Answer
(a) M = 540 kg
(b) T = 662 N
Work Step by Step
(a) We can set up a torque equation for the wheel.
$\tau = I\alpha$
$T~R = (\frac{1}{2}MR^2)(\frac{a}{R})$
$T = \frac{1}{2}Ma$
We can use this expression in the force equation for the person. Let $m$ be the mass of the person.
$\sum F = ma$
$mg-T = ma$
$T = mg - ma$
$\frac{1}{2}Ma = mg - ma$
$M = \frac{2mg}{a} - 2m$
$M = \frac{2mg}{(\frac{g}{4})} - 2m$
$M = 6m$
$M = (6)(90.0~kg)$
$M = 540~kg$
(b) We can find the tension in the rope.
$T = \frac{1}{2}Ma$
$T = \frac{1}{2}(540~kg)(\frac{9.80~m/s^2}{4})$
$T = 662~N$
