A catapult with a radial arm 3.81 m long accelerates a ball of mass 18.2 kg through a quarter circle. The ball leaves the apparatus at 49.8 m/s. The mass of the arm is 22.6 kg and the acceleration is constant. Hint: Use the time-independent rotational kinematics equation to find the angular acceleration, rather than the angular velocity equation.

(a) Find the angular acceleration.

rad/s2

(b) Find the moment of inertia of the arm and ball.

kg · m2

(c) Find the net torque exerted on the ball and arm.

N · m

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

Ametal ball with a mass of 0.028 kg is dropped from rest at a height of 1.0 meters above the ground. assuming the energy in the ball is conserved, how much kinetic energy will the ball have when it is 0.5 meters above the ground?

Which of the following situations is impossible? a) an object has velocity directed east and acceleration directed east. b) an object has zero velocity but non-zero acceleration. c) an object has constant non-zero velocity and changing acceleration. d) an object has velocity directed east and acceleration directed west. e) an object has constant non-zero acceleration and changing velocity.