Question

The body, weighing 4 kg, is released from a height of 30 cm above the spring. The coefficient of elasticity of the spring is 1600 N / m. Find how much will be the biggest compression of the spring?

Answer 1

As the body lands on the spring, the compression can be found by the conservation of energy: the gravitational potential energy is wasted to compress the spring. The gravitational potential energy is

$$GPE=mg(h+x),$$

the elastic potential energy is

$$EPE=\frac12 kx^2,\\\space\\ GPE=EPE.\\\space\\ mg(h+x)=\frac12 kx^2,\\\space\\ \frac12kx^2-mgx-mgh=0,\\\space\\ x=\frac{mg+\sqrt{(mg)^2+2kmgh}}{k}=0.15\text{ m}.$$