Answer to Question #112414 in Mechanics | Relativity for Jess

Question

A strong spring is used to launch a 2kg mass horizontally. The spring has a spring constant of k=8000Nm-1 and you wish the mass to have a velocity of 32ms-1 as it leaves the end of the spring. What initial compression of the spring, from its equilibrium position, is required to produce this velocity (in m)?

(a) 0.1
(b) 0.3
(c) 0.5
(d) 0.7
(e) 0.9

Answer 1

According to the law of conservation of energy we get

$\frac{}{}$ $\frac{k\times x^2}{2}=\frac{m\times v^2}{2};\\x=\sqrt\frac{m\times v^2}{k};\\x=\sqrt\frac{2kg\times (32\frac{m}{s})^2}{8000\frac{N}{m}};\\x=0.506m$ Answer: Initial compression of the spring is 0.506m