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

(a)

(b)   I =428

(c)

Explanation:

GIVEN

mass = 18.2 kg

radial arm length = 3.81 m

velocity = 49.8 m/s

mass of arm = 22.6 kg

we know using relation between linear velocity and angular velocity

for  angular acceleration, use the following equation.

since

here  for one circle is 2 π radians.   therefore for one quarter of a circle is π/2 radians

so   for one quarter

on solving

(b)

For the catapult,

moment of inertia

For the ball,

so total moment of inertia =  428

(c)

c. convergent boundary.

explanation:

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: