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

Step-by-step 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* 0.14* g-0.123* 3.96* g`

`T_(net)=6.793* 9.8`

`T_(net)=66.57 N-m`

Work done by
`T_(net)` is converted to rock kinetic Energy

thus

`T_(net)* \theta =(mv^2)/(2)`

Where
`\theta =angle\ turned =(\pi )/(2)`

`v= velocity\ at\ launch`

`66.57* (\pi )/(2)=(0.123* v^2)/(2)`

`v^2=66.57* \pi`

`v=√(1700.511)`

`v=41.23 m/s`