Momentum - AP Physics C Mechanics

1. How is impulse related to momentum change?

   Impulse equals the change in momentum. Impulse causes the momentum to change by that amount.

2. Identify the relationship between force and momentum.

   Force is the rate of change of momentum. Newton's second law: $F = \frac{dp}{dt}$.

3. What is the impulse experienced by a stationary object that remains at rest?

   Zero impulse. No force means no impulse on stationary object.

4. How does external force affect momentum?

   It changes momentum. Force causes a change in momentum over time.

5. Find the velocity of a 3 kg object with 15 kg·m/s momentum.

   $v = 5 \text{ m/s}$. From $p = mv$: $v = \frac{p}{m} = \frac{15}{3} = 5$ m/s.

6. Identify the impulse required to stop a 2 kg object moving at 5 m/s.

   $J = -10 \text{ Ns}$. Impulse equals initial momentum: $J = -mv = -2(5) = -10$ Ns.

7. What is the momentum change for a 3 kg object accelerating from 0 to 4 m/s?

   $\triangle p = 12 \text{ kg·m/s}$. $\triangle p = m(v_f - v_i) = 3(4-0) = 12$ kg·m/s.

8. In what type of collision is only momentum conserved?

   Inelastic collision. Kinetic energy is not conserved in inelastic collisions.

9. Calculate the final momentum of a 4 kg object initially moving at 5 m/s, with a 2 m/s increase.

   $p = 28 \text{ kg·m/s}$. $p_f = m(v_i + \triangle v) = 4(5+2) = 28$ kg·m/s.

10. Calculate the momentum of a 5 kg object moving at 3 m/s.

    $p = 15 \text{ kg·m/s}$. Using $p = mv$: $p = 5 \times 3 = 15$ kg·m/s.

11. Determine the momentum of a 10 kg object at rest.

    $p = 0 \text{ kg·m/s}$. Velocity is zero, so $p = mv = 10 \times 0 = 0$.

12. What happens to momentum in a perfectly inelastic collision?

    Momentum is conserved. Total momentum before equals total momentum after.

13. What does an impulse of zero imply about momentum change?

    No change in momentum. Zero impulse means zero change in momentum.

14. What is the effect of external forces on momentum conservation?

    Momentum is not conserved. External forces violate the conservation condition.

15. Determine the final velocity of a 1 kg object with 5 kg·m/s momentum.

    $v = 5 \text{ m/s}$. From $p = mv$: $v = \frac{5}{1} = 5$ m/s.

16. What is the effect of internal forces on a system's total momentum?

    No effect; momentum is conserved. Internal forces are Newton's third law pairs that cancel.

17. Calculate the change in momentum for a 5 kg object accelerating from 2 m/s to 4 m/s.

    $\triangle p = 10 \text{ kg·m/s}$. $\triangle p = m(v_f - v_i) = 5(4-2) = 10$ kg·m/s.

18. What is the symbol for momentum?

    $p$. Standard physics symbol for momentum is $p$.

19. What is the effect of a net external force on a system's momentum?

    Causes momentum to change. Newton's second law in momentum form.

20. What is conserved in an elastic collision?

    Momentum and kinetic energy. Elastic collisions conserve both quantities.

21. Calculate the impulse if a 10 N force is applied for 3 s.

    $J = 30 \text{ Ns}$. $J = F\triangle t = 10 \times 3 = 30$ Ns.

22. State the unit of momentum in the SI system.

    kg·m/s. Mass in kg times velocity in m/s gives kg·m/s.

23. Calculate impulse given a force of 10 N applied for 2 s.

    $J = 20 \text{ Ns}$. Using $J = F\triangle t$: $J = 10 \times 2 = 20$ Ns.

24. Calculate the change in momentum of a 2 kg object from 3 m/s to 5 m/s.

    $\triangle p = 4 \text{ kg·m/s}$. $\triangle p = m(v_f - v_i) = 2(5-3) = 4$ kg·m/s.

25. Describe the momentum of an isolated system.

    Momentum is conserved. No external forces means total momentum stays constant.

26. State the impulse-momentum theorem.

    $J = \triangle p$. Impulse $J$ equals change in momentum $\triangle p$.

27. What is the principle of conservation of momentum?

    Total momentum is constant in an isolated system. No external forces means total momentum stays the same.

28. What happens to the total momentum in a two-object system during collision?

    It remains constant. Conservation of momentum applies during all collisions.

29. What is the momentum of a 0.5 kg ball moving at 10 m/s?

    $p = 5 \text{ kg·m/s}$. $p = mv = 0.5 \times 10 = 5$ kg·m/s.

30. Identify the momentum of an object with mass 0 kg.

    $p = 0 \text{ kg·m/s}$. Zero mass means zero momentum regardless of velocity.

31. Find the momentum of a 6 kg object moving at 7 m/s.

    $p = 42 \text{ kg·m/s}$. $p = mv = 6 \times 7 = 42$ kg·m/s.

32. What is the formula for linear momentum?

    $p = mv$. Momentum equals mass times velocity.

33. Identify the vector nature of momentum.

    Momentum has both magnitude and direction. Velocity is a vector, so momentum is also a vector.

34. Describe momentum in terms of mass and velocity.

    Momentum is product of mass and velocity. Definition of momentum from Newton's laws.

35. Find the impulse given to a 4 kg object slowing from 8 m/s to 2 m/s.

    $J = -24 \text{ Ns}$. $J = m(v_f - v_i) = 4(2-8) = -24$ Ns.

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