Please show work when answering these questions: 1- There is an easy way to find
ID: 1522303 • Letter: P
Question
Please show work when answering these questions:
1- There is an easy way to find the equilibrium location for an object if you know the formula for its potential energy---you simply take a derivative and set it to zero. True or False.
2- If there no friction forces on an object, then its momentum must be conserved. True or False.
3- You slide an object across a level table and then slide it back to the exact point where it started from. The total work done by friction on the object is zero. True or False.
4- A rock is dropped from a high place. Which is true if wind resistance is neglected? Hint: think about energy conservation and a fundamental equation for velocity.
a- It will gain an equal amount of momentum during each second of falling.
b- It will gain an equal amount of kinetic energy during each second of falling.
c- The amount of momentum it gains is proportional to the height it loses.
d- It will gain an equal amount of speed during each meter of falling.
e- It will gain an equal amount of momentum during each meter of falling.
5- A stick has a linear mass density that varies with location according to the formula lamda= Cx. What is the total mass of the stick if it is 3 meters long?
a- 3C
b- 9C
c- C/3
d- C/9
e- 9C/2
6- There Is more biomass in the Earth’s northern hemisphere than its southern hemisphere. That means every Spring, when plants and trees begin to grow, trillions of tons of nutrients get a few meters farther from the Earth’s center, and the actually slows down. Likewise, the rotation of the Earth speeds up a tiny bit in autumn.
7- Astronomers using the Hubble Space Telescope have recently deduced the presence of what they think is a black hole in a distant galaxy. They measured the speed of orbiting gas, at a distance of 5.7*10^17 meters (60 light years) to be 780 kilometers/sec. Deduce the mass of the central object, and compare it to the mass of our sun.
a- 2.6 thousands suns.
b- 2.6 billion suns.
c- Approximately one sun.
d- 2.6 trillion suns.
e- 2.6 quadrillion suns.
8- A killer asteroid is placed at rest at a distance from the earth sufficient to avoid immediate detection by a very mean ET civilization (distance = 10^11 meters). It has a mass of 10^16 kg, and will fall towards the Earth because of gravity (ignore all other effects, including the orbital speed of the Earth, and gravity from the sun and other planets). How fast will this object be moving when it hits the earth?
a- 7,920 m/s
b- 11,200 m/s.
c- 9,800 m/s
d- 4.4 m/s
e- 1,400,000 m/s.
Explanation / Answer
Part 1: True
at equilibriumposition net Force = 0 and Force = derivative of potential energy
Part 2 : False
There may be other forces acting . For example the momentum of freely falling body is not constant however fricition is absent here
Part3: False
during each trip the direction of friction force was opposite to the velocity so workdone = -ve in each trip
Part 4: answer = a
since momentum gained per second = rate of change of momentum = net force acting on it , which is conastant thus rate of gaining momentum is same
Part 5 : answer = e