Physics, 24.03.2020 17:03 alejandramirand9836

A box of books weighing 325N moves at a constant velocity across the floor when the box is pushed with a force of 425 N exerted downward at a angle of 35.2 degrees below the horizontal. Find the coefficient of kinetic friction between the box and the floor

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Answer from: aaayymm

The coefficient of kinetic friction is 0.61

Explanation:A state of constant velocity connotes an acceleration equal to zero {this is evident from Acceleration=(final velocity-initial velocity)/time}

Consequently,a balanced forces system is attained

Force of pulling

F(x)=F×cosα=425N×0.817=347N

is equivalent to the resistance force.

F=U(k)×(Fw+Fsinα)=U(k)×(325N+425N×0,576)=U(k)×570N

Note; U(k) is the coefficient of kinetic friction

Equating the two force components,

The coefficient of static friction ×570N= 347N

The coefficient of static friction = 347N/570N

The coefficient of static friction =0.61

Please note that the coefficient of static friction is dimensionless .

This is as a result of the same unit of forces whose division resulted in the determination of the coefficient of kinetic friction.

Answer from: Quest

what is the actual question though?

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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