Working with force and mechanical advantage.

A 1m long crowbar is used to lift a heavy crate. The pivot point is 10 cm from one end. a) If 600 N is exerted on one end, what is the upward force exerted on the crate at the other end? b) Calculate the mechanical advantage, the ratio of forces.

Find by integration the moment of inertia of a uniform, hollow cylinder.

A uniform hollow cylinder such as a roll of paper towels, has mass M, inner radius Ri, outer radius Ro. By applying 'I= Int (r^2 dm)', find its moment of inertia about a center of mass axis along its diameter. SEE ATTACHMENT PDF #1 FOR DIAGRAM OF THE CYLINDER

Mass and density of system

Determine the mass of wire having a relative density of 8.77 which must be wrapped around a cork weighing 15 g in order that the cork shall just sink in fresh water. The cork's relative density=0.24.

Calculating coefficient of friction and how far a spike goes into the ground

1a) A steel block with a mass of 62 kg is drawn along a horizontal surface. It is pulled by a rope that is 27 degrees above the horizontal with a 73 N force. What is the coefficient of friction? Assume the object is moving at a constant speed. 1b) A block of steel weights 1.5 ton and is allowed to fall 1.5 m on to a spike. There is a 30% loss due to dissipation, the opposing force is 300 kN of ground resistance. How far does the spike go into the ground?

'Net torque = I alpha' applied to a hollow cylinder with force applied tangentially.

A roll of paper towels is a uniform hollow cylinder, mass M=.75 kg, outer radius Ro=.084 m, inside radius of the hollow core Ri=.036 m. The roll is mounted on frictionless bearings. See attachment #1 for a picture showing parameters. By pulling on the paper towel with a tangential force P=.25 nt, starting at rest, the roll is thus given initial angular acceleration Ao. a. Find the kinetic energy of the rotating roll at the end of t= 5.2 seconds. (Assume that the outer radius does not change during this time.) b. When exactly half of the roll has been removed, with the same force P applied tangentially, find the angular acceleration Af.