Answer:
a) 10.648 J
b) -10.648 J
c) h₀ = 0.9024 m
d) 0.500 m
Explanation:
The work done by the block on the spring is equal to the work done by the spring on the block
W = (1/2)(k)(x²) = 0.5 (440)(0.22²) = 10.648 J
c) The work done by the block on the spring is the change in potential energy of the block during this fall.
The change in potential energy is
Weight × Total distance fallen through by the block = mg(h₀ + 0.22)
This change in potential energy is now equal to the workdone by the spring on the block
W = mg(h₀ + 0.22)
9.4864 h₀ + 2.087008 = 10.648
h₀ = (8.560992/9.4864)
h₀ = 0.9024 m
d) If the block were released from a height of 6h₀, that is,
H = 6h₀ = (6×0.9024) = 5.415 m above the spring
Work done by the block in falling that height + compression = mg(H + x) = (0.968)(9.8)[5.415 + x)
This work is done on the spring
W = (1/2)(k)(x²)
9.4864[5.415 + x] = 0.5(440)(x²)
51.37 + 9.4864x = 220x²
220x² - 9.4864x - 51.37 = 0
Solving the quadratic equation
x = 0.50 m or - 0.47
The negative answer defies the laws of physics, hence, the decompression of the spring is 0.50 m.
Hope this Helps!!!
