript g with rightwards arrow on top space equals space m g

Derivation:

Step 1: Identify the fundamental principle

  • Newton's second law

F with rightwards arrow on top subscript n e t end subscript space equals space m a with rightwards arrow on top

  • Where:

    • F with rightwards arrow on top subscript n e t end subscript = net force exerted on the system

    • m = mass of the system

    • a with rightwards arrow on top = acceleration of the system

Step 2: Apply the specific conditions

  • When the gravitational force is the only force exerted on an object, the acceleration, a, towards the center of the object is equal to the magnitude of the gravitational field, g of the object

  • Hence, a space equals space g

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

  • The gravitational force exerted by an astronomical body on a relatively small nearby object is weight

Weight space equals space stack F subscript g with rightwards arrow on top space equals space m g

Weightlessness

  • A system appears weightless when:

    • there are no forces exerted on the system

    • when the force of gravity is the only force exerted on the system

  • When there are no forces exerted on the system, then the object must be infinitely far from any other object so a gravitational force is not exerted upon it

    • The only place where one object can be infinitely far from another is when both objects are located in space

  • An infinitely far object could have 'zero weight' when the force of gravity acting on the object is zero

F with rightwards arrow on top subscript g equals space m g space equals space m open parentheses 0 close parentheses space equals space 0

g space equals space fraction numerator G M over denominator r squared end fraction space equals space fraction numerator G M over denominator open parentheses infinity close parentheses squared end fraction space equals space 0

Infinitely far objects

Diagram visualizing the universe with stars scattered on a dark background, featuring red and green lines and arrows illustrating concepts related to light and infinity.
An object in space can be infinitely far from other objects meaning the gravitational force is zero.

  • When the force of gravity is the only force exerted on the system, then the system is in free-fall

    • An object is in free-fall only when air resistance is negligible

Free-fall

A person is falling with arms outstretched. An arrow points downward indicating weight as the only acting force, with text below: "Negligible air resistance, so the only force acting is weight."
When there is no air resistance acting on a falling object then it is in free-fall due to the gravitational force.

  • On Earth, when an object is in equilibrium, the normal force between the object and the surface is equal to the force of gravity,  resulting in a net vertical force of zero

    • Weightlessness is experienced when the normal force between an object and a surface is zero, resulting in the object losing physical contact with the surface

  • Astronauts predominantly experience weightlessness due to being in continuous free fall around the Earth

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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.