Newton's Second Law - AP Physics C Mechanics

1. Determine net force: $m = 4 \text{ kg}$, $a = 5 \text{ m/s}^2$.

   $F = 20 \text{ N}$. Use $F = ma$: $4 \times 5 = 20$ N.

2. Determine the net force: $m = 8 \text{ kg}$, $a = 1.5 \text{ m/s}^2$.

   $F = 12 \text{ N}$. Apply $F = ma$: $8 \times 1.5 = 12$ N.

3. What does $F$ represent in the equation $F = ma$?

   $F$ represents the net force acting on an object. The net or total force causes acceleration in the object.

4. What is the effect on acceleration if both force and mass double?

   Acceleration remains unchanged. From $a = F/m$, the ratio $F/m$ stays constant.

5. Find $F$: $m = 7 \text{ kg}$, $a = 1 \text{ m/s}^2$.

   $F = 7 \text{ N}$. Use $F = ma$: $7 \times 1 = 7$ N.

6. Find acceleration: $F = 32 \text{ N}$, $m = 8 \text{ kg}$.

   $a = 4 \text{ m/s}^2$. Apply $a = F/m$: $32/8 = 4$ m/s².

7. What is the effect on acceleration if force doubles and mass is constant?

   Acceleration doubles. From $a = F/m$, doubling $F$ doubles $a$ when $m$ is constant.

8. Calculate the force: $m = 5 \text{ kg}$, $a = 3 \text{ m/s}^2$.

   $F = 15 \text{ N}$. Apply $F = ma$: $5 \times 3 = 15$ N.

9. Calculate $F$: $m = 3 \text{ kg}$, $a = 4 \text{ m/s}^2$.

   $F = 12 \text{ N}$. Apply $F = ma$: $3 \times 4 = 12$ N.

10. What is the dimension of force in terms of mass, length, and time?

    Force has the dimension $[M][L][T]^{-2}$. Force equals mass times length divided by time squared.

11. Calculate the mass: $F = 50 \text{ N}$, $a = 10 \text{ m/s}^2$.

    $m = 5 \text{ kg}$. Apply $m = F/a$: $50/10 = 5$ kg.

12. Find $a$: $F = 25 \text{ N}$, $m = 5 \text{ kg}$.

    $a = 5 \text{ m/s}^2$. Use $a = F/m$: $25/5 = 5$ m/s².

13. What is the relationship between force and acceleration?

    Force is directly proportional to acceleration. From $F = ma$, doubling force doubles acceleration when mass is constant.

14. Identify the expression for mass from $F = ma$.

    $m = \frac{F}{a}$. Divide both sides of $F = ma$ by acceleration $a$.

15. Identify the expression for acceleration from $F = ma$.

    $a = \frac{F}{m}$. Divide both sides of $F = ma$ by mass $m$.

16. Identify the unit of force in the International System of Units (SI).

    The unit of force is the newton (N). One newton equals one kilogram-meter per second squared.

17. What does $a$ signify in the equation $F = ma$?

    $a$ signifies the acceleration of the object. Acceleration is the rate of change of velocity.

18. If $F = 24 \text{ N}$, $m = 8 \text{ kg}$, find $a$.

    $a = 3 \text{ m/s}^2$. Apply $a = F/m$: $24/8 = 3$ m/s².

19. What is $a$ if force is constant and mass quadruples?

    Acceleration is quartered. From $a = F/m$, quadrupling $m$ divides $a$ by four.

20. Calculate $a$: $F = 60 \text{ N}$, $m = 20 \text{ kg}$.

    $a = 3 \text{ m/s}^2$. Apply $a = F/m$: $60/20 = 3$ m/s².

21. Find $a$: $F = 45 \text{ N}$, $m = 15 \text{ kg}$.

    $a = 3 \text{ m/s}^2$. Use $a = F/m$: $45/15 = 3$ m/s².

22. Find $m$: $F = 10 \text{ N}$, $a = 2 \text{ m/s}^2$.

    $m = 5 \text{ kg}$. Rearrange to $m = F/a$: $10/2 = 5$ kg.

23. Calculate $F$: $m = 9 \text{ kg}$, $a = 2 \text{ m/s}^2$.

    $F = 18 \text{ N}$. Use $F = ma$: $9 \times 2 = 18$ N.

24. Find $F$: $m = 10 \text{ kg}$, $a = 2 \text{ m/s}^2$.

    $F = 20 \text{ N}$. Use $F = ma$: $10 \times 2 = 20$ N.

25. What does $m$ stand for in the formula $F = ma$?

    $m$ stands for the mass of the object. Mass is the object's resistance to acceleration (inertia).

26. Determine $m$: $F = 40 \text{ N}$, $a = 8 \text{ m/s}^2$.

    $m = 5 \text{ kg}$. Use $m = F/a$: $40/8 = 5$ kg.

27. What happens to acceleration if mass doubles and force is constant?

    Acceleration is halved. From $a = F/m$, doubling $m$ halves $a$ when $F$ is constant.

28. Explain the role of mass in Newton's Second Law.

    Mass acts as a measure of an object's inertia. Greater mass means greater resistance to acceleration.

29. Describe the net force in a system at equilibrium.

    The net force is zero. Equilibrium means no net force and no acceleration.

30. If $F = 36 \text{ N}$, $m = 12 \text{ kg}$, find $a$.

    $a = 3 \text{ m/s}^2$. Use $a = F/m$: $36/12 = 3$ m/s².

31. Identify the expression for force from $F = ma$.

    $F = ma$. This is Newton's Second Law in its standard form.

32. If $F = 20 \text{ N}$ and $m = 4 \text{ kg}$, find $a$.

    $a = 5 \text{ m/s}^2$. Rearrange to $a = F/m$: $20/4 = 5$ m/s².

33. State Newton's Second Law of Motion.

    The net force equals mass times acceleration, $F = ma$. This is the fundamental equation relating force, mass, and acceleration.

34. What is the acceleration if net force is zero?

    Acceleration is zero. From $F = ma$, zero force produces zero acceleration.

35. Determine the net force: $m = 6 \text{ kg}$, $a = 3 \text{ m/s}^2$.

    $F = 18 \text{ N}$. Apply $F = ma$: $6 \times 3 = 18$ N.

36. What is force if mass triples and acceleration remains constant?

    Force triples. From $F = ma$, force is proportional to mass when acceleration is constant.

37. Calculate $m$: $F = 30 \text{ N}$, $a = 6 \text{ m/s}^2$.

    $m = 5 \text{ kg}$. Apply $m = F/a$: $30/6 = 5$ kg.

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