A 0.100 kg limestone cube is released from rest, and proceeds to slide down a frictionless ramp. At the bottom of the ramp, the limestone cube makes an elastic collision with a steel cube whose mass is 0.200 kg, which is initially at rest. At what vertical height should the limestone cube be placed such that the steel cube has a velocity of 1.50 m/s after the collision

the height at which the limestone cube must be placed is 0.23 m.

Explanation:

Given;

mass of limestone cube, m₁ = 0.1 kg

initial velocity of the limestone cube, u₁ = 0

mass of steel cube, m₂ = 0.2 kg

initial velocity of the steel cube, u₂ = 0

final velocity of the steel cube, v₂ = 1.5 m/s

Apply the principle of conservation of energy to determine the height of the limestone cube.

Potential energy of the limestone cube at top = Kinetic energy of steel cube at base

m₁gh = ¹/₂m₂v₂²

where;

h is the height at which the limestone cube is placed

Therefore, the height at which the limestone cube must be placed is 0.23 m.

-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

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