8.01 Lecture Notes - Lecture 1: Kinetic Energy, Dot Product, Conservative Force

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amethystmuskrat145

13 Apr 2016

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Work done by a constant force: one-dimensional motion: The total work done is equal to the area bonded by the graph of the function f(x) between x and x. Scalar product: a (b + c) = a b + a c. Work done by a constant force: w = f s = | r||f|cos0. The work done by a constant force f on an object is equal to the projection of the force in the direction of the displacement s times the magnitude of the displacement. Work done by force along path from a to b: Then the work done only depends on the location of the point a and b.

Related Questions

1. Can work be done on a system if there is no motion?

A) Yes, if an outside force is provided B) Yes, since motion is only relative C) No, since a system which is not moving has no energy D) No, because of the way work is defined

2. The quantity 1/2 mv 2 is

A) the power supplied to the object by the force B) the work done on the object by the force C) the kinetic energy of the object. D) the potential energy of the object.

3. If you push twice as hard against a stationary brick wall, the amount of work you do

A) doubles. B) is cut in half C) remains constant but non-zero D) remains constant at zero

4. If the net work done on an object is positive, then the object's kinetic energy

A) increases. B) decreases C) remains the same D) is zero

5 A force of 20 N moves an object in the direction of the force. The work done when the object moves from 2.0 to 4.0 m is o A) 20 J OB) 40 J oC) 60 J D) 80 J

whitemosquito79

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.

Consider a damped oscillator with mass m, spring constant k anddamping coefficient b. The oscillator is driven by a force F = F0cos(wt).

(a) If the displacement is given by x = Acos (wt â Î´), what are thevalues of A and Î´ ?

(b) Calculate the energy dissipated in one cycle.

Note that for parts (b) and (c), you should not assume energyconservation. Calculate these directly, using the work done orpower supplied by or dissipated due to the appropriate forces.

8.01 Lecture Notes - Lecture 1: Kinetic Energy, Dot Product, Conservative Force

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