Question

A 0.230-kg block along a horizontal track has a speed of 1.30 m/s immediately before colliding with a light spring of force constant 4.00 N/m located at the end of the track. (a) What is the spring's maximum compression if the track is frictionless?

Answer 1

The maximum compression in the spring is 0.31 meters.

Step-by-step explanation:

Given that,

Mass of the block, m = 0.23 kg

Speed of the block, v = 1.3 m/s

It collides with the spring of force constant 4 N/m located at the end of the track. We need to find the spring's maximum compression if the track is frictionless. It can be calculated using conservation of energy. The kinetic energy of the block is converted to the potential energy of the spring i.e.

`(1)/(2)mv^2=(1)/(2)kx^2`

x is the spring's maximum compression

`x=\sqrt{(mv^2)/(k)} \\\\x=\sqrt{(0.23* (1.3)^2)/(4)} \\\\x=0.31\ m`

So, the maximum compression in the spring is 0.31 meters. Hence, this is the required solution.