A 30.0-kg block is resting on a flat horizontal table. On top of this block is resting a 15.0-kg block, to which a horizontal spring is attached, as the figure illustrates. The spring constant of the spring is 217 N/m. The coefficient of kinetic friction between the lower block and the table is 0.532, and the coefficient of static friction between the two blocks is 0.845. A horizontal force is applied to the lower block as shown. This force is increasing in such a way as to keep the blocks moving at a constant speed. At the point where the upper block begins to slip on the lower block, determine (a) the amount by which the spring is compressed and (b) the magnitude of the force . (a) Number (b) Number Units Units www. 15.0 30.0

Computation. Three objects are connected as in the figure with mд-7 kg, mB=6.43 kg, and mc-11.4 kg. The strings and frictionless pulleys have negligible masses, and the coefficients of friction between the block and the table are s-0.67 and u-0.151. If the system is released from rest, find the magnitude of its acceleration. [Hint: As part of your solution, check to see if block B experiences static or kinetic friction.] MA a = JACOPERTE mc E OL MB _m/s² Record your numerical answer below, assuming three significant figures. Ca O @ ✰ ✰ 0 A D 10:14 PM 10/19/2022 *** 2

Hanging Mass: A block of mass 14.1 kg is connected to a light cord of length 351.3 cm and a spring with an equilibrium length of 33.4 cm. The block hangs motionless as shown in the figure. The spring has a spring constant of 1799 N/ m. As the block hangs in equilibrium, the spring is horizontal and the cord makes an angle of 24 ° with respect to vertical. T k M (a) What is the tension in the cord? (b) How far is the spring stretched from its equilibrium length?

A block, whose mass is 0.560 kg, is attached to a spring with a force constant of 132 N/m. The block rests upon a frictionless, horizontal surface (shown in the figure below). (A block labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the block is displaced by a distance A to the right of its equilibrium position.)   The block is pulled to the right a distance A = 0.140 m from its equilibrium position (the vertical dashed line) and held motionless. The block is then released from rest.   (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the block?  N   (b) At that very instant, what is the magnitude of the block's acceleration (in m/s2)?  m/s2   (c) In what direction does the acceleration vector point at the instant of release?

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1 2 3 4 31 5 A 1.0 kg block is connected to a horizontal spring as shown with spring constant 200 N/m. You pull the block horizontally, stretching the spring a total of 20 cm from its equilibrium position. The kinetic frictional coefficient between the surface and the block is 0.25. What is the acceleration of the spring right after you let go of it? (b) 0 0 0 0 37.62 42.5 40 m 58.12 www Fspr x = 0 ↑

Example: A 1200 kg car rolling on a horizontal surface has speed v= 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring? Assume that all of the kinetic energy of the car becomes PE of the compressed spring.

A cube, whose mass is 0.700 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.110 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?

A 205 g object is attached to a spring that has a force constant of 76.5 N/m. The object is pulled 7.25 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed vmax of the object. Umax = m/s Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibrium position as zero, positions to the right as positive, and positions to the left as negative. position: cm position: cm

A box is motionless, sitting on a ramp with an incline of 0 =54.4 ° being pulled in the direction up the ramp by a spring with a spring constant of k=150 N/m that is stretched x=6.4 m. The coefficient of friction between the ramp and the box are u s=0.53 and u k=0.15 and the friction force is going down the ramp. What is the mass of the box? Solve symbolically: Solve numerically: m= Units: If the box starts moving up a ramp with an acceleration of a=2.41 m/s, what is the new length that the spring will stretch? Solve symbolically: Solve numerically: Units: