PHYS 2010 Chapter 6.5-6.7: Phys 2010 Week 9

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31 Jul 2017

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Conservative forces - forces such as gravity, for which the work done does not depend on the path taken but only the initial and final positions. Nonconservative forces - forces such as friction and a push or pull exerted by a person, for which the work done does depend on the path. Total mechanical energy - the sum of the kinetic and potential energies. If only conservative forces do work, the total mechanical energy of a system neither increases nor decreases in any process.

Related Questions

Which of the following statement are true mechanical energy? Include all that apply.

1.The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy.

2. Heat is a form of mechanical energy.

3. The mechanical energy of an object is always conserved.

4. When non-conservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved.

5. A bowling ball is mounted from a ceiling by way of a strong cable. It is a drawback and released, allowed to swing as a pendulum. As it swings from its highest position to its lowest position, the total mechanical energy is mostly conserved.

6. When a friction force does work on an object, the total mechanical energy of that object is changed.

7. The total mechanical energy of an object remains constant if the only forces doing work on the object are conservative forces.

8. If an object gains mechanical energy, then one can be certain that a non-conservative force is doing work.

lilacplatypus580

Goal Apply conservation of angular momentum to a simplesystem.

Problem A student sits on a pivoted stool while holding a pair ofweights. (See Figure) The stool is free to rotate about a verticalaxis with negligible friction. The moment of inertia of student,weights, and stool is 2.25 kg Â· m2. The student is set in rotationwith arms outstretched, making one complete turn every 1.26 s, armsoutstretched.

Question If the student suddenly releases the weights, how does hisown angular momentum, rotational kinetic energy, and angular speedchange? (Select all that apply.)

His rotational angular speed decreases.
His rotational angular speed remains the same.
His angular momentum remains the same.
His rotational kinetic energy remains the same.
His angular momentum increases.
His angular momentum decreases.
His rotational angular speed increases.
His rotational kinetic energy increases.
His rotational kinetic energy decreases.

A star with an initial radius of 1.00 108 m and period of 30.0 dayscollapses suddenly to a radius of 1.00 104 m.

(a) Find the period of rotation after collapse.

(b) Find the work done by gravity during the collapse if the massof the star is 2.00 1030 kg.

The only force doing work on the system is gravitation, so the workdone by gravitation is the change in kinetic energy of the star.J

(c) What is the speed of an indestructible person standing on theequator of the collapsed star? (Neglect any relativistic or thermaleffects, and assume the star is spherical before and after itcollapses).

HINTS
* Do you expect the initial angular speed to be larger or smallerthan the final angular speed? How is angular speed related toperiod of rotation?

* Is the initial moment of inertia larger or smaller than the finalmoment of inertia?

* Is angular momentum conserved?

* As the star collapses, do you expect the period of rotation tobecome smaller or larger?

A magnetic field of 0.1T forces a proton beam of 1.5 mA to move ina circle of radius 0.1 m. The plane of the circle is perpendicularto the magnetic field.

47. Of the following, which is the best estimate of the speed of aproton in the beam as it moves in the circle?
(A) 10-2 m/s (B) 103 m/s (C) 106 m/s (D) 108 m/s (E) 1015 m/s

52. An ideal gas is initially in a state that corresponds to point1 on the graph above, where it has presÂ¬sure p1, volume V1, andtemperature T1. The gas undergoes an isothermal process representedby the curve shown, which takes it to a final state 3 attemperature T3. If T2 and T4 are the temperaÂ¬tures the gas wouldhave at points 2 and 4, respecÂ¬tively, which of the followingrelationships is true?
(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 =T4

53. The absolute temperature of a sample of monatomic ideal gas isdoubled at constant volume. What effect, if any, does this have onthe pressure and density of the sample of gas?
Pressure Density
(A) Remains the same Remains the same
(B) Remains the same Doubles
(C) Doubles Remains the same
(D) Doubles Is multiplied by a factor of 4
(E) Is multiplied by a factor of 4 Doubles

62. A sample of an ideal gas is in a tank of constant volume. Thesample absorbs heat energy so that its temperature changes from 300K to 600 K. If v1 is the average speed of the gas molecules beforethe absorption of heat and v2 is their average speed after theabsorption of heat, what is the ratio v2/ v1 ?
(A) 1/2 (B) 1 (C) (D) 2 (E) 4

63. Two people of unequal mass are initially standing still on icewith negligible friction. They then simulÂ¬taneously push each otherhorizontally. Afterward, which of the following is true?
(A) The kinetic energies of the two people are equal.
(B) The speeds of the two people are equal.
(C) The momenta of the two people are of equal magnitude.
(D) The center of mass of the two person system moves in thedirection of the less massive person.
(E) The less massive person has a smaller initial acceleration thanthe more massive person.

64. Two parallel conducting plates, separated by a distance d, areconnected to a battery of emf e. Which of the following is correctif the plate separaÂ¬tion is doubled while the battery remainsconnected?
(A) The electric charge on the plates is doubled.
(B) The electric charge on the plates is halved.
(C) The potential difference between the plates is doubled.
(D) The potential difference between the plates is halved
(E) The capacitance is unchanged.

68. A rod on a horizontal tabletop is pivoted at one end and isfree to rotate without friction about a vertical axis, as shownabove. A force F is applied at the other end, at an angle ? to therod. If F were to be applied perpendicular to the rod, at whatdistance from the axis should it be applied in order to proÂ¬ducethe same torque?
(A) L sin ? (B) L cos ? (C) L (D) L tan ? (E) L

70. A 4 ÂµF capacitor is charged to a potential differÂ¬ence of 100V. The electrical energy stored in the capacitor is
(A) 2 x 10-10 J (B) 2 x 10 8 J (C) 2 x 10 6 J (D) 2x 10-4 J (E) 2 x10-2 J

PHYS 2010 Chapter 6.5-6.7: Phys 2010 Week 9

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