PPH$0046$

MECHANICS

TRIMESTER $12023/2024(2310)$

Problem $1$:

Scenario $1$:

A circular grinding disk of diameter $50cm$ and mass $400kg$ is spun by an electric motor to rotate at high speed. When the motor is turned off and the speedometer is recording a constant reading of $100re\frac{v}{m}in.$ When an axe is pressed against the rim of the disk, as shown in Figure P$1$S$1,$ it is found that the speedometer reading drops to $80re\frac{v}{m}in$ in $2\mathrm{.}0s.$ The rotational inertia, I, of the grinding disk is $\frac{1}{2}m{R}^2,$ where $m$ and $R$ are the mass and radius of the disk respectively.

a$)$ Find the net force that causes the drop in the speed of the disk. What type of force that contributed to this net force?

b$)$ How far the axe has been grinded in this $2\mathrm{.}0s?$

c$)$ If this net force were to be constantly and continuously applied, how much longer the disk would be moving until it stopped?

d$)$ The motor is turned on when the operator noticed that the speedometer reading dropped to $80re\frac{v}{m}in.$ With the axe still being grinded, how long it takes for the motor to spin the disk back to the speed of $100re\frac{v}{m}in?$ The motor has a stated constant torque of $16N.m$ for a range of speed up to $300re\frac{v}{m}in.$

e$)$ What would the answer in d$)$ be if the axe is taken away?