Question

A 2.5 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.4 N is exerted on it by water resistance. Let y=0 be at the bottom of the pond.

Part A

Calculate the nonconservative work, Wnc, done by water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K, and the total mechanical energy of the system, E, when the depth of the rock below the water's surface is 0 m.

Express your answers using two significant figures separated by commas.

Wnca, Ua, Ka, Ea =

  J

Part B

Calculate the nonconservative work, Wnc, done by water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K, and the total mechanical energy of the system, E, when the depth of the rock below the water's surface is 0.50 m.

Express your answers using two significant figures separated by commas.

Wncb, Ub, Kb, Eb =

  J  

Part C

Calculate the nonconservative work, Wnc, done by water resistance on the rock, the gravitational potential energy of the system, U, the kinetic energy of the rock, K, and the total mechanical energy of the system, E, when the depth of the rock below the water's surface is 1.0 m.

Express your answers using two significant figures separated by commas.

Wncc, Uc, Kc, Ec =

  J  

Answer 1

on the surface of pond

initial potential energy Ui = m*g*y = 2.5*9.8*1.8 = 44.1 J

initial kinetic energy Ki = 0

part(A)

Wnca = f*dy = 4.4*(0-1.8) = 7.92 J

Ua = m*g*y = 0

from energy conservation

Wg + Wnc = dK

Ka - Ki = Ui-Ua + wnca

Ka = 44.1-7.92 = 36.18 J

Ea = Ua + Ka = 36.18 J

part(B)

Wncb = f*dy = 2.2*(1.5-1.8) = -0.66 J

Ub = m*g*y = 2.5*9.8*1.5 = 36.5 J

Kb = Ui - Ub + Wncb = 44.1-36.5-0.66 = 6.94 J

Eb = Kb + Ub = 36.5+6.94 = 43.44 J

part(c)

Wncc = f*dy = 2.2*(0.8-1.8) = -2.2 J

Uc = m*g*y = 2.5*9.8*1 = 24.5 J

Kc = Ui - Ub + Wncb = 44.1-24.5-2.2 = 17.4 J

Ec = Kc + Uc = 17.4 + 24.5 = 41.9 J