PROBLEM 14-5 (page 184, 12th edition) The 1.5 kg block slides along a smooth surface and strikes a nonlinear spring with speed v = 4 m/s. The spring's resistive force is F = ks2 where s is the compression of the spring in metres and k = 900 N/m2. . Determine the speed of the block after it has compressed the spring 20 cm. Ā„ Determine the time for the block to compress the spring 20 cm. V PROB14_005.jpg Copyright @ 2010 Pearson Prentice Hall, Inc.
14-5 (page 184, 12th edition) COMPLETION OF PROBLEM Ā„ Data m = 1.5kg V1= 4m/s . Energy Balance Equation S2 1 "mv2 + [ F ds= = mv? 1 N 2 2 0 where t F =1 ks2 k = 900N/m2 Speed of the block when the spring is compressed: Integrating yields V2 = 161 400s2 3 = 3.58m/s when s2 = 0.2m Ā„ Time for the spring to be compressed It follows from ds v= 45 = 161 400s 3 that 0.2 ds t = 3 = 51.4ms 0 161 900s' when s2 = 0.2m The integral was evaluated numerically. A block moving freely at 4 m/s travels 0.2 m in 50.0 ms.
PROBLEM 14-87 (page 212, 12th edition) The roller-coaster car has a mass of 800 kg, including its passenger, and starts from the top of hill A at 3 m/s. Ā· Determine the minimum height of the hill so that the car travels around the first inside loop without leaving the track. . Determine the normal force on the car at C. Neglect friction, the mass of the wheels, and the size of the car. A B h C 10 m 7 m PROB14_087-088.jpg Copyright 2010 Pearson Prentice Hall, Inc.