Question

A war wolf is a device used during the middle ages to assault fortifications with large rocks. A simple trebuchet is constructed with a large, stiff 4.1 m rod (assume it has negligible mass) with a heavy object of mass 52 kg and 14 cm from the axle around which the device pivots and a cup on the far end that holds the rock. The war wolf is loaded when it is in a horizontal position, and the rock is projected horizontally when after it has rotated to a vertical position. If the rock has a mass of 123 g, how fast (linear speed) does it move when launched?

Answer 1

Answer:v=41.23 m/s

Explanation:

Given

mass of heavy object $m_1=52 kg$

distance of $m_1$ from the axle $r_1=14 cm$

mass of rock $m_2=123 gm$

Length of rod $=4.1 m$

distance of $m_2$ from axle $r_2=4.1-0.14=3.96 m$

Net torque acting is

$T_{net}=m_1gr_1-m_2gr_2$

$T_{net}=52\times 0.14\times g-0.123\times 3.96\times g$

$T_{net}=6.793\times 9.8$

$T_{net}=66.57 N-m$

Work done by $T_{net}$ is converted to rock kinetic Energy

thus

$T_{net}\times \theta =\frac{mv^2}{2}$

Where $\theta =angle\ turned =\frac{\pi }{2}$

$v= velocity\ at\ launch$

$66.57\times \frac{\pi }{2}=\frac{0.123\times v^2}{2}$

$v^2=66.57\times \pi$

$v=\sqrt{1700.511}$

$v=41.23 m/s$