Physics, 08.04.2020 01:52 gtjermaine3249

A 2kg ball is attached to a ceiling by a string. The distance from the ceiling to the center of the ball is 1.0m, and the height of the room is 3.0m. What is the potential energy associated with the ball relative to each of the following:
a. the ball relative to the ceiling?
b. the ball relative to the floor?
c. the ball realtive to a point at the same elevation as the ball?

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Answer from: bryanna0105

part(a): The potential energy is $\bf{19.6~J}$ .

part(b): The potential energy is $\bf{39.2~J}$ .

part(c): The potential energy is $\bf{0}$ .

Explanation:

Given:

The mass of the ball, m = 2~Kg .

The distance from the ceiling to the center of the ball, d = 1.0~m

The height of the room, H = 3.0~m .

The potential energy of any particle of mass situated at a height from ground is given by

V = mgh

where is the acceleration due to gravity.

(a) The distance of the ball relative to ceiling is d = 1.0~m . Thus, the potential energy will be

$V &=& (2~Kg)(9.8~m/s^{2})(1.0~m)\\~~~&=& 19.6~J$

(b) The distance of the ball from the ground is h' = (3.0 - 1.0)~m = 2.0~m

Thus, the potential energy will be

$V = (2~Kg)(9.8~m/s^{2})(2.0~m)\\~~~= 39.2~J$

Thus, the potential energy will be

$V = (2~Kg)(9.8~m/s^{2})(0~m)\\~~~= 0$

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

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

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