7.42 A2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, hori- zontal surface and then up a frictionless incline with slope 37.0° (Fig. P7.42). (a) What is the speed of the block as it slides along the horizontal surface after having left the spring? (b) How far does the block travel up the incline before starting to slide back down? Figure P7.42 k = = 400 N/m m = 2.00 kg www ΜΑΛΑΔΙ |-0.220 m 37.0°

If a spring compressed by 76 cm contains 2.4 J of potential energy, what is the spring constant (k) for that spring? Express your answer in N/m.

A particle can move along only an x axis, where conservative forces act on it (see the figure and the table below). The particle is released at x = 5.00 m with a kinetic energy of K = 14.0 J and a potential energy of U = 0.0 J. If its motion is in the negative direction of the x axis, what are its (a) K and (b) U at x = 2.00 m and its (c) K and (d) U at x = 0? If its motion is in the positive direction of the x axis, what are its (e) K and (f) U at x = 11.0 m, its (g) K and (h) U at x = 12.0 m, and its (i) K and (j) U at x = 13.0 m? Next, the particle is released from rest at x = 0. What are (k) its kinetic energy at x = 5.0 m and (I) the maximum positive position xmax it reaches? F, x (m) 4 6. 8 10 12 Range Force F = +(3.00 N)i F, = +(5.00 N)i O to 2.00 m 2.00 m to 3.00 m 3.00 m to 8.00 m F = 0 F, = -(4.00 N)i F, = -(1.00 N)i 8.00 m to 11.0 m 11.0 m to 12.0 m 12.0 m to 15.0 m F = 0

A 6.00 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring?