1-A 8000 kg freight car rolls along rails with negligible friction. The car is b
ID: 1401870 • Letter: 1
Question
1-A 8000 kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by Hooke's law with
k1 = 1500 N/m and k2 = 3400 N/m. After the first spring compresses a distance of 10.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The
car comes to rest 50.0 cm after first contacting the two-spring system. Find the car's initial speed.
Explanation / Answer
let v is the speed of the car before contacting the spring.
Apply conservation of energy
initial kinetic energy of car = final potential energy of two springs
0.5*m*v^2 = 0.5*k1*x2^2 + 0.5*k2*(x2-x1)^2
v = sqrt( (k1*x2^2 + k2*(x2-x1)^2)/m)
= sqrt( (1500*0.5^2 + 3400*(0.5-0.1)^2)/8000)
= 0.3389 m/s <<<<----Answer
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