Question

In order to launch a projectile over a wall, you need to obtain a

tangential velocity of 30 m/s at a launching angle of 45 degrees

from horizontal. Your projectile is attached to the arm of a

catapult of length 3.5 m which is initially oriented horizontally.

When the arm is released, the catapult will provide a constant

angular acceleration until ejecting the projectile at the 45 degree

angle. The projectile has a mass of 70 kg.

What angular acceleration does the catapult need to provide to

successfully launch the projectile over the wall?

At this acceleration, how much time elapses between releasing the

catapult and ejecting the projectile?

How much rotational kinetic energy does the projectile at the

moment before ejection from the catapult? (unit kJ)

How much translational kinetic energy does the projectile have at

the moment after ejection from the catapult?(unit kJ)

Answer 1

V = w R     where w = angular (final) velocity
w = 30 / 3.5 = 8.57 / sec
theta = 1/2 a t^2    where a = angular acceleration
theta = 1/2 (w / t) * t^2 = 1/2 w t
pi / 4 = 1/2 * 8.57 t
t = .183 sec
alpha = w / t = 8.57 / .183 = 46.8 / sec^2
E = 1/2 M V^2    transational energy
E = 1/2 * 70 * 900 = 31,500 J
E= 1/2 I w^2 = 1/2 M R^2 * w^2 = 1/2 M R^2 * (V / R)^2 = 1/2 M V^2
So the rotational energy equals the translational energy
(I = 1/2 M R^2)