4. A ball of clay, of mass m, traveling at speed vo, collides and sticks to a stationary stick. The ball approaches the stick in a direction perpendicular to the length, striking the stick at a distance D from the CM of the stick. The stick + ball system then moves, rotating about a new center of mass, CM’.
1. Where is the new CM' relative to the CM 'of the stick?
2.What is the final speed of the new CM'?
3. What is the final angular velocity of the sustem about the new CM'?

1) X' = mD/(M + m)

2)

3)

Explanation:

1)  mass of stick  = M

mass of clay = m

Location of original center of mass of stick, =  0 (at the origin)

Location of center of mass of clay, = D

X' = location of center of mass of the stick + ball system

The equation below applies for center of mass

X'(M+m) =

But and

X'(M+m) = M (0) + m (D)

X' = mD/(M + m)

2)  Let = speed of the clay ball before collision

speed of the stationary stick before collision = 0 m/s

V = speed of the stick-ball system after collision

Applying the principle of momentum conservation

3)

I = moment of inertia of the stick about the center of mass of the system  

Using conservation of angular momentum

But X' = mD/(M + m)

carla slowed down in the beginning of her trip, stopped, and then sped up

-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