An object of mass 200 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of StartFraction 1 Over 40 EndFraction times the weight of the object is pushing the object up (weight = mg). If we assume that water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 50 m/sec? Assume that the acceleration due to gravity is 9.81 m divided by sec squared .

= 7.08 s

Explanation:

Given that,

- The mass of the object m = 200 kg

- The buoyancy force F_b = W / 40

- The weight of the object = W = m*g

- Water resistance F_w = k*v

- Where, k = 10 Ns/m

Use Newton's Second law of motion to evaluate the acceleration a.

                                    F_net = m*a

                               W - W/40 - 10*v = m*a

                                a = 39/40*g - 10/m *v

                                a = 39/40 * 9.81 - 10/200 * v

                                a = 9.56 - 0.05*v

- Using the first kinematic equation of motion we have:

                                v_f = v_i + a*t

object was dropped from rest, v_i = 0, Hence:

                                v_f = (9.56 -0.05*v)*t  

                               v_f = 9.56*t / ( 1 + 0.05*t)

Find the time t when v_f = 50 m/s

                                50(1 + 0.05*t) = 9.56*t

                                 50 + 2.5*t = 9.56*t

                                 t = 50 / 7.06

                                     = 7.08 s

vapour or gas assuming atmospheriv pressure

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this