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0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

25. Electric Potential

Work From Electric Force

Physics

25. Electric Potential

Work From Electric Force

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Problem 45

Textbook Question

An arrangement of source charges produces the electric potential V=5000x² along the x-axis, where V is in volts and x is in meters. What is the maximum speed of a 1.0 g, 10 nC charged particle that moves in this potential with turning points at ±8.0 cm?

Verified step by step guidance

Identify the given quantities: The electric potential is given as \( V = 5000x^2 \) (in volts), the charge of the particle is \( q = 10 \text{ nC} = 10 \times 10^{-9} \text{ C} \), the mass of the particle is \( m = 1.0 \text{ g} = 0.001 \text{ kg} \), and the turning points are at \( x = \pm 0.08 \text{ m} \).

Understand the relationship between electric potential energy and kinetic energy: The total mechanical energy of the particle is conserved. At the turning points, the particle's kinetic energy is zero, and all the energy is stored as electric potential energy. The maximum speed occurs when all the potential energy difference is converted into kinetic energy.

Write the expression for the electric potential energy: The electric potential energy \( U \) is given by \( U = qV \). Substituting \( V = 5000x^2 \), we get \( U = q \cdot 5000x^2 \).

Determine the change in potential energy between the turning points and the origin: At the turning points \( x = \pm 0.08 \text{ m} \), the potential energy is \( U_{\text{turning}} = q \cdot 5000 \cdot (0.08)^2 \). At the origin \( x = 0 \), the potential energy is \( U_{\text{origin}} = q \cdot 5000 \cdot 0^2 = 0 \). The change in potential energy is \( \Delta U = U_{\text{turning}} - U_{\text{origin}} = q \cdot 5000 \cdot (0.08)^2 \).

Use energy conservation to find the maximum speed: The change in potential energy \( \Delta U \) is equal to the maximum kinetic energy \( K_{\text{max}} \). Kinetic energy is given by \( K = \frac{1}{2}mv^2 \). Set \( \Delta U = \frac{1}{2}mv_{\text{max}}^2 \) and solve for \( v_{\text{max}} \): \( v_{\text{max}} = \sqrt{\frac{2 \cdot \Delta U}{m}} \). Substitute \( \Delta U = q \cdot 5000 \cdot (0.08)^2 \) and \( m = 0.001 \text{ kg} \) to find \( v_{\text{max}} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Potential

Electric potential (V) is the amount of electric potential energy per unit charge at a point in an electric field. It is measured in volts (V) and indicates how much work would be done to move a charge from a reference point to a specific point in the field. In this question, the potential is given as a function of position along the x-axis, which influences the motion of the charged particle.

Conservation of Energy

The principle of conservation of energy states that the total energy in a closed system remains constant. For a charged particle in an electric potential, the total mechanical energy is the sum of its kinetic energy and electric potential energy. As the particle moves through the potential, its speed will vary, but the total energy will remain constant, allowing us to calculate its maximum speed at turning points.

Kinetic Energy

Kinetic energy (KE) is the energy that an object possesses due to its motion, calculated using the formula KE = 0.5mv^2, where m is the mass and v is the velocity of the object. In this scenario, the kinetic energy of the charged particle will be at its maximum when it is at the turning points, where the electric potential energy is at its minimum, allowing us to determine the maximum speed of the particle.

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Textbook Question

(II) A + 25 μC point charge is placed 6.0 cm from an identical +25 μC point charge. How much work would be required by an external force to move a +0.15 μC test charge from a point midway between them to a point 1.0 cm closer to either of the charges?

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Textbook Question

In an older television tube (CRT), electrons are accelerated by thousands of volts through a vacuum. If such a television set is laid on its back, would electrons be able to move upward against the force of gravity? What potential difference, acting over a distance of 2.4 cm, would be needed to balance the downward force of gravity so that an electron would remain stationary? Assume that the electric field is uniform.

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Textbook Question

A parallel-plate capacitor with a 1.0 mm plate separation is charged to 75 V. With what kinetic energy, in eV, must a proton be launched from the negative plate if it is just barely able to reach the positive plate?

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Textbook Question

A proton's speed as it passes point 1 is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton's speed at point 2?

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Textbook Question

The luminous efficiency of a lightbulb is the ratio of luminous flux to electric power input.

(a) What is the luminous efficiency of a 100-W, 1600-lm bulb?

(b) How many 40-W, 60-lm/W fluorescent lamps would be needed to provide an illuminance of 250 lm/m² on a factory floor of area 22 m x 30 m? Assume the lights are 10 m above the floor and that half their flux reaches the floor.

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Multiple Choice

An electron moves from point A to point B. The potential difference between these two points is 100 V. What is

a. the point of higher potential?

b. the work done on the electron?

c. the final speed of the electron if its initial speed is zero?

What work is needed to assemble an equilateral triangle of side length 5 cm, with a 5µC charge at each vertex?