A 20.0 kg block is connected to a 30.0 kg block by a stringthat passes over a li

Question

A 20.0 kg block is connected to a 30.0 kg block by a stringthat passes over a light, frictionless pulley. The 30.0 kg block isconnected to a spring that has negligible mass and a force constantof 280 N/m, as shown in the figure below.The spring is unstretched when the system is as shown in thefigure, and the incline is frictionless. The 20.0 kg block ispulled 22.0 cm down the incline (so thatthe 30.0 kg block is 42.0 cm above thefloor) and released from rest. Find the speed of each block whenthe 30.0 kg block is 20.0 cm above the floor (that is, when thespring is unstretched).

Explanation / Answer

.           Given that the spring constant is K = 280 N/m             masses are m1 = 20 kg and m2 = 30 kg             The extended length is x = 22cm = 0.22m -------------------------------------------------------------------------------------------         Apply conservationof energy after spring extended to length 0.22m                        m2*g*(0.22m) + (1/2)Kx2=  (1/2)m1*U2 +m1*g*x*sin      (30 kg)*(9.8m/s2)*(0.22m)+ (1/2)(280 N/m)(0.22m)2 =  (1/2)(20kg)*U2+(20kg)*(9.8m/s2)*(0.22m)*sin400          slove for U = ------ m/s                              

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