Physics, 19.11.2019 05:31 angie249

Amass executes shm at the end of a light spring. (a) what fraction of the total energy of the system is potential and what fraction is kinetic at the instant when the displacement of the mass is equal to half the amplitude? (b) if the maximum amplitude of the oscillations is doubled, what will be the change in (i) the total energy of the system, (ii) the maximum velocity of the mass and (iii) the maximum acceleration of the mass. will the period of oscillation change?

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Answer from: jay5902

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Explanation:

A) The total energy of the system is defined by the energy at maximum amplitude, which we'll call A. At that point, the energy of the system is

E = 1/2×m×A^2;

since energy is conserved, this is also the total amount of energy that the system ever has.

So at x=1/2A,

the potential energy of the system is 1/8×m×A^2

which is one-fourth of the system's total energy. Therefore, the remaining three-fourths is kinetic.

B) (i) Doubling the maximum amplitude will quadruple the total energy:

$E= \frac{1}{2}m(2A)^2$

(ii) Doubling the maximum amplitude will double the maximum velocity

$\frac{1}{2}m(2A)^2= \frac{1}{2}mV^2$

(iii) Doubling the maximum amplitude will double the maximum acceleration: m×a = -k(2A)

(iv) Doubling the maximum amplitude leaves the period unchanged:

$T= 2\pi\sqrt{\frac{m}{k} }$

(neither m nor k has changed).

Answer from: Quest

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

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Amass executes shm at the end of a light spring. (a) what fraction of the total energy of the system...