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1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

13. Rotational Inertia & Energy

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

18. Waves & Sound

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

36. Special Relativity

[BOOK PHYS] !CLUTCH

A system in which only one particle moves has the potential energy shown in FIGURE EX10.31. What is the x-component of the force on the particle at x = 5, 15, and 25 cm? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/8b5e532b8411e8f7-1678287927359.jpg" alt="" />

A particle moving along the y-axis is in a system with potential energy U = 4y^3 J, where y is in m. What is the -component of the force on the particle at y = 0 m, 1 m, and 2 m?

Potential Energy Graph of a Marble

Force & Potential Energy

Computing force from a potential energy function (calculus based physics)

Calculating Force From Potential Energy

A system has potential energy U(x)=(10 J)[1−sin((3.14 rad/m) x)] as a particle moves over the range 0 m≤x≤3 m 
b. For each, is it a point of stable or unstable equilibrium?

FIGURE EX10.24 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle's speeds at B, C, and D? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/27c5f3fef93e7ccb-1678293647185.jpg" alt="" />

Force and Potential Energy Example | Physics with Professor Matt Anderson | M10-09

FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. (a) Where are the particle's turning points? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/4b3632aa3b407fe8-1679584932185.jpg" alt="" />

CALC A particle that can move along the x -axis is part of a system with potential energy 
U(x)= A/x2 − B/x where A and B are positive constants.
a. Where are the particle's equilibrium positions?

Forces & Equilibrium Positions

A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is (delta)U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?

Anderson Video - Force and Potential Energy Example

In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/5ea31309c5c9313c-1678288518927.jpg" alt="" />

FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0m. (b) What is the particle's maximum speed? At what position does it have this speed? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/50e57a0aac43e0c6-1678292631358.jpg" alt="" />

A particle with a mass of 0.1kg moves according to the Potential Energy graph shown. What minimum speed does the particle need at Point A to reach Point B?<img src="https://cdn.clutchprep.com/problem_images/238340-d957f37d492ee91e.png" alt="" />

CALC A clever engineer designs a 'sprong' that obeys the force law Fx=−q(x−xeq)³ , where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we'll let xeq=0 m .Then Fx=−qx³.
b. Find an expression for the potential energy of a stretched or compressed sprong.

25.1 Force is the Derivative of Potential

Potential energy function and equilibria starting from a force function.

Potential Energy Graphs

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