Translational Kinetic Energy - AP Physics 1

1. What does $m$ represent in the translational kinetic energy formula?

   Mass of the object. Mass is the scalar quantity representing the amount of matter in the object.

2. Determine the kinetic energy if mass is 10 kg and velocity is 0.

   $KE = 0 \text{ J}$. Any object at rest has zero kinetic energy.

3. A car increases speed from 10 m/s to 20 m/s. By what factor does its kinetic energy increase?

   Increases by a factor of 4. Velocity doubles, so $KE$ increases by $(2)^2 = 4$ times.

4. If velocity is doubled, how does kinetic energy change?

   Increases by a factor of 4. Since $v^2$ appears in the formula, doubling $v$ increases $KE$ by $2^2 = 4$.

5. Find kinetic energy: mass = 0.5 kg, velocity = 10 m/s.

   $KE = 25 \text{ J}$. $KE = \frac{1}{2}(0.5)(10^2) = \frac{1}{2}(0.5)(100) = 25$ J.

6. Calculate the mass of an object with 50 J of kinetic energy moving at 5 m/s.

   $m = 4 \text{ kg}$. $50 = \frac{1}{2}m(5^2)$, so $m = \frac{2(50)}{25} = 4$ kg.

7. If mass is tripled and velocity is constant, how does $KE$ change?

   Triples. Kinetic energy scales linearly with mass when velocity is constant.

8. A 1 kg object moves at 3 m/s. Find its kinetic energy.

   $KE = 4.5 \text{ J}$. $KE = \frac{1}{2}(1)(3^2) = \frac{1}{2}(1)(9) = 4.5$ J.

9. What is the kinetic energy formula rearranged for velocity?

   $v = \text{sqrt}(\frac{2KE}{m})$. Solve $KE = \frac{1}{2}mv^2$ for $v$ by isolating the velocity term.

10. Calculate velocity: kinetic energy = 18 J, mass = 2 kg.

    $v = 3 \text{ m/s}$. $18 = \frac{1}{2}(2)v^2$, so $v = \sqrt{\frac{36}{2}} = 3$ m/s.

11. Convert 100 J to kilojoules (kJ).

    $0.1 \text{ kJ}$. Divide by 1000 to convert joules to kilojoules.

12. What is the formula to find mass from kinetic energy and velocity?

    $m = \frac{2KE}{v^2}$. Rearrange $KE = \frac{1}{2}mv^2$ to solve for mass.

13. Calculate the kinetic energy: mass = 4 kg, velocity = 5 m/s.

    $KE = 50 \text{ J}$. $KE = \frac{1}{2}(4)(5^2) = \frac{1}{2}(4)(25) = 50$ J.

14. If mass is halved, how does kinetic energy change?

    Halved. Kinetic energy is directly proportional to mass.

15. What is the kinetic energy of a 5 kg object at rest?

    $KE = 0 \text{ J}$. Zero velocity means zero kinetic energy regardless of mass.

16. If kinetic energy is 200 J and velocity is 4 m/s, find the mass.

    $m = 25 \text{ kg}$. $200 = \frac{1}{2}m(4^2)$, so $m = \frac{2(200)}{16} = 25$ kg.

17. If kinetic energy is 64 J and mass is 4 kg, what is the velocity?

    $v = 4 \text{ m/s}$. $64 = \frac{1}{2}(4)v^2$, so $v = \sqrt{\frac{128}{4}} = 4$ m/s.

18. Identify the SI unit for mass used in the kinetic energy formula.

    Kilogram (kg). Standard SI base unit for measuring the amount of matter.

19. If velocity remains constant, how does kinetic energy change as mass increases?

    Increases linearly. Direct proportional relationship when velocity remains constant.

20. What factor affects translational kinetic energy the most?

    Velocity, as $v$ is squared. The squared term makes velocity changes more impactful than mass changes.

21. A 10 kg object moves at 0 m/s. What is its kinetic energy?

    $KE = 0 \text{ J}$. Zero velocity means zero kinetic energy regardless of mass.

22. What is the kinetic energy of a 3 kg object moving at 2 m/s?

    $KE = 6 \text{ J}$. $KE = \frac{1}{2}(3)(2^2) = \frac{1}{2}(3)(4) = 6$ J.

23. What are the SI units of translational kinetic energy?

    Joules (J). Energy units derived from $kg \cdot m^2/s^2$ in the SI system.

24. Identify the SI unit for velocity in the kinetic energy formula.

    Meters per second (m/s). SI derived unit combining distance per unit time.

25. State the relationship between kinetic energy and mass.

    Directly proportional. Doubling mass doubles kinetic energy when velocity is constant.

26. Calculate the kinetic energy of a 2 kg object moving at 3 m/s.

    $KE = 9 \text{ J}$. $KE = \frac{1}{2}(2)(3^2) = \frac{1}{2}(2)(9) = 9$ J.

27. How is translational kinetic energy related to work done?

    Equal to work done to bring object to current speed. Work-energy theorem states work done equals change in kinetic energy.

28. What is the kinetic energy of a 2 kg object moving at 0 m/s?

    $KE = 0 \text{ J}$. Zero velocity results in zero kinetic energy.

29. Convert 1 Joule into base SI units.

    $1 \text{ J} = 1 \text{ kg} \times \text{m}^2/\text{s}^2$. Breaking down the joule into fundamental SI base units.

30. State the relationship between kinetic energy and velocity.

    Proportional to the square of velocity. The $v^2$ term creates a quadratic relationship with velocity.

31. A 0.5 kg object has 8 J of kinetic energy. What is its velocity?

    $v = 4 \text{ m/s}$. $8 = \frac{1}{2}(0.5)v^2$, so $v = \sqrt{\frac{16}{0.5}} = 4$ m/s.

32. A 3 kg object has 27 J of kinetic energy. Find its velocity.

    $v = 3 \text{ m/s}$. $27 = \frac{1}{2}(3)v^2$, so $v = \sqrt{\frac{54}{3}} = 3$ m/s.

33. What does $v$ represent in the translational kinetic energy formula?

    Velocity of the object. Velocity is the vector quantity representing the object's speed and direction.

34. State the formula for translational kinetic energy.

    $KE = \frac{1}{2}mv^2$. Fundamental formula where kinetic energy equals half the product of mass and velocity squared.

35. What happens to kinetic energy if both mass and velocity are doubled?

    Increases by a factor of 8. Mass doubles ($\times 2$) and velocity squared doubles ($\times 4$): $2 \times 4 = 8$.

36. A 6 kg object moving at 2 m/s. Calculate its kinetic energy.

    $KE = 12 \text{ J}$. $KE = \frac{1}{2}(6)(2^2) = \frac{1}{2}(6)(4) = 12$ J.

37. Determine the kinetic energy change if velocity triples.

    Increases by a factor of 9. Tripling velocity increases $KE$ by $(3)^2 = 9$ times.

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