Resistive Forces - AP Physics C Mechanics

1. Find the resistive force on an object with $v = 3 \text{ m/s}$ and $b = 0.1$ in high-speed.

   $F_{\text{drag}} = -0.9 \text{ N}$. Using $F = -bv^2 = -0.1 \times 3^2 = -0.9$ N.

2. Identify the resistive force acting on an object moving through a fluid.

   Drag force. Force opposing motion when objects move through fluids like air or water.

3. Calculate the frictional force with $\text{μ} = 0.3$ and $N = 50 \text{ N}$.

   $f = 15 \text{ N}$. Multiplying coefficient by normal force: $0.3 \times 50 = 15$ N.

4. What happens to net force when an object reaches terminal velocity?

   Net force becomes zero. Balanced forces produce constant terminal velocity.

5. Identify the force type: A car slowing down due to air resistance.

   Drag force. Air resistance opposes vehicle motion through atmosphere.

6. What is the formula for terminal velocity in terms of $b$, $m$, and $g$?

   $v_t = \frac{mg}{b}$. Weight divided by drag coefficient gives terminal velocity.

7. What does the symbol $\text{μ}$ represent in the frictional force formula?

   The coefficient of friction. Dimensionless constant depending on surface materials and conditions.

8. Which force counteracts forward motion in a vehicle?

   Air resistance. Atmospheric resistance opposes vehicle forward motion.

9. Which type of friction generally has a higher coefficient, static or kinetic?

   Static friction. Static friction is typically stronger than kinetic friction.

10. Calculate $v_t$ for $m = 5 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, $b = 0.4$.

    $v_t = 122.5 \text{ m/s}$. Using $v_t = \frac{mg}{b} = \frac{5 \times 9.8}{0.4} = 122.5$ m/s.

11. State the expression for terminal velocity in terms of $mg$ and $b$.

    $v_t = \frac{mg}{b}$. When drag force equals weight, acceleration becomes zero.

12. Find the resistive force on an object with $v = 5 \text{ m/s}$ and $b = 0.2$ in low-speed.

    $F_{\text{drag}} = -1 \text{ N}$. Using $F = -bv = -0.2 \times 5 = -1$ N.

13. State the effect of increased velocity on fluid resistive force.

    Increases resistive force. Higher speeds create proportionally greater fluid resistance.

14. What is the net force if $F_{\text{applied}} = 10 \text{ N}$ and $f = 5 \text{ N}$?

    $F_{\text{net}} = 5 \text{ N}$. Applied force minus opposing friction gives net force.

15. Identify the two types of frictional forces.

    Static friction and kinetic friction. Static prevents motion initiation, kinetic acts during sliding.

16. Which force opposes the motion of a bicycle moving through air?

    Air resistance. Atmospheric drag opposes forward bicycle motion.

17. Find the terminal velocity with $m = 2 \text{ kg}$, $g = 9.8 \text{ m/s}^2$, $b = 0.5$.

    $v_t = 39.2 \text{ m/s}$. Using $v_t = \frac{mg}{b} = \frac{2 \times 9.8}{0.5} = 39.2 \text{ m/s}$

18. State the difference between static and kinetic friction.

    Static friction acts when motion hasn't started, kinetic during motion. Static friction prevents motion, kinetic acts during ongoing motion.

19. At terminal velocity, what is the net force on the object?

    Zero. Balanced forces result in constant velocity motion.

20. Calculate the drag force for $v = 4 \text{ m/s}$ and $b = 0.3$ in low-speed.

    $F_{\text{drag}} = -1.2 \text{ N}$. Using $F = -bv = -0.3 \times 4 = -1.2$ N.

21. What is the formula for resistive force due to air resistance in low-speed conditions?

    $F_{\text{drag}} = -bv$. Linear relationship for low speeds where drag is proportional to velocity.

22. Calculate resistive force for $v = 6 \text{ m/s}$ and $b = 0.2$ in low-speed.

    $F_{\text{drag}} = -1.2 \text{ N}$. Using $F = -bv = -0.2 \times 6 = -1.2$ N.

23. What occurs to resistive forces when an object reaches terminal velocity?

    They equal the gravitational force. Force balance occurs when drag matches gravitational force.

24. State the relationship between resistive force and velocity in high-speed conditions.

    Quadratic relationship. Drag force increases with velocity squared at high speeds.

25. What is the effect of increasing surface roughness on friction?

    Increases friction. Rougher surfaces have higher friction coefficients.

26. Find the normal force if $m = 10 \text{ kg}$ and $g = 9.8 \text{ m/s}^2$ on a flat surface.

    $N = 98 \text{ N}$. Weight equals normal force on horizontal surface.

27. State the formula for resistive force due to a viscous fluid.

    $F_{\text{viscous}} = -bv$. Viscous fluids create linear drag proportional to velocity.

28. What is the formula for resistive force due to air resistance in high-speed conditions?

    $F_{\text{drag}} = -bv^2$. Quadratic relationship for high speeds where drag is proportional to velocity squared.

29. Calculate the frictional force with $\text{μ} = 0.4$ and $N = 100 \text{ N}$.

    $f = 40 \text{ N}$. Multiplying friction coefficient by normal force: $0.4 \times 100 = 40$ N.

30. What is the primary cause of resistive forces in fluids?

    Viscosity and drag. Internal friction in fluids creates resistance to relative motion.

31. Identify the resistive force when an object slides along a surface.

    Frictional force. Surface contact force opposing sliding motion between solid objects.

32. What happens to resistive forces as speed increases?

    Resistive forces increase. Higher velocities create greater fluid resistance.

33. State the formula for the frictional force on a flat surface.

    $f = \mu N$. Product of friction coefficient and normal force.

34. What is the role of mass in determining terminal velocity?

    Higher mass increases terminal velocity. Heavier objects need higher speeds to balance drag with weight.

35. Identify the resistive force in a viscous liquid.

    Viscous drag. Thick liquids create velocity-dependent resistance.

36. What does the coefficient $b$ represent in the resistive force equations?

    The drag coefficient or damping constant. Material and shape-dependent constant that determines drag magnitude.

37. State the direction of the resistive force relative to the velocity vector.

    Opposite to the velocity vector. Resistive forces always oppose motion, creating deceleration.

38. Identify the resistive force in a medium with high viscosity.

    Viscous drag. Thick fluids create velocity-proportional resistance.

39. Identify the resistive force opposing an object sliding down an incline.

    Frictional force. Surface contact creates sliding resistance on inclined planes.

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