Question

You place the spring vertically with one end on the floor. You then drop a mmm = 1.20 kgkg book onto it from a height of hhh = 0.900 mm above the top of the spring. Find the maximum distance the spring will be compressed.

Answer 1

Answer:

11.9 cm

Explanation:

We are given that

Mass of book=1.2 kg

Height,h=0.9 m

Spring constant,k=1700 N/m

We have to find the maximum distance the spring will be compressed.

By conservation law of energy

Gravitational potential energy=Spring potential energy

$\frac{1}{2}kx^2=mg(0.9+x)$

Where g=$9.8 m/s^2$

$\frac{1}{2}(1700)x^2=1.2\times 9.8(0.9+x)$

$850x^2=10.58+11.76 x$

$850x^2-11.76x-10.58=0$

Using quadratic formula

$x=\frac{11.76\pm\sqrt{(-11.76)^2-4(-10.58)(850)}}{2(850)}$

$x=\frac{11.76\pm 190}{1700}$

$x=\frac{11.76+190}{1700}=0.119 m$

$x=\frac{11.76-190}{1700}=-\frac{178.24}{1700}$

It is not possible because distance cannot be negative.

x=$0.119=0.119\times 100=11.9 m$

1m=100 cm