SOLUTION: A 2.80 kg block is dropped onto a spring from a height of 0.830 m above the top of the spring, which has a force constant k = 1570 N/m. Find the maximum distance (in meters) the sp

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: A 2.80 kg block is dropped onto a spring from a height of 0.830 m above the top of the spring, which has a force constant k = 1570 N/m. Find the maximum distance (in meters) the sp      Log On


   

Question 1056857: A 2.80 kg block is dropped onto a spring from a height of 0.830 m above the top of the spring, which has a force constant k = 1570 N/m. Find the maximum distance (in meters) the spring will be compressed (neglecting friction).
Answer by ikleyn(52810) About Me  (Show Source):
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A 2.80 kg block is dropped onto a spring from a height of 0.830 m above the top of the spring, which has a force constant k = 1570 N/m.
Find the maximum distance (in meters) the spring will be compressed (neglecting friction).
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Let "d" = the maximum distance (in meters) the spring will be compressed (in meters).

In the block's lowest position the change of its potential energy is equal to the potential energy of the compressed spring.

The change of the block's potential energy is m*(0.830 + d),
where "m is the given mass of the block.

The potential energy of the compressed spring is %28kd%5E2%29%2F2.

So, the equation is

2.80*(0.83+d) = %281570%2Ad%5E2%29%2F2.

Solve it for "d".