Dynamics of Engineering Systems $\backslash$Friction Tutorial Assignment $-$ Pulley with variable masses

Pulley Friction Tutorial Assignment $-$ Pulley with variable masses

A $40$ kg mass rests on an inclined plane. The $40$ kg mass is attached to a hanger where masses

can be added. When a mass of $25$ kg is placed on the hanger, the direction of the impending

motion of the $40$ kg mass is up the inclined plane and when a mass of $15$ kg is placed on the

hanger, the direction of the impending motion of the $40$ kg mass is down the inclined plane.

If the coefficient of friction between the pulley wheel and the cable connecting the mass $40$ kg

mass to the hanger $($with the added masses$)$ is $0\mathrm{.}23$ and the angle of lap of the cable around the

pulley wheel is $135^($@$),$ determine the angle, alpha, of the inclined plane to the horizontal and the co$-$

efficient of friction mu$\_($p$)$ between the $40$ kg mass and the surface of the inclined plane.

Information

For a pulley wheel with a frictional effect, T$\_(2)=$T$\_(1)$e$^($mu theta$)$