ME$3301$ Dynamics $-$ Fall $2020$

$2$

Problem $1[20$ points$]$

Figure Q$1$ shows a gear box is attached to a shaft $F$ is used to lift a weight $W.$ The input power is supplied to the shaft carrying gear $A.$ The input shaft starts rotating from rest with a constant angular acceleration of ${}_A=5ra\frac{d}{s^2}.$ It operates for a shorter duration where the weight $W$ will reach a velocity of $0\mathrm{.}3\frac{m}{s}.$

$($a$)$ Calculate the time taken to achieve this speed.

$($b$)$ Calculate the number of revolutions made by the shaft $F$ and the corresponding distance travelled by the weight $W.$

The pitch circle radii of the gears are; $r_A=30mm,r_B=100mm,r_C=40mm$ and $r_D=210mm.$