Work Energy and Power flash cards

1. 1.Define work done by a constant force.

   Work is the dot product of force and displacement: $W = \vec{F}\cdot\vec{d} = Fd\cos\theta$, where $\theta$ is the angle between $\vec{F}$ and displacement $\vec{d}$.

   Hint: Scalar product of force and displacement.

2. 2.Is work a scalar or vector quantity? What is its SI unit?

   Work is a scalar quantity. Its SI unit is the joule (J), where $1\ \text{J} = 1\ \text{N}\cdot\text{m}$.

   Hint: Dot product gives a scalar.

3. 3.When is the work done by a force zero even though force and displacement are non-zero?

   When $\theta = 90^\circ$, i.e. force is perpendicular to displacement, since $\cos 90^\circ = 0$. Example: centripetal force in uniform circular motion.

   Hint: Think perpendicular force.

4. 4.What determines whether work done is positive, negative or zero?

   The angle $\theta$ between force and displacement: positive if $0^\circ \le \theta < 90^\circ$, zero if $\theta = 90^\circ$, negative if $90^\circ < \theta \le 180^\circ$.

   Hint: Sign of $\cos\theta$.

5. 5.Give an example of negative work.

   Work done by friction on a moving body (force opposite to displacement, $\theta = 180^\circ$). Also work done by gravity on a body moving up.

   Hint: Force opposes motion.

6. 6.What is the dimensional formula of work?

   $[W] = [ML^2T^{-2}]$, same as energy.

   Hint: Force times distance.

7. 7.How is work done by a variable force calculated?

   By integration: $W = \int_{x_i}^{x_f} F\,dx$ (in 1D), which equals the area under the force–displacement graph.

   Hint: Integral of $F$ over displacement.

8. 8.What does the area under a force–displacement ($F$ vs $x$) graph represent?

   It represents the work done by the force. Area above the axis is positive work; area below is negative work.

   Hint: $W=\int F\,dx$.

9. 9.State the work–energy theorem.

   The net work done by all forces on a body equals the change in its kinetic energy: $W_{net} = \Delta K = K_f - K_i = \tfrac{1}{2}mv^2 - \tfrac{1}{2}mu^2$.

   Hint: Net work = change in KE.

10. 10.Does the work–energy theorem hold for variable forces?

    Yes. The work–energy theorem $W_{net} = \Delta K$ is valid for both constant and variable forces, and along any path.

    Hint: It is general.

11. 11.Define kinetic energy and give its formula.

    Kinetic energy is the energy possessed by a body due to its motion: $K = \tfrac{1}{2}mv^2$. It is a scalar and always non-negative.

    Hint: Energy of motion.

12. 12.Relate kinetic energy to linear momentum.

    $K = \dfrac{p^2}{2m}$, where $p = mv$ is the linear momentum. Also $p = \sqrt{2mK}$.

    Hint: Substitute $v=p/m$.

13. 13.If momentum of a body doubles, how does its kinetic energy change?

    Since $K = p^2/2m$, doubling $p$ makes $K$ become 4 times the original (for constant mass).

    Hint: $K\propto p^2$.

14. 14.If kinetic energy of a body increases by a factor of 4, how does momentum change?

    Since $p = \sqrt{2mK}$, $p \propto \sqrt{K}$, so momentum doubles.

    Hint: $p\propto\sqrt{K}$.

15. 15.Define potential energy.

    Potential energy is the energy possessed by a body due to its position or configuration in a force field. It is defined only for conservative forces.

    Hint: Energy of position/configuration.

16. 16.Write the expression for gravitational potential energy near Earth's surface.

    $U = mgh$, where $h$ is height above a chosen reference level. Only the change $\Delta U = mg\,\Delta h$ is physically meaningful.

    Hint: Depends on height.

17. 17.Why is only the change in potential energy physically meaningful?

    Because the reference (zero) level of PE is arbitrary; forces depend on the gradient of PE, so a constant shift in $U$ has no physical effect.

    Hint: Zero level is a choice.

18. 18.Relate a conservative force to its potential energy in one dimension.

    $F = -\dfrac{dU}{dx}$. Force is the negative gradient (slope) of the potential energy curve.

    Hint: Negative slope of $U(x)$.

19. 19.What is a conservative force? Give two examples.

    A force is conservative if the work done by it around any closed path is zero (path-independent work). Examples: gravitational force and spring (elastic) force.

    Hint: Path-independent, zero work in a loop.

20. 20.What is a non-conservative force? Give an example.

    A force for which work done depends on the path taken and is non-zero over a closed loop. Example: friction and air resistance (viscous drag).

    Hint: Path-dependent, dissipative.

21. 21.How can potential energy be defined for a conservative force?

    $U_f - U_i = -W_{conservative} = -\int_{i}^{f}\vec{F}\cdot d\vec{r}$. PE change equals negative of work done by the conservative force.

    Hint: $\Delta U = -W$.

22. 22.State the principle of conservation of mechanical energy.

    If only conservative forces act, the total mechanical energy $E = K + U$ of a system remains constant: $K_i + U_i = K_f + U_f$.

    Hint: KE + PE = constant.

23. 23.Under what condition is mechanical energy NOT conserved?

    When non-conservative forces (friction, air drag) do work, or when external forces add/remove energy. Then $\Delta(K+U) = W_{nc}$.

    Hint: Friction present.

24. 24.For a freely falling body, what happens to KE and PE?

    PE decreases and KE increases such that their sum stays constant (neglecting air resistance): $mgh + \tfrac{1}{2}mv^2 =$ constant.

    Hint: PE converts to KE.

25. 25.Write the work done by a spring obeying Hooke's law when stretched by $x$.

    Work done by the spring force is $W_{spring} = -\tfrac{1}{2}kx^2$; work done against it (stored PE) is $+\tfrac{1}{2}kx^2$.

    Hint: Spring force $=-kx$.

26. 26.Write the expression for elastic potential energy stored in a spring.

    $U = \tfrac{1}{2}kx^2$, where $k$ is the spring (force) constant and $x$ is the deformation from natural length.

    Hint: Half k x squared.

27. 27.Is spring potential energy the same for compression and extension by equal amounts?

    Yes. Since $U = \tfrac{1}{2}kx^2$ depends on $x^2$, equal compression or extension stores the same PE.

    Hint: $U\propto x^2$.

28. 28.What is the spring constant $k$ and its SI unit?

    $k$ measures spring stiffness; $F = kx$. Its SI unit is N/m ($\text{N m}^{-1}$). Larger $k$ means a stiffer spring.

    Hint: Force per unit extension.

29. 29.Define power and give its formula.

    Power is the rate of doing work (or energy transfer): $P = \dfrac{dW}{dt}$. Average power $P_{av} = \dfrac{W}{t}$.

    Hint: Work per unit time.

30. 30.Express instantaneous power in terms of force and velocity.

    $P = \vec{F}\cdot\vec{v} = Fv\cos\theta$, where $\vec{v}$ is the instantaneous velocity.

    Hint: Dot product of force and velocity.

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