Analyze Force Interactions Using Data - Physics

1. What is the formula for spring force magnitude using Hooke's law?

   $F_s = kx$. Hooke's law: spring force is proportional to displacement.

2. What is the momentum formula for an object of mass $m$ moving at speed $v$?

   $p=mv$. Momentum is the product of mass and velocity.

3. What is the formula for centripetal net force in uniform circular motion?

   $F_c = \frac{mv^2}{r}$. Apply $F=ma$ with centripetal acceleration $a_c=\frac{v^2}{r}$.

4. What deck type best fits analyzing force interactions using data (recall, application, or both)?

   both. This skill requires memorizing formulas and applying them to solve problems.

5. Identify the impulse if a constant net force of $6\,\text{N}$ acts for $0.50\,\text{s}$.

   $3.0\,\text{N}\cdot\text{s}$. Using $J=F_{net}\Delta t=6\times 0.50=3.0\,\text{N}\cdot\text{s}$.

6. What is the formula relating net force, mass, and acceleration (Newton's 2nd law)?

   $\sum F = ma$. Newton's second law states net force equals mass times acceleration.

7. Identify the acceleration if $F_{net}=18\,\text{N}$ and $m=6\,\text{kg}$ in the same direction.

   $3\,\text{m/s}^2$. Using $a=\frac{F_{net}}{m}=\frac{18}{6}=3\,\text{m/s}^2$.

8. What is the maximum possible static friction force magnitude before slipping begins?

   $f_s\le \mu_s N$. Static friction can vary up to coefficient times normal force.

9. What is the magnitude of the friction force for kinetic friction on a level surface?

   $f_k=\mu_k N$. Kinetic friction equals coefficient times normal force.

10. Identify the normal force on a $10\,\text{kg}$ object resting on a level surface (no other vertical forces).

    $N=mg=98\,\text{N}$. Normal force balances weight when at rest on level surface.

11. Identify the centripetal force if $m=0.50\ \text{kg}$, $v=6\ \text{m}\cdot\text{s}^{-1}$, and $r=3\ \text{m}$.

    $6\ \text{N}$. Apply $F_c=\frac{mv^2}{r}$: $F_c=\frac{0.50\times6^2}{3}=\frac{18}{3}=6$.

12. Identify $f_k$ if $\mu_k=0.20$ and $N=50\,\text{N}$.

    $10\,\text{N}$. Using $f_k=\mu_k N=0.20\times 50=10\,\text{N}$.

13. Identify $f_{s,max}$ if $\mu_s=0.40$ and $N=30\,\text{N}$.

    $12\,\text{N}$. Using $f_{s,max}=\mu_s N=0.40\times 30=12\,\text{N}$.

14. Identify the average net force if momentum changes by $4.0\,\text{kg}\cdot\text{m/s}$ in $0.20\,\text{s}$.

    $20\,\text{N}$. Using $F_{avg}=\frac{\Delta p}{\Delta t}=\frac{4.0}{0.20}=20\,\text{N}$.

15. Identify the weight of a $3.0\,\text{kg}$ object using $g=9.8\,\text{m/s}^2$.

    $29.4\,\text{N}$. Using $W=mg=3.0\times 9.8=29.4\,\text{N}$.

16. What is the action-reaction rule for forces between two interacting objects?

    Forces are equal in magnitude and opposite in direction. Newton's third law: every action has an equal and opposite reaction.

17. Identify $f_k$ if $\mu_k=0.20$ and $N=50\ \text{N}$.

    $10\ \text{N}$. Apply $f_k=\mu_k N$: $f_k=0.20\times50=10\ \text{N}$.

18. Identify the net force if a $2.0\,\text{kg}$ cart accelerates at $4.0\,\text{m/s}^2$.

    $8.0\,\text{N}$. Using $F_{net}=ma=2.0\times 4.0=8.0\,\text{N}$.

19. Identify the spring constant $k$ if $F=20\ \text{N}$ stretches a spring by $x=0.50\ \text{m}$.

    $40\ \text{N}\cdot\text{m}^{-1}$. Rearrange Hooke's law: $k=\frac{F}{x}=\frac{20}{0.50}=40$.

20. Identify the spring force magnitude if $k=200\,\text{N/m}$ and $x=0.15\,\text{m}$.

    $30\,\text{N}$. Using $F_s=kx=200\times 0.15=30\,\text{N}$.

21. Identify $f_s^{\max}$ if $\mu_s=0.40$ and $N=30\ \text{N}$.

    $12\ \text{N}$. Apply $f_s^{\max}=\mu_s N$: $f_s^{\max}=0.40\times30=12\ \text{N}$.

22. What is the formula for centripetal acceleration for uniform circular motion?

    $a_c = \frac{v^2}{r}$. Velocity squared divided by radius gives centripetal acceleration.

23. Identify the centripetal acceleration if $v=4\ \text{m}\cdot\text{s}^{-1}$ and $r=2\ \text{m}$.

    $8\ \text{m}\cdot\text{s}^{-2}$. Apply $a_c=\frac{v^2}{r}$: $a_c=\frac{4^2}{2}=\frac{16}{2}=8$.

24. Identify the net force when forces of $12\,\text{N}$ right and $5\,\text{N}$ left act on an object.

    $7\,\text{N}$ to the right. Net force is the vector sum: $12-5=7\,\text{N}$ rightward.

25. What is the formula for static friction magnitude when it is at its maximum value?

    $f_s^{\max} = \mu_s N$. Maximum static friction equals coefficient times normal force.

26. What is the SI unit of force expressed in base units?

    $1\ \text{N} = 1\ \text{kg}\cdot\text{m}\cdot\text{s}^{-2}$. Newton is derived from $F=ma$, giving kilogram-meter per second squared.

27. What is the spring force magnitude formula (Hooke's law) for displacement $x$?

    $F_s=kx$. Spring force is proportional to displacement from equilibrium.

28. What is the impulse-momentum relation for constant net force over time interval $\Delta t$?

    $J=F_{net}\Delta t=\Delta p$. Impulse equals force times time, which equals momentum change.

29. What is the formula for kinetic friction magnitude for a sliding object?

    $f_k = \mu_k N$. Kinetic friction equals kinetic coefficient times normal force.

30. What is the weight (gravitational force) formula for an object of mass $m$ near Earth?

    $W=mg$. Weight equals mass times gravitational acceleration ($g=9.8\,\text{m/s}^2$).

31. Identify the acceleration if $\sum F=10\ \text{N}$ and $m=2\ \text{kg}$.

    $5\ \text{m}\cdot\text{s}^{-2}$. Rearrange $F=ma$ to get $a=\frac{F}{m}=\frac{10}{2}=5$.

32. What is the formula for weight near Earth's surface in terms of mass and $g$?

    $W = mg$. Weight is gravitational force, calculated as mass times gravitational acceleration.

33. What is the formula for gravitational force between two masses separated by distance $r$?

    $F_g = G\frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation with inverse square dependence.

34. What is the formula relating net force, mass, and acceleration in one dimension?

    $F_{net}=ma$. Newton's second law relates force to mass times acceleration.

35. Identify the mass if $\sum F=12\ \text{N}$ and $a=3\ \text{m}\cdot\text{s}^{-2}$.

    $4\ \text{kg}$. Rearrange $F=ma$ to get $m=\frac{F}{a}=\frac{12}{3}=4$.

36. Identify the mass if $F_{net}=15\,\text{N}$ produces $a=3.0\,\text{m/s}^2$.

    $5.0\,\text{kg}$. Using $m=\frac{F_{net}}{a}=\frac{15}{3.0}=5.0\,\text{kg}$.

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