Change in Momentum and Impulse - AP Physics C Mechanics

1. Express impulse in terms of integral calculus.

   $J = \int_{t_1}^{t_2} F : dt$. Impulse as integral of force over time.

2. What is the relationship between force and impulse?

   Impulse equals force times time: $J = F \triangle t$. Force applied over time produces impulse.

3. What property of momentum makes it a vector quantity?

   Direction along with magnitude. Vectors have both magnitude and direction.

4. Name two factors affecting impulse.

   Force magnitude and duration of force application. Greater force or longer time increases impulse.

5. Calculate final velocity if $m = 2 \, kg$, $p = 8 \, kg \cdot m/s$.

   $v = 4 \, m/s$. Using $v = \frac{p}{m} = \frac{8}{2}$.

6. Explain the relationship between impulse and momentum in collisions.

   Impulse causes a change in momentum during collisions. Impulse transfers momentum between colliding objects.

7. What is the formula for average force in terms of impulse?

   $F_{avg} = \frac{J}{\triangle t}$. Average force equals impulse divided by time.

8. What does it mean if two objects have equal momentum?

   Product $mv$ is equal for both objects. Same $mv$ product indicates equal momentum.

9. Determine the final velocity if $m = 4 \, kg$, $u = 3 \, m/s$, $J = 20 \, N \cdot s$.

   $v = 8 \, m/s$. Using $v = u + \frac{J}{m} = 3 + \frac{20}{4}$.

10. What is the vector nature of momentum?

    Momentum is a vector; it has both magnitude and direction. Vector quantities have direction and magnitude.

11. What is the formula for change in momentum?

    $\triangle p = m \triangle v$. Change in momentum equals mass times velocity change.

12. Find $\triangle v$ if $J = 25 \, N \cdot s$, $m = 5 \, kg$.

    $\triangle v = 5 \, m/s$. Using $\triangle v = \frac{J}{m} = \frac{25}{5}$.

13. Calculate momentum if $m = 3 \, kg$, $v = 10 \, m/s$.

    $p = 30 \, kg \cdot m/s$. Direct calculation using $p = mv$.

14. What does the area under a force-time graph represent?

    Impulse. Force-time graph area represents total impulse.

15. State the formula relating impulse and velocity change.

    $J = m \triangle v$. Alternative form using $J = \triangle p$.

16. Identify the unit of impulse in the SI system.

    Newton second (N·s). Newton second is equivalent to $kg \cdot m/s$.

17. What is the formula for linear momentum?

    $p = mv$. Product of mass and velocity defines linear momentum.

18. What is the effect of a longer contact time on impulse?

    Increases impulse if force remains constant. Longer contact time increases total impulse.

19. What is the significance of zero net external impulse?

    Momentum is conserved. Zero net impulse means no momentum change.

20. Determine the average force if $J = 40 \, N \cdot s$, $\triangle t = 4 \, s$.

    $F_{avg} = 10 \, N$. Using $F_{avg} = \frac{J}{\triangle t} = \frac{40}{4}$.

21. What is the result of an impulse acting on a stationary object?

    The object gains momentum. Impulse gives initially stationary object momentum.

22. What is the relationship between momentum and kinetic energy?

    Momentum depends on velocity, kinetic energy depends on velocity squared. Different velocity dependencies distinguish the quantities.

23. How is impulse related to change in momentum?

    Impulse equals change in momentum: $J = \triangle p$. The impulse-momentum theorem connects force and motion.

24. Find the impulse given $F = 10 \, N$ and $\triangle t = 2 \, s$.

    $J = 20 \, N \cdot s$. Using $J = F \triangle t = 10 \times 2$.

25. What changes when an object experiences impulse?

    Its momentum changes. Impulse directly changes object's momentum.

26. Find the impulse given force graph is a rectangle with $F = 6 \, N$, $t = 5 \, s$.

    $J = 30 \, N \cdot s$. Rectangle area equals base times height.

27. Calculate impulse for $F = 5 \, N$, $t = 3 \, s$.

    $J = 15 \, N \cdot s$. Direct application of $J = F \triangle t$.

28. What is the impulse-momentum theorem?

    Impulse on an object equals its change in momentum. Connects impulse directly to momentum change.

29. Define impulse in terms of force and time.

    $J = F \times \triangle t$. Impulse is force multiplied by time interval.

30. Calculate momentum for $m = 5 \, kg$ and $v = 3 \, m/s$.

    $p = 15 \, kg \cdot m/s$. Using $p = mv = 5 \times 3$.

31. Determine the velocity change for $J = 16 \, N \cdot s$, $m = 4 \, kg$.

    $\triangle v = 4 \, m/s$. Using $\triangle v = \frac{J}{m} = \frac{16}{4}$.

32. Calculate $\triangle p$ if $m = 10 \, kg$, $v_i = 2 \, m/s$, $v_f = 5 \, m/s$.

    $\triangle p = 30 \, kg \cdot m/s$. Using $\triangle p = m(v_f - v_i) = 10(5-2)$.

33. What is the SI unit for momentum?

    Kilogram meter per second (kg·m/s). Momentum units combine mass (kg) and velocity (m/s).

34. Calculate change in momentum if $F = 12 \, N$, $\triangle t = 3 \, s$.

    $\triangle p = 36 \, kg \cdot m/s$. Using impulse-momentum theorem $\triangle p = J$.

35. Identify the change in velocity if $F = 10 \, N$, $\triangle t = 2 \, s$, $m = 2 \, kg$.

    $\triangle v = 10 \, m/s$. Using $\triangle v = \frac{F \triangle t}{m} = \frac{10 \times 2}{2}$.

36. State the principle of conservation of momentum.

    Total momentum before collision = Total momentum after collision. Momentum is conserved in isolated systems.

37. What does a negative impulse signify?

    A decrease in momentum. Negative impulse reduces object's momentum.

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