Question

Please answer all parts

a)A child of mass 35 kg is sitting on the seat of a swing, suspended from a rigid bar on ropes that are 2.0 m long. Calculate the moment of inertia of the child with respect to the bar about which the swing rotates. b) Two very thin concentric circular hoops of mass 0.20 kg and 0.30 kg have radi of 1.5 m and 0.90 m respectively. They are connected by rigid links of negligible mass such that they lie in the same plane. Calculate the system's moment of inertia about an axis through the centre and perpendicular to the plane of the hoops. c)Two charges of +2.0 uC and +3.0 uC are held fixed at the lower two corners of an equilateral triangle of side length 1.0 m, in a vacuum. How much energy is required to move a point charge of -4.0 uC from a point midway between the other two charges to the apex of the triangle?

Answer 1

(a) Given mass of boy = 35 kg, L = 2m Recall I = ML^2 = rotational inertia of a mass about axis of rotation, where L is distance from axis of rotation to mass. I = 35 times 2^2 = 140.0 kg-m^2 [neglecting mass of rope] (b) m_1 = 0.2 kg r_1 = 1.5 m m_2 = 0.3 kg r_2 = 0.9 m I_1 = m_1r^2_1 = 0.2 times 1.5^2 = 0.45 kg.m^2 I_2 = m_2r^2_2 = 0.3 times .9^2 = 0.243 kg-m^2 So I_f = I_1 + I_2 = 0.45 + 0.243 = 0.693 kg-m^2 U_1 degree = initial electric P > E when 4 mu C is at P = K(-2 times 10^-6 times 4 times 10^-6)/-5^2 + K(-12 times 10^-12)/-5^2 U_f = When charge is at open, at B = K(-8 times 10^-12)/1 + K(-12 times 10^-13)/1 So, delta U = change in P.E = U_f - U_i = K times 10^-12(-20)-{-K times 10^-12/.5^2 times 20}