Work - AP Physics 1
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What is the work done if $F = 0$?
What is the work done if $F = 0$?
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Zero, as no force means no work is done. Work requires both force and displacement to be nonzero.
Zero, as no force means no work is done. Work requires both force and displacement to be nonzero.
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Calculate work: $F = 30 \text{ N}$, $d = 2 \text{ m}$, $\theta = 0^\text{o}$.
Calculate work: $F = 30 \text{ N}$, $d = 2 \text{ m}$, $\theta = 0^\text{o}$.
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60 J. Using $W = Fd\cos(0°) = 30 × 2 × 1 = 60$ J.
60 J. Using $W = Fd\cos(0°) = 30 × 2 × 1 = 60$ J.
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What is the work done by a force in the direction opposite to displacement?
What is the work done by a force in the direction opposite to displacement?
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Negative work. When $\theta = 180°$, the cosine equals $-1$.
Negative work. When $\theta = 180°$, the cosine equals $-1$.
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What does it mean if net work is zero?
What does it mean if net work is zero?
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The object's kinetic energy remains constant. No net energy transfer occurs to the object.
The object's kinetic energy remains constant. No net energy transfer occurs to the object.
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What is the work done by a conservative force over a closed path?
What is the work done by a conservative force over a closed path?
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Zero. Conservative forces store and return energy without loss.
Zero. Conservative forces store and return energy without loss.
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Find force $F$: $W = 60 \text{ J}$, $d = 4 \text{ m}$, $\theta = 0^\text{o}$.
Find force $F$: $W = 60 \text{ J}$, $d = 4 \text{ m}$, $\theta = 0^\text{o}$.
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$F = 15 \text{ N}$. From $W = Fd$, so $F = W/d = 60/4 = 15$ N.
$F = 15 \text{ N}$. From $W = Fd$, so $F = W/d = 60/4 = 15$ N.
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What is the work done when no displacement occurs?
What is the work done when no displacement occurs?
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Zero, as work requires displacement. Work formula requires movement to occur.
Zero, as work requires displacement. Work formula requires movement to occur.
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Calculate work: $F = 50 \text{ N}$, $d = 2 \text{ m}$, $\theta = 30^\text{o}$.
Calculate work: $F = 50 \text{ N}$, $d = 2 \text{ m}$, $\theta = 30^\text{o}$.
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86.6 J. Using $\cos(30°) = \frac{\sqrt{3}}{2} ≈ 0.866$, so $W = 50 × 2 × 0.866 = 86.6$ J.
86.6 J. Using $\cos(30°) = \frac{\sqrt{3}}{2} ≈ 0.866$, so $W = 50 × 2 × 0.866 = 86.6$ J.
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Find displacement $d$: $W = 50 \text{ J}$, $F = 10 \text{ N}$, $\theta = 0^\text{o}$.
Find displacement $d$: $W = 50 \text{ J}$, $F = 10 \text{ N}$, $\theta = 0^\text{o}$.
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$d = 5 \text{ m}$. Rearranging gives $d = W/F = 50/10 = 5$ m.
$d = 5 \text{ m}$. Rearranging gives $d = W/F = 50/10 = 5$ m.
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What is the relation between work and power?
What is the relation between work and power?
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Power is the rate at which work is done. Power equals work divided by time taken.
Power is the rate at which work is done. Power equals work divided by time taken.
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Calculate work: $F = 25 \text{ N}$, $d = 3 \text{ m}$, $\theta = 60^\text{o}$.
Calculate work: $F = 25 \text{ N}$, $d = 3 \text{ m}$, $\theta = 60^\text{o}$.
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37.5 J. Using $\cos(60°) = 0.5$, so $W = 25 × 3 × 0.5 = 37.5$ J.
37.5 J. Using $\cos(60°) = 0.5$, so $W = 25 × 3 × 0.5 = 37.5$ J.
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What happens to work when force is doubled?
What happens to work when force is doubled?
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Work doubles, assuming displacement and angle are constant. Work is directly proportional to applied force magnitude.
Work doubles, assuming displacement and angle are constant. Work is directly proportional to applied force magnitude.
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Find displacement: $W = 200 \text{ J}$, $F = 50 \text{ N}$, $\theta = 0^\text{o}$.
Find displacement: $W = 200 \text{ J}$, $F = 50 \text{ N}$, $\theta = 0^\text{o}$.
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$d = 4 \text{ m}$. From $W = Fd$, so $d = W/F = 200/50 = 4$ m.
$d = 4 \text{ m}$. From $W = Fd$, so $d = W/F = 200/50 = 4$ m.
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Define negative work.
Define negative work.
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Work is negative when force opposes displacement. Force component removes energy from the system.
Work is negative when force opposes displacement. Force component removes energy from the system.
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Identify the scalar quantity: work or force?
Identify the scalar quantity: work or force?
