Question

_{A 5kg mass slides without friction down a 30° inclined plane l.after sliding 2m,it hits and stick to a pan attached to a light spring whose force constant is 4300Nm.}

By how much is the spring compressed.

Calculate the period of the resulting simple harmonic motion of the mass

Answer 1

The 2m-long incline at 30° is equivalent to the following height:

$$h=L\sin30°=1\text{ m}.$$

The potential energy is, therefore:

$$PE=mgh=49\text { J}.$$

According to energy conservation, this is the kinetic energy:

$$KE=49\text{ J}.$$

According to energy conservation, this is the elastic potential energy:

$$49=\frac12kx^2,\\\space\\ x=\sqrt{\frac{2·49}{k}}=0.15\text{ m}.$$

The period of oscillations:

$$T=2\pi\sqrt{\frac mk}=0.0214\text{ s}.$$