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 i ...continues

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 ...continues

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 ...continues

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).

Calculating the center of mass of a cylinder.

Determine the position of the center of mass of a thin parabolical shell defined by z = a^2 - r^2 in cylindrical polar coordinates, glued to a flat bottom where z = 0, r < a of the same thickness.

Projectile problem A marble fired from a roof at a known angle. Location of origin and impact point known.

A marble is fired at angle +30° from a roof top x,y origin 50 m above ground with velocity such that it falls into a bowl on the ground at (218, -50). a. Find the original speed Vo. b. Find the total time of flight of the marble. See diagram attachment for picture showing known data.

Potential Stablitiy

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. Note that the top is the hemishpere: therefore the hemisphere is the only part touching the ground.

Equilibrium with torques on a cylinder on an inclined plane

A unifom cylinder, mass M= 15 kg, rests on a plane inclined at angle b=30°, held stationary by a cord attached to the plane at angle a= 50° which applies tangential force C to the cylinder. A mass m= 5 kg is suspended on a cable which is wrapped on the surface of the cyiinder. The radius R is unknown. See the attachment for a ...continues

Calculating the frequency of a tuning fork. A diagram of the setup is provided in jpg format.

A tuning fork is set into vibration above a vertical open tube filled with water. Please see the figure attached. The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is L1 = 0.1 ...continues