a. How far d 2, in meters, will the second spring compress when the block runs i

Question

a. How far d2, in meters, will the second spring compress when the block runs into it?

b. How fast v, in meters per second, will the block be moving when it strikes the second spring?

c. Now assume friciton is present on the surface in between the ends of the springs at their equillibrium lengths, and the coefficient of kinetic friction is uk= 0.5. If the distnce betwen the springs is x=1 m, how far d2, in meters, will the second spring now compress?

(11 %) Problem 3: A block of mass m 0.44 kg is set against a spring with a spring constant of kj 637 N/m which has been compressed by a distance of 0.1 m. Some distance in front of it, along a frictionless surface, is another spring with a spring constant of k2-328 N/m y

Explanation / Answer

Energy stored = 0.5*k1*0.1^2 = 3.185 J
Energy stored in spring 2 = 3.145 = 0.5*328*x^2
x = 0.13935 m

b) 0.5mv^2 = 3.185 J
v = 3.8049 m/s
c) Energy wasted by friction = mu*m*g*l = 0.5*0.44*9.8*1 = 2.156 J
from energy conservation
3.185 - 2.156 = 0.5*328*x^2
x = 0.079211 m

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