IB Physics Topic A.3.2 Work and Energy Transfer Revision Notes (SL/HL)

IB Physics Topic A.3.2 Work and Energy Transfer Revision Notes (SL/HL) | RevisionDojo

Written by official IB examiners

Definition of Work: The Relationship Between Force and Displacement

Definition

Work

Work is defined as the product of the force applied to an object, the displacement of the object, and the cosine of the angle between the force and the displacement.

Mathematically, this is expressed as:

$$
W = Fs \cos \theta
$$

where:

$W$ is the work done (measured in joules, J).
$F$ is the magnitude of the force applied (in newtons, N).
$s$ is the displacement of the object (in meters, m).
$\theta$ is the angle between the force and the displacement.

Note

Work is only done when the force has a component in the direction of the displacement.
If the force is perpendicular to the displacement ($\theta = 90^\circ$), no work is done because $\cos 90^\circ = 0$.

Positive, Negative, and Zero Work

Positive Work: When the force and displacement are in the same direction ($0^\circ \le \theta< 90^\circ$), work is positive.
Negative Work: When the force opposes the displacement ($90^\circ < \theta \le 180^\circ$), work is negative.
Zero Work: When the force is perpendicular to the displacement ($\theta = 90^\circ$), no work is done.

Example question

A person pulls a sled with a force of 50 N at an angle of $30^\circ$ to the horizontal. The sled moves 10 m along the ground.

Calculate the work done by the force.

Solution

Using the formula:$$
W = Fs \cos \theta
$$
Substitute the values:$$ W = 50 \times 10 \times \cos 30^\circ = 50 \times 10 \times 0.866 = 433\ \text{J} $$
The work done is 433 joules.

The Work-Energy Theorem: Connecting Work Done to Changes in Kinetic Energy

Definition

The work-energy theorem

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

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Note

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Definition of Work: The Relationship Between Force and Displacement

Definition

Work

Work is defined as the product of the force applied to an object, the displacement of the object, and the cosine of the angle between the force and the displacement.

Mathematically, this is expressed as:

$$
W = Fs \cos \theta
$$

where:

$W$ is the work done (measured in joules, J).
$F$ is the magnitude of the force applied (in newtons, N).
$s$ is the displacement of the object (in meters, m).
$\theta$ is the angle between the force and the displacement.

Note

Work is only done when the force has a component in the direction of the displacement.
If the force is perpendicular to the displacement ($\theta = 90^\circ$), no work is done because $\cos 90^\circ = 0$.

Positive, Negative, and Zero Work

Positive Work: When the force and displacement are in the same direction ($0^\circ \le \theta< 90^\circ$), work is positive.
Negative Work: When the force opposes the displacement ($90^\circ < \theta \le 180^\circ$), work is negative.
Zero Work: When the force is perpendicular to the displacement ($\theta = 90^\circ$), no work is done.

Example question

A person pulls a sled with a force of 50 N at an angle of $30^\circ$ to the horizontal. The sled moves 10 m along the ground.

Calculate the work done by the force.

Solution

Using the formula:$$
W = Fs \cos \theta
$$
Substitute the values:$$ W = 50 \times 10 \times \cos 30^\circ = 50 \times 10 \times 0.866 = 433\ \text{J} $$
The work done is 433 joules.

The Work-Energy Theorem: Connecting Work Done to Changes in Kinetic Energy

Definition

The work-energy theorem

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics A.3.2 Work and Energy Transfer Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Definition of Work: The Relationship Between Force and Displacement

Positive, Negative, and Zero Work

The Work-Energy Theorem: Connecting Work Done to Changes in Kinetic Energy

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Definition of Work: The Relationship Between Force and Displacement

Positive, Negative, and Zero Work

The Work-Energy Theorem: Connecting Work Done to Changes in Kinetic Energy

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account