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Work is a scalar quantity. Work has magnitude only, no direction like force vectors.
Work is a scalar quantity. Work has magnitude only, no direction like force vectors.
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State the SI unit of work.
State the SI unit of work.
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Joule (J). Same as Newton-meter (N⋅m) in physics.
Joule (J). Same as Newton-meter (N⋅m) in physics.
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Find work done: $F = 10 \text{ N}$, $d = 5 \text{ m}$, $\theta = 0^\text{o}$.
Find work done: $F = 10 \text{ N}$, $d = 5 \text{ m}$, $\theta = 0^\text{o}$.
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50 J. Using $W = Fd\cos(0°) = 10 × 5 × 1 = 50$ J.
50 J. Using $W = Fd\cos(0°) = 10 × 5 × 1 = 50$ J.
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If $W = 100 \text{ J}$ and $d = 5 \text{ m}$, find force $F$ for $\theta = 0^\text{o}$.
If $W = 100 \text{ J}$ and $d = 5 \text{ m}$, find force $F$ for $\theta = 0^\text{o}$.
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$F = 20 \text{ N}$. Rearranging $W = Fd$ gives $F = W/d = 100/5 = 20$ N.
$F = 20 \text{ N}$. Rearranging $W = Fd$ gives $F = W/d = 100/5 = 20$ N.
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Calculate power: $W = 120 \text{ J}$, time $t = 4 \text{ s}$.
Calculate power: $W = 120 \text{ J}$, time $t = 4 \text{ s}$.
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30 W. Using $P = W/t = 120/4 = 30$ W.
30 W. Using $P = W/t = 120/4 = 30$ W.
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Define positive work.
Define positive work.
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Work is positive when force and displacement are in the same direction. Force component aids the motion, adding energy to the system.
Work is positive when force and displacement are in the same direction. Force component aids the motion, adding energy to the system.
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What is an example of a non-conservative force?
What is an example of a non-conservative force?
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Friction. Force depends on the path taken between points.
Friction. Force depends on the path taken between points.
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What is the work done if the angle $\theta$ is $90^\text{o}$?
What is the work done if the angle $\theta$ is $90^\text{o}$?
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Zero, as $\text{cos}(90^\text{o}) = 0$. No force component exists parallel to displacement direction.
Zero, as $\text{cos}(90^\text{o}) = 0$. No force component exists parallel to displacement direction.
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State the work-energy theorem.
State the work-energy theorem.
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The work done equals the change in kinetic energy. Fundamental principle connecting force and energy in mechanics.
The work done equals the change in kinetic energy. Fundamental principle connecting force and energy in mechanics.
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Calculate work: $F = 20 \text{ N}$, $d = 3 \text{ m}$, $\theta = 90^\text{o}$.
Calculate work: $F = 20 \text{ N}$, $d = 3 \text{ m}$, $\theta = 90^\text{o}$.
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0 J. Since $\cos(90°) = 0$, making $W = 20 × 3 × 0 = 0$ J.
0 J. Since $\cos(90°) = 0$, making $W = 20 × 3 × 0 = 0$ J.
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What is the work-energy principle?
What is the work-energy principle?
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Net work done on an object equals its change in kinetic energy. Also known as the work-energy theorem in physics.
Net work done on an object equals its change in kinetic energy. Also known as the work-energy theorem in physics.
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How is work calculated when force is perpendicular to displacement?
How is work calculated when force is perpendicular to displacement?
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Work is zero because $\text{cos}(90^\text{o}) = 0$. Perpendicular force components do no work on the object.
Work is zero because $\text{cos}(90^\text{o}) = 0$. Perpendicular force components do no work on the object.
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What is the unit of power related to work?
What is the unit of power related to work?
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Watt (W). One watt equals one joule per second.
Watt (W). One watt equals one joule per second.
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If displacement is zero, what is work done regardless of force?
If displacement is zero, what is work done regardless of force?
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Zero work. Work formula requires displacement to be nonzero.
Zero work. Work formula requires displacement to be nonzero.
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What is the effect of angle on work done?
What is the effect of angle on work done?
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Work depends on $\text{cos}(\theta)$; maximum at $0^\text{o}$, zero at $90^\text{o}$. The cosine function determines the effective force component.
Work depends on $\text{cos}(\theta)$; maximum at $0^\text{o}$, zero at $90^\text{o}$. The cosine function determines the effective force component.
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Calculate work: $F = 15 \text{ N}$, $d = 4 \text{ m}$, $\theta = 180^\text{o}$.
Calculate work: $F = 15 \text{ N}$, $d = 4 \text{ m}$, $\theta = 180^\text{o}$.
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-60 J. Using $\cos(180°) = -1$, so $W = 15 × 4 × (-1) = -60$ J.
-60 J. Using $\cos(180°) = -1$, so $W = 15 × 4 × (-1) = -60$ J.
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