ractice Gradebook ORION Downloadable eTextbook gnment BACK NEXT Question 1 Two b

Question

ractice Gradebook ORION Downloadable eTextbook gnment BACK NEXT Question 1 Two blocks, of masses M 2.2 kg and 2M, are connected to a spring of spring constant k 220 N/m that has one end fixed, as shown in the figure. The horizontal surface and the pulley are frictionless, and the pulley has negligible mass. The blocks are released from rest with the spring relaxed. (a) What is the combined kinetic energy of the two blocks when the hanging block has fallen 0.095 m? (b) what is the kinetic energy of the hanging block when it has fallen that 0.095 m? (e) What maximum distance does the hanging block fall before momentarily stopping? Y(a) Number (b) Number (c) Number dy Units Units Units

Explanation / Answer

Q-1

a)

h = height dropped = 0.095 m

x = stretch of the spring = h = 0.095 m

v = speed of masses = ?

using conservation of energy

Loss of gravitational potential energy = gain in kinetic energy + spring potential energy

2M gh = (0.5) (2M + M) v2 + (0.5) k x2

2(2.2) (9.8 x 0.095) = (0.5) (3) (2.2) v2 + (0.5) (220) (0.095)2

v = 0.97 m/s

b)

KE of hanging block = (0.5) (2M) v2 = (0.5) (2 x 2.2) (0.97)2 = 2.1 J

c)

H = maximum height dropped = ?

x = stretch of the spring = H

v = speed of masses = 0 m/s

using conservation of energy

Loss of gravitational potential energy = gain in kinetic energy + spring potential energy

2M gH = (0.5) (2M + M) v2 + (0.5) k H2

2(2.2) (9.8 H) = (0.5) (3) (2.2) (0)2 + (0.5) (220) H2

H = 0.392 m

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