Question

A 1.07 kg block is held in place against the spring by a 31 N horizontal external force. The external force is removed, and the block is projected with a velocity v1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2 = 1.6 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B extending to E. The coefficient of kinetic friction is 0.34. The velocity of the block is v3 = 1.4 m/s at C. The block moves on to D, where it stops. (a) Find the height of the ramp. (b) Find the distance that the block travels between points B and C. (c) Find the coefficient of elasticity for the spring?

Answer 1

090 90m5 D Imve? - 1 mv = Mengs Cosido V2 V3² - - MexgxS Ammo Olamst 2 1.ums Sa V8²_Vc? 1.6² 1.42 2x9. 8x0.34 Q 16ml 2 Mx g 8 u= 0.34 S=0.09m 0.09 F = kx and kx² = mv² a) According to low of conservation of energy A potential energy + AKE=0 - Ou I'm ve - 1 m² - (mgxo-ugh) KX = 31N AKE = so my? 1 x 1.07 (1.6² 1.2²) - migh 2x107x (1.6² – 1.22) - 1.0749.8th 8x1:07 * 1:12 = 1:07x9.8h 13kx.x = **31N*X = {x107x 12? 1:0781.22 31 he 0.56 x- 0.ougm 31 0.049 ka F d/m = 0.057 m friction force = 0.34x20789 .811 fr = 3.56524 N - ang K= 623.7 l/m

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