A 50kg block is dropped from a point 10m above, as shown in the figure above. if the force constant of the spring is 4.0 x 10\(^4\)Nm-1, find the maximum compression of the spring. [g = 10ms\(^{-2}\)]
Attached Figure / Diagram
A
1.25m
B
0.50m
C
0.25m
D
0.05m
Verified Correct Answer: B.
Physical Principles & Numerical Solution
P.E\(_{mgh}\) = \(\frac{1}{2}\) * k * x\(^2\)
mgh = \(\frac{1}{2}\) * k * x\(^2\)
50 * 10 * 10 = \(\frac{1}{2}\) * 4 * 10\(^4\) * x\(^2\)
→ x\(^2\) = \(\frac{5000 * 2}{4 * 10^4}\)
→ x = \sqrt[0.25]
: x = 0.50m
Source: Myschool Past Questions Archive (Record #41662)