Name: work done and kinetic energy
Uploaded: 2026-04-07T12:02:40.000Z
Duration: 1 min 41 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Energy

PS.PSc.7.3

Work-energy Theorem

The work-energy theorem states that the total work done by all the forces on an object is equal to the change in kinetic energy of that object, where m is the mass and v1 and v2 are the initial and final velocities of the object.
For instance, when a force is applied to a box, the velocity of the box increases, which increases its kinetic energy. Hence, the work done by the force contributes to a change in the kinetic energy of the box.
According to Newton&#x27;s second law of motion, force is equal to mass times acceleration.
Consider a case where the box is moving with an acceleration a&#xA0;along a straight line. From the third equation of motion, the relationship between velocity and acceleration can be rearranged to obtain the displacement covered by the box.
By substituting the force and displacement terms in the work formula, a relationship between work done and change in kinetic energy is obtained. This expression is called the work-energy theorem.
According to this theorem, when an applied force increases the velocity of an object, the work done is positive. If the applied force causes no change in the velocity of the object or its&#xA0;kinetic energy, the work done is said to be zero.
If the net force applied is used to stop the moving object, the kinetic energy decreases, and hence the work done is negative.

work-energy theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the momentum of the particle (motion). Therefore, we should consider the work done by all forces acting on a particle, or the net work, to see its effect on the particle&#x2019;s motion.
The work-energy theorem equates work done by all the forces on an object to the change in its kinetic energy. The theorem can be used to calculate work done by a force when acceleration is not constant, provided we know the change in velocity. When approaching a problem using the work-energy theorem, the following steps should be considered.
<ol>
	<li>Identify the given quantities and draw a free-body diagram based on the forces acting on the object. Calculate the work done by the known forces, keeping the sign of work done in mind. Add the total amount of work done by each force.&#xA0;</li>
	<li>Use the work-energy theorem and equate the total work to the change in kinetic energy. Substitute the known quantities and solve for the unknown.&#xA0;</li>
	<li>Evaluate the answer. If the object is traveling at a constant speed, there is no change in kinetic energy; therefore, the total work done should be zero. If the object has accelerated or has increased kinetic energy, the total work done is positive. If the object has slowed down, the total work done is negative.</li>
</ol>
This text is adapted from<a href="https://openstax.org/books/university-physics-volume-1/pages/7-3-work-energy-theorem"> Openstax, University Physics Volume 1, Section 7.3: Work-Energy Theorem.</a>

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

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Education

JoVE Core

Physics

Unit 1

Work and Kinetic Energy

KEY TERMS AND CONCEPTS

work done and kinetic energy

Work done by the net force is linked to an object's kinetic energy. In physics, the net force is the total force acting on an object. Kinetic energy is the energy of motion. The work-energy theorem states that the work done by all forces on an object equals the change in its kinetic energy.

This relationship is useful when acceleration is not constant. If the change in velocity is known, the theorem can still help calculate the work done by a force. It connects force, motion, and energy in a single equation.

To solve a problem, first identify the given quantities and draw a free-body diagram. A free-body diagram shows the forces acting on the object. Then calculate the work done by each known force and keep track of the sign of the work. Add the work from all forces to find the net work. Next, use the work-energy theorem and set the net work equal to the change in kinetic energy. Substitute the known values, solve for the unknown, and check the answer.

The sign of the total work tells you how the motion changes. If an object moves at constant speed, its kinetic energy does not change, so the total work is zero. If the object speeds up and gains kinetic energy, the total work is positive. If the object slows down, the total work is negative.

Work Done and Kinetic Energy

work

Work in Physics: Force and Motion

Work in physics connects force, motion, and energy transfer. Work is done when a force acts on an object and that object moves from one position to another. If there is no displacement, no work is done, even if a force is present. The amount of work depends on the force and the direction of motion. For a very small displacement, the work done is written as the dot product of force and displacement vectors. That means work depends on the size of the vectors and the angle between them. You can...

positive, negative, and zero work

How Force Direction Changes Work

Work in physics depends on the direction of a force and the way an object moves. Work is done when energy is transferred to an object. It happens when a force acts on a body that moves from one position to another. The work done by a force is defined as the integral of the force with respect to displacement along the path. Forces can change with position, and an object can move along different paths between the same two points. In vector form, the size of a force times the cosine of the angle...

energy

Energy Sources and Forms in Matter

Energy in matter comes from the Sun and changes form in many everyday processes. The universe is made of matter in different forms, and all forms of matter contain energy. On Earth, many energy sources can be traced back to the Sun, which is the ultimate energy source. Plants capture light energy from the Sun during photosynthesis and convert it into chemical energy. This stored energy can then be used in several ways. People get energy from plant foods, and wood or coal, which are fossilized...

types of potential energy

Potential Energy Examples in Everyday Physics

Potential energy is stored energy, and it appears in several everyday forms. It is also called energy at rest because it is ready to be used later. In physics, different systems can store energy in different ways. Gravitational potential energy is the energy stored by an object because of its position. An apple hanging from a tree is one clear example. Electrical potential energy is stored when electric charges attract or repel each other. Chemical potential energy is stored in the bonds...

types of kinetic energy

How Mass and Speed Affect Kinetic Energy

Kinetic energy depends on an object’s mass and speed. A heavier object moving at the same speed has more kinetic energy than a lighter one. An object moving faster also has more kinetic energy when the mass stays the same. The transcript also describes several forms of kinetic energy. Mechanical energy is linked to the motion of an object. A bullet fired from a gun and water flowing down a dam are examples of mechanical energy. Electrical energy comes from the flow of electric charges.

