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: $3.92\ m/s$

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

$\Rightarrow \dfrac{T}{2}=0.4\\\\\Rightarrow T=0.8\ s$

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

$\Rightarrow \omega T=2\pi\\\\\Rightarrow \omega=\dfrac{2\pi }{T}\\\\\Rightarrow \omega =\dfrac{2\pi }{0.8}\\\\\Rightarrow \omega=\dfrac{5\pi }{2}$

Maximum speed for S.H.M. is $v_{max}=A\omega$

$\Rightarrow v_{max}=0.5\times 2.5\pi\\\Rightarrow v_{max}=3.92\ m/s$