Physics, 04.08.2019 14:00 emocow

As a pendulum moves closer to the equilibrium position, how do the velocity, acceleration, and force change? a. the velocity decreases, the acceleration decreases, and the net force decreases. b. the velocity increases, the acceleration decreases, and the net force decreases. c. the velocity increases, the acceleration increases, and the net force decreases. d. the velocity decreases, the acceleration increases, and the net force increases.

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Answer from: bob7220

B. The velocity increases, the acceleration decreases, and the net force decreases.

Explanation:

- Velocity: as the pendulum moves closer to the equilibrium position, its gravitational potential energy decreases (because the height decreases), and therefore for the law of conservation of energy, the kinetic energy increases. But the kinetic energy is proportional to the square of the velocity:

$K=\frac{1}{2}mv^2$

So, this means that the velocity increases as well.

- Acceleration: the acceleration of the pendulum is equal to the horizontal component of the gravitational acceleration, given by:

$a=g sin \theta$

where g=9.8 m/s^2 and $\theta$ is the angle the pendulum forms with the vertical. As the pendulum approaches the equilibrium position, $\theta$ becomes smaller, therefore the acceleration decreases.

- Net force: the net force is the force acting on the horizontal direction, i.e. the horizontal component of the weight :

$F=mg sin \theta$

where m is the mass of the pendulum. As the pendulum approaches the equilibrium position, $\theta$ becomes smaller, therefore the net force decreases.

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

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As a pendulum moves closer to the equilibrium position, how do the velocity, acceleration, and force...

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