Question

The conical pendulum shown consists of a sphere of mass m and a cable of length l, whose massit is despicable. The pendulum rotates around a vertical axis with constant angular velocitytheta = (constant). Determine:a) The height h.b) The tension T of the cable.

Answer 1

The height h of the pendulum can be calculated using the equation h = l - l*cos(angle), where l is the length of the cable. The tension T of the cable can be determined using the equation T = mg + m*omega^2*l, where m is the mass of the sphere, g is the acceleration due to gravity, and omega is the angular velocity.

Step-by-step explanation:

a) The height h:

To calculate the height h, we can use trigonometry. Since the pendulum is released from rest at an angle of 30 degrees, the height can be found using the equation h = l - l*cos(angle), where l is the length of the cable. In this case, l is given as the length of the rod, so h = 2 - 2*cos(30) = 2 - 2*sqrt(3)/2 = 2 - sqrt(3) m.

b) The tension T of the cable:

The tension T can be determined using the equation T = mg + m*omega^2*l, where m is the mass of the sphere, g is the acceleration due to gravity, and omega is the angular velocity. Since the mass of the cable is negligible, we only need to consider the mass of the sphere. Therefore, T = m*g + m*omega^2*l = m*(g + omega^2*l) N.