Physics, 15.07.2021 17:20 cat20220

A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (k = 250 N/m) which has its other end fixed. The block passes through the equilibrium position with a speed of 2.6 m/s and first comes to rest at a displacement of 0.20 m from equilibrium. What is the coefficient of kinetic friction between the block and the horizontal surface?

Answers: 2

Show answers

Answers

Suppose the spring begins in a compressed state, so that the block speeds up from rest to 2.6 m/s as it passes through the equilibrium point, and so that when it first comes to a stop, the spring is stretched 0.20 m.

There are two forces performing work on the block: the restoring force of the spring and kinetic friction.

By the work-energy theorem, the total work done on the block between the equilbrium point and the 0.20 m mark is equal to the block's change in kinetic energy:

$W_{\rm total}=\Delta K$

$W_{\rm friction}+W_{\rm spring}=0-K=-K$

where K is the block's kinetic energy at the equilibrium point,

$K=\dfrac12\left(2.0\,\mathrm{kg}\right)\left(2.6\dfrac{\rm m}{\rm s}\right)^2=6.76\,\mathrm J$

Both the work done by the spring and by friction are negative because these forces point in the direction opposite the block's displacement. The work done by the spring on the block as it reaches the 0.20 m mark is

$W_{\rm spring}=-\dfrac12\left(250\dfrac{\rm N}{\rm m}\right)(0.20\,\mathrm m)^2=-5.00\,\mathrm J$

Compute the work performed by friction:

$W_{\rm friction}-5.00\,\mathrm J=-6.76\,\mathrm J \implies W_{\rm friction}=-1.76\,\mathrm J$

By Newton's second law, the net vertical force on the block is

∑ F = n - mg = 0 ==> n = mg

where n is the magnitude of the normal force from the surface pushing up on the block. Then if f is the magnitude of kinetic friction, we have f = µmg, where µ is the coefficient of kinetic friction.

So we have

$W_{\rm friction}=-f(0.20\,\mathrm m)$

$\implies -1.76\,\mathrm J=-\mu\left(2.0\,\mathrm{kg}\right)\left(9.8\dfrac{\rm m}{\mathrm s^2}\right)(0.20\,\mathrm m)$

$\implies \boxed{\mu\approx0.45}$

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

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000

Another question on Physics

Physics, 21.06.2019 16:20

Luke and carrie are driving down a straight section of the interstate at 70 mph in luke's new convertible. carrie is drinking a soda in the passenger seat. when she is done she tosses the bottle straight up in the air, just above the height of the car. what will happen to the bottle if air resistance is neglected? a. the bottle will land in carrie's lap. b. not enough information is given. c. the bottle will land on the interstate in front of the car. d. the bottle will land on the interstate behind the car.

Answers: 1

Answer

Physics, 22.06.2019 06:30

What are similarities and differences between refraction, reflection, diffraction and absorption?

Answers: 3

Answer

Physics, 23.06.2019 00:10

An astronaut floating in space is trying to use her jetpack to get back to her space station, but she is being pulled away by a nearby planet, as shown in the image below. her jetpack provides a constant thrust of 310 n. if she angles her jetpack in such a way that it cancels out the vertical force due to the planet's gravity, what is her net horizontal force? thaud 487 o a. 54.8 n toward the space station o b. 212.9 n toward the space station o c. 185.2 n toward the space station o d 956 n toward the space station

Answers: 1

Answer

Physics, 23.06.2019 02:00

How many electrons does each element require in its valence shell to become stable?

Answers: 1

Answer

You know the right answer?

A 2.0-kg block sliding on a rough horizontal surface is attached to one end of a horizontal spring (...

Questions