kinetic energy - i

Motion Energy in Collisions

Kinetic energy is the energy of motion. It depends on how fast an object moves, not on the direction of its velocity. In classical mechanics, this idea helps explain how moving bodies affect other bodies during collisions. A classic example is a perfectly elastic, head-on collision between two identical bodies, with one body initially at rest. After the collision, the first body stops, and the second body moves away with the first body's original velocity. This same pattern can be seen in...

kinetic energy - ii

Kinetic Energy, Momentum, and Reference Frames

Kinetic energy depends on mass, speed, momentum, and the frame of reference. For a particle, it is one-half of the particle’s mass times the square of its speed. The same idea can also be written in terms of mass and momentum instead of mass and velocity. The units of kinetic energy are mass times speed-squared. These units match the units of work. Force times distance also gives the same units, so kinetic energy and work are measured in joules. That is why work and kinetic energy are two...

Work done by the net force is linked to an object's kinetic energy. In physics, the net force is the total force acting on an object. Kinetic energy is the energy of motion. The work-energy theorem states that the work done by all forces on an object equals the change in its kinetic energy. This relationship is useful when acceleration is not constant. If the change in velocity is known, the theorem can still help calculate the work done by a force. It connects force, motion, and energy in a...

work and energy for variable forces

Variable Force Work via Graphs and Energy

Variable force work and energy can be found by using force-displacement graphs and the work-energy principle. When a force changes as an object moves, the calculation is more complex than for a constant force. Work is the product of force and displacement, and energy is the capacity of a system to do work. For a constant force, work is found by multiplying the force by the distance moved in the direction of the force. For a variable force, the work done is the area under the force-displacement...

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work-energy theorem for motion along a curve

work-energy-theorem-for-motion-along-a-curve

Work-Energy Along Curved Paths

The work-energy theorem can be applied to motion along a curved path. A curved path can be treated as many tiny straight paths added together. On each small part, the force can be taken as constant, so the work-energy theorem can be used there. The total result comes from adding the work done along all of those small path segments. The net work is found with an integral, which adds the work from each infinitesimal path. The total change in kinetic energy is the sum of the changes along the way.

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work done over an inclined plane

Gravity and Work on Sloped Motion

Gravity and work on sloped motion can be described with the center-of-mass framework. For a rigid body, internal forces do no work, so they can be ignored. The work-energy theorem then uses only the external forces. The work done by gravity depends on the path of the body’s center of mass. If gravity helps increase kinetic energy, the work is positive. If an object is lifted against gravity, the work is negative because kinetic energy decreases. For horizontal motion, the work done by or...

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work done by many forces

Calculating Work from Multiple Forces

Calculating work from multiple forces can be done in two ways, and both methods give the same result. One method finds the work done by each force first. The other method finds the net force by adding the force vectors first.

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work done by gravity

Gravity and Positive vs Negative Work

Gravity is one of the four fundamental forces in nature. On Earth, the force between an object and Earth is called gravity. Gravity does work on an object when it moves the object toward Earth’s center. In that case, the work done by gravity is positive. When an external force lifts an object away from Earth’s center, that force works against gravity. The net work done in this case is negative. If an object moves along the Earth with no change in distance toward or away from Earth’s center,...

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power

Power in Work and Motion

Power connects work with the time needed to do it. Work depends on force and displacement. The work-energy theorem also links net work on an object to the change in its kinetic energy between two points on its path. These ideas do not include time directly, but time still matters in many real situations. A sprinter is a clear example. Two runners may reach the same finish speed, so they do the same amount of work. The winner is the one who reaches that speed in less time. Power describes this...

power expended by a constant force

Power as the Rate of Doing Work

Power describes how fast work is done. In physics, two sprinters can cross the finish line with the same velocity and do the same amount of work, but the one who finishes first has greater power because the work takes less time. Average power is the work done during a time interval divided by that time interval. When the time interval becomes very small, this becomes instantaneous power. That gives the power at a specific moment instead of over a longer stretch of time. Power can also be...

key terms and concepts

Learn how net work relates to kinetic energy, how to use a free-body diagram, and how to tell whether total work is positive, negative, or zero.

Work Done and Kinetic Energy | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PS.Phy.6.2

Tennessee Academic Standards

High School

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.11

PHYS.PS3.6

Minnesota Academic Standards in Science

2.2.1 9P.2.1.1.1

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New Jersey Student Learning Standards for Science

HS-PS3-2

Arizona Science Standards

HS.P4

HS.P4U1.8

HS+Phy.P4

HS+Phy.P4U1.6

Alabama Course of Study Science

9-12.PS.1.1

9-12.PS.1.1.a

9-12.P.2.3.b

9-12.P.2.3.c

Next Generation Science Standards

HS-PS3-1

HS-PS3-5

Florida Department of Education

SC.912.P.10

SC.912.P.10.1

Texas Essential Knowledge and Skills

PHYS.7

PHYS.7.C

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-1.

Georgia Standards of Excellence

SP3.

Work-Kinetic Energy Theorem.

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PS.PSc.7.2

Work

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Positive, Negative, and Zero Work

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Work and Energy for Variable Forces

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Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

Work Done Over an Inclined Plane

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Work Done by Many Forces

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Work Done by Gravity

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Power

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Power Expended by a Constant Force

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PS.PSc.7.4

Analyze energy transfers and transformations within a mechanical system.

Work Done and Kinetic Energy

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