Consider the mass-on-a-spring system as shown in the figure below. The spring has a spring constant of 1.86e+3 N/m, and the block has a mass of 1.39 kg. There is a constant force of kinetic friction between the mass and the floor of 4.71 N. Starting with the spring compressed by 0.117 m from its equilibrium position, how far will the block travel once it leaves the spring? (Assume that block leaves the spring at the spring's equilibrium position, marked x=0 in the figure. Give your answer as the distance from the equilibrium position to the final position of the block.) Hint: How much work must friction do in order to bring the mass to a stop? How much distance is required for friction to do this work? Image size: S M L Max

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A box of mass m = 0.7 kg is attached to a rope which is wrapped around a physical pulley with a radius of R = 10.2 cm and a rotational inertia of I = 0.075 kg·m2. When the box is released it starts to fall down with a constant acceleration and, at the same time, the pulley starts to spin up, see the picture below. Assuming that the pulley is frictionless, what is the magnitude of the box's acceleration and what is the tension in the rope?   The acceleration of the box, a ? The tension in the rope, T? If the box starts from rest and traveled downwards a distance of h = 28 cm, what is the speed of the box and what is the angular velocity of the pulley? The speed of the box, v =? The angular velocity of the pulley, ω? -------------------------------------------------------------- A Merry Go Round carousel has a radius of R = 2.4 m and a rotational inertia of I = 695 kg·m2. A 75‑kg student is on the carousel at the midpoint between the carousel's center and the rim (at R/2 distance from…

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