Each of the bodies shown is homogeneous and has a mass of 30 kg. Assume friction at all contact surfaces. Draw the fully dimensioned FBD for each body and determine the number of unknowns.

The 50-kg homogeneous smooth sphere rests on the 30° incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. B 30° | A

The 60 kg two-wheeled cart is described in the figure and parameter table below, with G indicating the location of the center of gravity. It is to be pulled so that it goes up the small step. Find the normal force on each wheel, and the magnitude and direction of the force applied at handle. HINT: remember that there are two wheels sharing the load @080 BY NO SA 2021 Cathy Zupke 4₁1 G L₁ L₂ parameter value 0.6 0.5 0.8 0.7 0.2 A L3 LA d L3 units m m m m m B L₂ F For the answers, take to the right and up to be the positive directions. The normal force at each wheel at A in the x direction is Ax= 150 XN The magnitude of the force at B is F Measured from the positive horizontal axis, the angle of F= 45 X° = 212 XN

A uniform ladder of length 12 mand mass 30 kg rests with one ed on rough horizontal ground and the other end against a smooth vertical wall. The ladder is indined 65°. The coefficient of friction, H, between the ladder and the ground is 0.35. A woman of mass 65 kg is slowly dimbing up the ladder. She wants to know how far up the ladder she can dimb safely. Drawa diagramshowing all the force adting on the ladder when the woman is x metres fromthe foot of the ladder. (a) (b) Find the reaction of the ground on the ladder. (c) Show that the reaction of the wall on the ladder is less than 33.25g By taking moments about the base of the ladder, find how far up th ladder she an dimb safely. (d)