Question

Medieval soliders build a counterweight trebuchet, a device that rotates about a fulcrum to launch a small projectile of mass m₁ = 1 kg from one arm of length L₁ = 8 m when a large weight of mass m₂ = 300 kg is placed on the other arm of length L₂ = 1 m. The arms of the trebuchet are approximately massless.

a) At the moment m₁ is launched, the arms of the trebuchet are parallel to the vertical direction. What is the angular velocity of the rotation of the trebuchet at this point?

b) What is the angular momentum of the trebuchet at the same moment as part a?

c ) What is the (linear) speed of m₁ at the moment it is launched?

d) The axis of rotation of the trebuchet is elevated a height H = 10 m above the horizontal surface of the ground. How much horizontal distance does the projectile travel before falling to the ground?

Answer 1

Given,

, , , ,

(a)

The torque acting on the arm is given by,

  

  

  

The moment of inertia about the axis is given by,

The angular acceleration is:

  

.•. Angular velocity is given by,

Here, the arms are parallel to the vertical on launching from horizontal. So,

Hence,

  

(b) The angular momentum of the trebuchet in part (a) is

  

(c)

The linear speed of when it is launched is given by,

(d) The projectile at the time of launching is at a height of from the ground. The horizontal distance travelled before falling on the ground is given by