Work - AP Physics 1

1. Define the term 'conservative force'.

   A force with work independent of path, e.g., gravity. Work depends only on initial and final positions.

2. What is the work done by gravity on an object moving horizontally?

   Zero, as displacement is perpendicular to gravity. Gravity acts vertically while motion is horizontal.

3. What does it mean if net work is zero?

   The object's kinetic energy remains constant. No net energy transfer occurs to the object.

4. What is the work done by a conservative force over a closed path?

   Zero. Conservative forces store and return energy without loss.

5. Find displacement $d$: $W = 50 \text{ J}$, $F = 10 \text{ N}$, $\theta = 0^\text{o}$.

   $d = 5 \text{ m}$. Rearranging gives $d = W/F = 50/10 = 5$ m.

6. What is the work done by friction?

   Negative, as friction opposes motion. Friction force acts opposite to the direction of motion.

7. How is work calculated when force is perpendicular to displacement?

   Work is zero because $\text{cos}(90^\text{o}) = 0$. Perpendicular force components do no work on the object.

8. Define negative work.

   Work is negative when force opposes displacement. Force component removes energy from the system.

9. What happens to work when force is doubled?

   Work doubles, assuming displacement and angle are constant. Work is directly proportional to applied force magnitude.

10. State the SI unit of work.

    Joule (J). Same as Newton-meter (N⋅m) in physics.

11. Define work in terms of force and displacement.

    Work is the product of force and displacement in the direction of force. Only the component of force parallel to displacement contributes to work.

12. What is the unit of power related to work?

    Watt (W). One watt equals one joule per second.

13. If displacement is zero, what is work done regardless of force?

    Zero work. Work formula requires displacement to be nonzero.

14. Calculate work: $F = 25 \text{ N}$, $d = 3 \text{ m}$, $\theta = 60^\text{o}$.

    37.5 J. Using $\cos(60°) = 0.5$, so $W = 25 × 3 × 0.5 = 37.5$ J.

15. State the work-energy theorem.

    The work done equals the change in kinetic energy. Fundamental principle connecting force and energy in mechanics.

16. Calculate work: $F = 20 \text{ N}$, $d = 3 \text{ m}$, $\theta = 90^\text{o}$.

    0 J. Since $\cos(90°) = 0$, making $W = 20 × 3 × 0 = 0$ J.

17. Define work done by a non-conservative force.

    Work depends on the path taken. Examples include friction and air resistance forces.

18. Calculate work: $F = 50 \text{ N}$, $d = 2 \text{ m}$, $\theta = 30^\text{o}$.

    86.6 J. Using $\cos(30°) = \frac{\sqrt{3}}{2} ≈ 0.866$, so $W = 50 × 2 × 0.866 = 86.6$ J.

19. What is the work done by a force in the direction opposite to displacement?

    Negative work. When $\theta = 180°$, the cosine equals $-1$.

20. Calculate work: $F = 15 \text{ N}$, $d = 4 \text{ m}$, $\theta = 180^\text{o}$.

    -60 J. Using $\cos(180°) = -1$, so $W = 15 × 4 × (-1) = -60$ J.

21. What is the work-energy principle?

    Net work done on an object equals its change in kinetic energy. Also known as the work-energy theorem in physics.

22. What is the dot product of vectors in the work formula?

    The dot product is $F \times d \times \text{cos}(\theta)$. The mathematical operation for work between two vectors.

23. If $W = 100 \text{ J}$ and $d = 5 \text{ m}$, find force $F$ for $\theta = 0^\text{o}$.

    $F = 20 \text{ N}$. Rearranging $W = Fd$ gives $F = W/d = 100/5 = 20$ N.

24. Define positive work.

    Work is positive when force and displacement are in the same direction. Force component aids the motion, adding energy to the system.

25. Find work done: $F = 10 \text{ N}$, $d = 5 \text{ m}$, $\theta = 0^\text{o}$.

    50 J. Using $W = Fd\cos(0°) = 10 × 5 × 1 = 50$ J.

26. Calculate work: $F = 10 \text{ N}$, $d = 10 \text{ m}$, $\theta = 45^\text{o}$.

    70.7 J. Using $\cos(45°) = \frac{\sqrt{2}}{2} ≈ 0.707$, so $W = 10 × 10 × 0.707 = 70.7$ J.

27. Find displacement: $W = 200 \text{ J}$, $F = 50 \text{ N}$, $\theta = 0^\text{o}$.

    $d = 4 \text{ m}$. From $W = Fd$, so $d = W/F = 200/50 = 4$ m.

28. What is the work done if the angle $\theta$ is $90^\text{o}$?

    Zero, as $\text{cos}(90^\text{o}) = 0$. No force component exists parallel to displacement direction.

29. For $W = 75 \text{ J}$, $F = 15 \text{ N}$, find $d$ when $\theta = 0^\text{o}$.

    $d = 5 \text{ m}$. Solving $d = W/F = 75/15 = 5$ m.

30. What is an example of a non-conservative force?

    Friction. Force depends on the path taken between points.

31. What is the relation between work and power?

    Power is the rate at which work is done. Power equals work divided by time taken.

32. Find force $F$: $W = 60 \text{ J}$, $d = 4 \text{ m}$, $\theta = 0^\text{o}$.

    $F = 15 \text{ N}$. From $W = Fd$, so $F = W/d = 60/4 = 15$ N.

33. Calculate power: $W = 120 \text{ J}$, time $t = 4 \text{ s}$.

    30 W. Using $P = W/t = 120/4 = 30$ W.

34. Identify the scalar quantity: work or force?

    Work is a scalar quantity. Work has magnitude only, no direction like force vectors.

35. Calculate work: $F = 30 \text{ N}$, $d = 2 \text{ m}$, $\theta = 0^\text{o}$.

    60 J. Using $W = Fd\cos(0°) = 30 × 2 × 1 = 60$ J.

36. What is the work done when no displacement occurs?

    Zero, as work requires displacement. Work formula requires movement to occur.

37. What is the effect of angle on work done?

    Work depends on $\text{cos}(\theta)$; maximum at $0^\text{o}$, zero at $90^\text{o}$. The cosine function determines the effective force component.

38. What is the work done if $F = 0$?

    Zero, as no force means no work is done. Work requires both force and displacement to be nonzero.

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