(0 Three blocks, each of mass M Gkg, slide with speed v 4n/s along frictionless

Question

(0 Three blocks, each of mass M Gkg, slide with speed v 4n/s along frictionless horizontal plane. a segnent of (a) Compute the initial kinetic energy of each member of the set of three blocks. (b) One block passes smoothly from the horizontal plane onto a frictionless incline with angl -30°-?/6 rad. Determine the distance from the bottom of the ramp at which the block stops [comes to instantaneous rest) (c) The second block runs into a spring with force constant k 24 N/m. Determine the maximum distance from the end of the spring at which the block stops [comes to instantaneous rest at the maximum compression of the spring]. (d) The final block runs into a spring with force constant k 36 N/m which is aligned with a frictionless plane inclined at 30°. Determine the distance from the bottom of the incline at which the block stops. (e) In all three will move to the left. Determine the speed of each of the blocks as it moves leftward along the horizontal frictionless segnent of the plane. cases, after the block encounters the ramp/spring/combination, the block Page 1 of 4

Explanation / Answer

(A) initial KE = m v0^2 /2

KE = 6 x 4^2 / 2 = 48 J ......Ans

(B) Applying energy conservation,

PEi + KEi = PEf + KEF

0 + 48 = m g h + 0

h = 48 / (6 x 9.8) = 0.816 m

and h = d sin30

d = h/ sin30 = 1.63 m

(C) 48 = k x^2 /2

48 = (24)(x^2)/2

x = 2 m

(D) 48 = 0 - (6 x 9.8 x d x sin30) - (36 d^2 / 2)

18 d^2 + 29.4 d - 48 = 0

d = 1 m

(E) as they comes back, from energy conservation,

KE= 48 J  

so v = 4 m/s

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