Consider two elastically constrained carts that are free to oscillate in the ver
ID: 1940615 • Letter: C
Question
Consider two elastically constrained carts that are free to oscillate in the vertical plane over a smooth horizontal surface. As illustrated, the cart of mass m1 is attached to a wall via a spring with stiffness k1, and the coordinate x1 measures the cart’s distance away from its equilibrium position. Cart m2 is connected to m1 by a spring of stiffness k2, where x2 describes the cart’s oscillation about equilibrium. Given the following, determine the system’s total energy:
m1 = 7 kg
k1 = 220 N/m
x1 = 0.4 m
v1 = 6.5 m/s
m2 = 6 kg
k2 = 208 N/m
x2 = 1 m
v2 = 4.2 m/s
Round your answer to the nearest N*m.
Explanation / Answer
Total Energy = (Kinetic E + Elastic Potential E)1+(Kinetic E + Elastic Potential E)2
Stretched length of spring 1 = x1 = 0.4m
Stretched length of spring 2 = x2-x1 = 0.6m
Total Energy = 0.5m1v12+0.5k1x12+0.5m2v22+0.5k2x22
Total Energy = 0.5*7*6.52+0.5*220*0.42+0.5*6*4.22+0.5*208*0.62
Total Energy = 255.84 Nm or 256 Nm