Physics, 03.03.2020 21:32 moinhajra

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 1.00 m and while being driven into rotation around a fixed axis, its angular position is expressed as
θ = 2.50t2 - 0.600t3
where θ is in radians and t is in seconds.
a) Find the maximum angular speed of the roller
b) what is the maximum tangential speed of the point an the rim of the roller?
c) at what time t should the driven force be removed from the roller so that the roller does not reverse its direction of rotation?
d) Through how many rotations has the roller turned between t=0 and the time found in part c?

Answers: 1

Show answers

Answers

Answer from: conyabrew82

A) 3.47rad/a

B) 1.47m/s

C) t = 2.78s

D) 5.4 rotation

Explanation:

(a) angular speed w = dθ/dt = 5t - 1.8t^2

dw/dt = 5 - 3.6t = 0 for max w

so max w occurs at t = 5/3.6 s = 1.39s

so w max = 5*1.39 - 1.8*(1.39)^2 = 3.47 rad/s

(b) tangential speed v = r*w

r = D/2 = 0.5m

so v = 0.5*w = 1.74 m/s

so t = 5/1.8s = 2.78s (or t = 0 invalid)

After t = 2.87s, w is negative (starts reversing direction of rotation)

Driving force would actually have to be removed some time before t=2.78s because the roller can't stop instantaneously, but insufficient info to calculate this.

(d) Up to t = 2.78s, θ = 2.5*(2.78)^2 - 0.6*(2.78)^3 rad = 33.95 rad = 5.40 rotations

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

That depends on what kind of environ meant it is in in space it has the same force that was applied when the velocity was gained

Another question on Physics

Physics, 21.06.2019 16:30

As , plants meet their needs for making food from air, soil, water, and the sun's energy in a process called there are plants called grow high in trees without here are words to put in the blanks. 1.) producers 2.) consumers 3.) chloroplasts 4.) epiphytes

Answers: 3

Answer

Physics, 21.06.2019 17:30

The ballistic pendulum was invented in 1742 by english mathematician benjamin robins. it consists of an initially stationary pendulum that moves after being struck by a bullet, and it is used to measure the original velocity of the bullet. the known variables are the bullet's mass m, the pendulum's mass m, and the height to which the block and bullet swing, determined by the length of the pendulum l and final angle θ. two principles of physics are necessary to solve for the bullet's original velocity. what are these principles? conservation of momentum and newton's third law conservation of energy and conservation of angular momentum grade summary deductions 0% potential 100% conservation of momentum and newton's second law. newton's second law and conservation of angular momentum. conservation of energy and newton's third law conservation of momentum and conservation of angular momentum. conservation of momentum and conservation of energy conservation of energy and newton's second law.

Answers: 2

Answer

Physics, 22.06.2019 05:50

Astudent wears sunglasses to her read a book more easily which wave interaction occurs as light passes from the air into the plastic lenses? a polarization b.refraction c.diffraction d. interference

Answers: 1

Answer

Physics, 22.06.2019 12:30

Awheel of mass 48 kg is lifted to a height of 0.8 m. how much gravitational potential energy is added to the wheel? acceleration due to gravity is g = 9.8 m/s2. a. 30.4 j b. 3.1 j c. 297.9 j d. 11,321 j

Answers: 1

Answer

You know the right answer?

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it....

Questions