Physics, 09.03.2020 05:20 AT3P

A 200 kg block is lifted at a constant speed of 0.5 m/s by a steel cable that passes over a massless, frictionless pulley to a motor driven wheel. the radius of the wheel is 30cm

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Answer from: tydendf10

Questions

(a) What is the magnitude of the force exerted by the cable?

(b) What is the magnitude of the torque exerted by the cable on the winch drum?

(d) What power must be developed by the motor to drive the winch drum?

(a) 1962 N

(b) 588.6 N.m

(d) 982.962 W

Explanation:

(a)

Force, F=mg where m is the mass of the block and g is acceleration due to gravity. Taking the value of acceleration due to gravity as 9.81 m/s2 and substituting 200 Kg for mass then the force exerted on the cable will be

F=200*9.81=1962 N

(b)

Torque is a product of force and distance. Since the force is already derived in part (a) above and the radius is given as 30 cm converted to m we have 0.3 m then torque, T= 1962*0.3=588.6 N.m

(c)

Angular velocity= $\frac {v}{r}$ where v is the speed of block and r is the radius of the wheel. Substituting 0.5 m/s for v and 0.3 m for r then the angular velocity will be $\frac {0.5}{0.3}=1.6667\approx 1.67 rads/s$

(d)

Power, P is a product of torque and angular velocity and since torque is already given in part b above as 588.6 N and the angular velocity in part c then power, P= 588.6*1.67=982.962 W

Answer from: Quest

2. they have negligible mass.

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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