HW $25$

CE $250/260$

$(60$ pts $)$ A $50-kg$ wheel with a diameter of $1\mathrm{.}5$ m has a moment of $75N-m$ applied at its center, causing it to roll along a surface with ${}_s=0\mathrm{.}35$ and ${}_k=0\mathrm{.}29.$

a$.$ Determine the acceleration of the center of gravity G $,$ as well as the angular velocity and the displacement of G after $20$ seconds. Assume the wheel starts from rest.

b$.$ What is the maximum moment M that can be applied to the wheel without causing slip?

$(40$ pts$)$ A group of friends are attempting to move a sofa with a weight of $90$ lb $.$ Starting from rest, the friends lift the sofa with the forces shown. Assume the mass is uniformly distributed and model the sofa as a slender rod.

a$.$ Determine the magnitude of acceleration of the center of gravity of the sofa as well as the angular acceleration of the sofa at this instant.

b$.$ Determine the magnitude of the acceleration for a point on the right side of the sofa at a time $t=0\mathrm{.}2$ seconds after the forces start to be applied. Assume the $$ found in part a remains constant. Please let an expert or a professional solve and not ai