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

a)
`k = 2851.2\,(N)/(m)`, b)
`v = 0.54\,(m)/(s)`

Step-by-step explanation:

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

`(1)/(2)\cdot (2.2\,kg)\cdot (1.8\,(m)/(s) )^(2) = (1)/(2)\cdot k \cdot (0.05\,m)^(2)`

The spring constant is:

`k = 2851.2\,(N)/(m)`

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

`(1)/(2)\cdot (2.2\,kg)\cdot v^(2) = (1)/(2)\cdot (2851.2\,(N)/(m) )\cdot (0.015\,m)^(2)`

`v = 0.54\,(m)/(s)`