PHYS201 Lecture Notes - Lecture 9: Conservative Force, Mechanical Energy, Gravitational Energy

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greenhippopotamus619

2 Nov 2016

School

University of Delaware

Department

Physics and Astronomy

Course

PHYS201

Professor

Gogoladze Ilia

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Document Summary

The work it does is stored in the form of energy that can be released at a later time. Work done cannot be recovered later as kinetic energy; instead, it is converted to other forms of energy. A force that does zero total work on any closed path. Work done by friction on a closed path is not zero. Work done by gravity on a closed path is zero: =(cid:1832) (cid:1856) =(cid:1832)(cid:1856)(cid:1855, =(cid:1832) (cid:1856) =(cid:1832)(cid:1856)(cid:1855) The force is conservative if the work done by a force in going from an arbitrary point a to an arbitrary point b is independent of the path from a to b. Energy is the capacity of a physical system to perform work. Energy is a property of objects transferable among them via interaction. Potential energy is defined as stored energy due to position, shape, or state. In its stored state, energy has the potential for doing work.

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

A 270 g block is dropped onto a relaxed vertical spring that has aspring constant of k = 2.1 N/cm. The block becomes attached to thespring and compresses the spring 11 cm before momentarilystopping.
(a) While the spring is being compressed, what work is done on theblock by the gravitational force on it?
1Your answer is correct. J

(b) What work is done on the block by the spring force while thespring is being compressed?
2Your answer is incorrect. J

(c) What is the speed of the block just before it hits the spring?(Assume that friction is negligible.)
3Your answer is incorrect. m/s

(d) If the speed at impact is doubled, what is the maximumcompression of the spring?
4 m

Work done by a constant force is the dot product of the force andthe displacement. Work done by a variable force is calculated withan integral. The net work done on an object is equal to the changein the object's kinetic energy. If the object stops, its kineticenergy is zero.

Some Problems on Work
1. Joe is pulling a box of mass m = 10 kg up an inclined surface (?= 30degrees) using
a rope. The coefficient of kinetic friction between the surface andthe box is
Âµk = 0.5. It takes 10 seconds for Joe to bring up a box at aconstant velocity
V = 0.8m=s.
(a) What is the tension of the rope?
(b) What is the work done by the tension?
(c) What is the work done by the normal force?
(d) What is the work done by gravity?
(e) What is the total work done on the box?
(f) What is the power output necessary to Joe to bring up thebox?
maximal compression of the spring?
2. A block (m=50 kg) slides down a 3 m long inclined surface (? =30). The
coefficient of kinetic friction between the block and the surfaceis Âµk = 0.3.
Calculate the nal velocity of the block using the work-energytheorem.
3. A pendulum of length l and mass m is released from rest at anangle ? from
the equilibrium position.
(a) Neglect air friction. Calculate the velocity of the pendulumwhen the angle
is zero. Express your result in terms of ?, l, and m.
(b) Suppose ? = 60 degrees and l = 1 m. Suppose that the velocityof the pendulum
when the angle is zero is 1 m/s. Calculate the work done by the airfriction.
4. A point particle of mass m = 20 g is moving on a
at
surface when it reaches a slope which brigs it up by h = 08 m. Thespeed of
the particle in position A is v = 5 m/s.
(a) Suppose that there is no friction. What is the velocity of theparticle when
it reaches position B?
(b) Suppose that there is friction, and that the velocity of theparticle in B is
0. What is the work done by the friction from A to B?
5. A ball is shoot vertically with initial speed v, from a
table of height h.
(a) Calculate the maximal height ymax that the ball can reach (b)Calculate the velocity of the ball just before it hits thefloor.

PHYS201 Lecture Notes - Lecture 9: Conservative Force, Mechanical Energy, Gravitational Energy

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