Question

NEED ASAP

A pendulum is made up of a massless rod of length 1.6 m attached to a 4 kg mass. It’s released from rest when the pendulum is horizontal. When the pendulum is vertical, the mass is moving at 4.8 m/s.

a) Taking the gravitational potential energy to be zero at the bottom of the swing, what is the initial total mechanical energy?

b) How much energy is lost due to air resistance as the pendulum moves from its horizontal to its vertical position? (Assume no other nonconservative forces do work on the pendulum.)

c) As the pendulum continues to swing, it again reaches a point where its speed is zero. At what elevation is the mass of the pendulum at this point if an additional 8.25 J of mechanical energy was lost since the pendulum was vertical?

Answer 1

Y]) 2 m = Given L = 1.6m 4 kg bottom= 4.8 m/s a) Total métial mechanical energy - L 0 m Picco, ů given by Ei mgh 62.729 (4 x 9.8 x1.6) 1 E. = 62.72 ] b) Using Consewation of Hostal mechanical energy, we have, E; -Wnc Ef I mv² 2 botton Whe Wnc -) Whe ngh - Who = migh- 1 voton = m ( gh - A vente) = 4(9.81x1.6 - 4x4.8) = 4(15.696 - 11.52) 1 = 16.7041 Hence work done by air resistance is 16.70 I again using using conservation of mechanical energy, Wnc c) Now We have, Ei - Who=Ef Em Varta Wal = mgh. =) ( 2 x 4x4. 3) - 8.25) = 4x3.81th = 37.83 9 → h = 0.96 m Hence new horizontal height is 0.96m. - 39.24 h