Equilibrium Net force must equal zero Two connected masses on a plane

Two masses are at rest on a plane inclined at angle s=35° above horizontal. A cord from mass A=4 kg, passes over a frictionless pulley at the top of the plane to unknown mass B. The coefficient of friction is f= .25. See attachment for picture showing blocks and plane. a. Find the maximum mass of B for the masses to remain in place. b. Find the minimum mass of B for the masses to remain in place.

Equilibrium with torques on a Ladder leaning on frictionless wall with man climbing maximum distance d on it.

Equilibrium with torques on a ladder A uniform ladder, length L= 4.5 m, and having mass M= 36 kg, leans against a frictionless wall with angle c= 50° above the floor. The coefficient of friction between ladder and floor is f=.55. A man whose weight is W= 480 newtons, climbs the ladder. Find the maximum distance d, that he can climb until the ladder slides down. See problem attachment for picture.

Rotational Motion

A small marble is rolling on the inside of a parabolic bowl whose surface is given by z = ®r2 in cylindrical polar coordinates. There is no friction, but the gravity is pulling down (in the negative-z direction). Consider the most general case where the marble is free to move in any direction on the surface. (a) Identify all the forces and write down the projection of Newton's equations on the axes of your coordinate system. (b) Use the constraint(s) and/or integration to reduce the system of these three scalar equations to one scalar equation in terms of r alone. (You don't have to solve this equation). (c) Can we find the trajectory of the marble by using the energy conservation ins... click for more

Calculating the center mass at which a system is in equilibrium.

Determine when a solid shape produced by gluing a cylinder of height H and radius R to a hemisphere of radius R made from the same material will be in a stable equilibrium standing on its top.

Center of Mass

Determine the position of the center of mass of a solid triangular pyramid with vertices at (0; 0; 0), (1; 0; 0), (1; 1; 0), and (1; 1; 2).