A 0250kg mass is traveling to the right with a speed of 560

A 0.250kg mass is traveling to the right with a speed of 5.60 m/s block at point A on the frictionless track shown in Figure 8.P11 What is the maximum speed of the mass? What is the maximum compression of the 100N/m spring?

Solution

since there is only opposing force from the sring, the velocity goes on decreases.... so maximum speed is 5.6 m/s

the initial KE of the mass = 1/2*m*v^2 = 1/2*0.25*5.6^2 = 3.92 J

this is converted into the spring energy when compressed.. let it be compressed by x...

so 1/2*K*x^2 = 3.92

1/2*100*x^2 = 3.92

x= 0.28 m

max compression is 0.28m

maximum speed is 5.6 m/s... unless there is some other force acting....