Physics, 18.07.2019 12:00 elizaa94

"a force of 40 pounds compresses a 12-inch spring by 3 inches. how much work is done in compressing the spring to a final length of 4 inches? "

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Given force = 40 pounds
Unstretched length of spring= 12 in
initial compression= s₁ =3 in
Now, first we find the spring constant K from the above given conditions;
F=K*s₁
(40)= K*(3)
K= 13.333 pounds/in
Now, the final compression makes the spring length= 4 in so the final compression from the unstretched lenght = s₂=8 in

Work done= 1/2K(s₂)² - 1/2K(s₁)²
=   1/2(13.333)(8)² - 1/2(13.333)(3)²
= 366.58 pounds*in

Answer from: Quest

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.

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.

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