Question

You attach a 2.30 kg weight to a horizontal spring that is fixed at one end. You pull the weight until the spring is stretched by 0.500 m and release it from rest. Assume the weight slides on a horizontal surface with negligible friction. The weight reaches a speed of zero again 0.400 s after release (for the first time after release). What is the maximum speed of the weight (in m/s)

Answer 1

Answer:
`3.92\ m/s`

Step-by-step explanation:

Given

Mass of the attached object is
`m=2.3\ kg`

Spring is stretched by
`A=0.5\ m`

Speed reaches zero after
`t=0.4\ s`

Speed is zero at the extremities of the S.H.M motion that is

`\Rightarrow (T)/(2)=0.4\\\\\Rightarrow T=0.8\ s`

Time period of motion is
`0.8\ s` which can also be given by

`\Rightarrow \omega T=2\pi\\\\\Rightarrow \omega=(2\pi )/(T)\\\\\Rightarrow \omega =(2\pi )/(0.8)\\\\\Rightarrow \omega=(5\pi )/(2)`

Maximum speed for S.H.M. is
`v_(max)=A\omega`

`\Rightarrow v_(max)=0.5* 2.5\pi\\\Rightarrow v_(max)=3.92\ m/s`