Problem 12:
Problem 3: A block of mass m = 160 kg rests against a spring with a spring constant of k = .730 N/m on an inclined plane which makes an angle of 6 degrees with the horizontal. Assume the spring has been compressed a distance d from its neutral position. Refer to the gure. "lltcnpcrlluxuln Part C. Assuming the plane is frictionless, what will the angle of the plane be, in degrees, if the spring is compress ed by gravity 3 distance 0.1 m'? Part ((1) Assuming 6 : 45 degrees and the surface is frictionless, how far will the spring be compressed, d in meters? Problem 5: A particular kind of BB gun uses a spring-driven plunger to launch the BB from its barreL Part (2]) Calculate the force constant in newtons per meter, of the plunger's spring if you must compress it 0.15 In to drive the 0.075 kg BB to a top speed ofI9 m/s. k = Pa rt (1)) What force must be exerted to compress the spring. in newtons? F = Problem 9: The length of nylon rope from which a mountain climber is suspended has a force constant of 1.05 X 10*L N/m. Part (b) How much would this rope stretch. in centimeters. to break the climber's fall if he free-falls 2.8 111 before the rope starts to stretch? x 2 Part (c) What is the frequency, in Hz, at which he bouncengiven his mass and the mass ofhis equipment is 82 kg ifthe rope is twice as long? r = Part ((1) How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 2.8 m before the rope runs out of slack if the rope was twice the length? x; = Problem 10: A novelty clock has a 0.0065kg mass object bouncing on a spring which has a force constant of 1. 3 Wm. Part (1)) How much kinetic energy, in ioules, does the obiect have at its maximum velocity? ICE = Problem 11: Suppose a spring has a spring constant k; = (:20 N/m as the spring is stretched om x = 0 to x; = 31 cm. The spring constantthen changes to k2 = 240 Win as the spring is stretched to x2 = 65 cm. From x; = 05 cm to x; = .96 cm the spring force is constant at F; = 115 N. Part (b) Use the area under the curve to calculate the wor in 'oules necessa to stretch the s rin om x = 0 to in. Wag] 2 Part (c) Write an equation for the work done in stretching the spring from x; to 3:2. W142 = Part ((1) Calculate the work done, in ioules, in stretching the spring from x; to 35;. W14; = Part (e) Calculate the work, in ioules, necessary to stretch the spring om x = 0 to 3:3. Woe; =
