#2) Two boxes are connected by a massless string on a frictionless surface. Mass m2 does not touch the table. Box m1 moves to the right on the table when released from rest and box m2 moves down at constant acceleration. The mass of m1 is 1.80kg and the mass of m2 is 3.00kg. (Remember you need to draw a sketch and FBDs, remember the three-step process for these problems, remember equations first, numbers last). Assume no torques are present in the problem.
(A) Derive an expression for the magnitude of the acceleration of the system (do not use numbers, just use the variables)?
(B) Now, plug in numbers to your expression to determine the magnitude of the acceleration of the system.
(C) Calculate the magnitude of the tension in the string?
#3) Two boxes, connected by a rope, are at equilibrium (need to consider friction on the incline). Box B is not touching the incline, it is just hanging from the outer rim of the pulley. Assume the tension force is greater than the wx component of mass A (this should help you determine the direction of the static friction force). Draw the FBD for both box A and box B separately. Use N, for Normal Force, use fs for the static friction force, use proper variations of wx and wy for the weight components (two masses, so they should have different labels, not just wx and wy for both, need to tell them apart), and use T for the Tension Force. Somewhere in your work show what your variations of wx and wy are equal to in terms of the masses and g and appropriate trigonometric terms like sine, cosine, and tangent (the problem should not have m's as you have mA and mB in the problem).
(A) Find an algebraic expression for the coefficient of static friction between a box A and the surface of incline when two bodies are equilibrium. Your expression should only contain mB, mA, and θ (of course trig anomic expressions that contain θ such as sin(θ) and cos(θ), if used properly, are allowed).
(B) Now the system starts to move at a non-constant velocity. Mass B starts to move down and the mass A starts to move up the incline. Find an expression for the acceleration of mass B (and hence the acceleration of mass A since the two are linked by a rope). Your expression should only contain mB, mA, g, μk and θ (of course trig anomic expressions that contain θ such as sin(θ) and cos(θ), if used properly, are allowed). Must redraw correct FBDs for this new situation now that it is moving.