Question

A 2.2 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring. (a) Determine the force constant (in N/m) of the spring, if the box compresses the spring 5.0 cm before coming to rest. N/m (b) Determine the initial speed (in m/s) the box would need in order to compress the spring by 1.5 cm. m/s

Answer 1

Answer:

a) $k = 2851.2\,\frac{N}{m}$, b) $v = 0.54\,\frac{m}{s}$

Explanation:

a) According to the Principle of Energy Conservation, the kinetic energy of the box is transformed into elastic potential energy.

$\frac{1}{2}\cdot (2.2\,kg)\cdot (1.8\,\frac{m}{s} )^{2} = \frac{1}{2}\cdot k \cdot (0.05\,m)^{2}$

The spring constant is:

$k = 2851.2\,\frac{N}{m}$

b) The initial speed needed to compress the spring by 1.5 centimeters is:

$\frac{1}{2}\cdot (2.2\,kg)\cdot v^{2} = \frac{1}{2}\cdot (2851.2\,\frac{N}{m} )\cdot (0.015\,m)^{2}$

$v = 0.54\,\frac{m}{s}$