Question

1) A simple pendulum has a length of 0.4m and amplitude of 0.2m. Calculate it's potential energy at it's max height if the Bob has a mass of 400g?

2) The angular velocity of a vibrating loaded spring is 20rads^-1. Calculate urs new angular velocity when the force constant is quadrapled?

3) A circular circus weighing 6MN moves round with a force of 40KN in a merry-go-round. If it covers an area of 36πm^2, calculate the time taken to make 12 complete revolutions?

4)The difference between the range of a projectile and the magnitude of the time of flight doubles the time taken to reach max height. If it's projected at 30° to the horizontal, calculate the time of flight and the max height respectively?

Answer 1

1) Potential energy:

$U=mgh$

where $m$ is mass, $h$ is difference of max height and height at equilibrium point.

$h=L-\sqrt{L^2-s^2}$

where $L$ is length of pendulum, $s$ is amplitude.

$h=0.4-\sqrt{0.4^2-0.2^2}=0.654\ m$

$U=0.4\cdot9.8\cdot0.654=2.56\ J$

2)

$m\omega_0^2R=k_0x$

If $k=4k_0$ , then:

$\omega=\omega_0\sqrt{4}=2\omega_0=2\cdot20=40\ rad/s$