3.) A 1000N block is in contact with a plane inclined at 30° to the horizontal. A force P, parallel to and acting up the plane, is applied to the body. If the coefficient of static friction 0.20, a.) find the value of P to just cause motion to impend up the plane and b.) find the value of P to just prevent the motion down the plane.

According to the following figure, A) Make the free-body diagram including all the forces acting on you and the bicycle at the time of descent. Define each of them. B) Argue for which cases you have jobs equal to zero according to your free-body diagram from part (A)

4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“. a) Draw the three free body diagrams, and write out Newton's 2nd Law for each. b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system. c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE. d) Assume the position x as a function of time t is of the form x(t) = A cos (wt + p) I disk for undamped natural frequency w, phase angle P, and amplitude A. The initial conditions are: x(0) v(0) = -3. 00 m/s. Solve for the position of the mass as a function of time (you need to solve for w, 4, and A). = 2. 00 m and Mz

A sled of mass 500kg sits at rest on a rough slope that is inclined at 10* to the horizontal. The coefficient of friction between the slope and the sled is 0.3. The sled is held in place by a wire attached to a winch. The tension in the wire is TN. a) Find the maximum possible value of T.   A load of mass mkg is added to the sled, and tension in the wire is increased to 5000N in order to pull the sled and load up the slop. Given that the sled and load are pulled a distance of 100m in 80seconds, b) Work out the value of m