1) Mass of one copper atom:
2) There are atoms in the cube
3) Mass of the cubical block: 992 kg
Explanation:
1)
We are told here that the mass of one mole of copper is
for
(number of moles)
We also know that the number of atoms inside 1 mole of substance is equal to Avogadro number:
This means that atoms of copper have a mass of M = 64 g. Therefore, we can find the mass of one copper atom by dividing the total mass by the avogadro number:
2)
We are told that the diameter of a copper atom is
We can assume that the atoms are arranged in a cube, and that they are all attached to each other; so the side of the cube can be written as size of one atom multiplied by the number of atom per side:
where
N is the number of atoms (rows) in one side of the cube
Since the side of the cube is
L = 4.8 cm = 0.048 m
We find N:
This is the number of atom rows per side; therefore, the total number of atoms in the cube is
3)
The total mass of the cubical block of copper will be given by the mass of one atom of copper multiplied by the total number of atoms, so:
where:
is the number of atoms in the cube
is the mass of one atom
Therefore, substituting, we find:
So, the mass of the cubical block is 992 kg.
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Answer:
v = 79.2 m/s
Solution:
As per the question:
Mass of the object, m = 250 g = 0.250 kg
Angle,
Coefficient of kinetic friction,
Mass attached to the string, m = 0.200 kg
Distance, d = 30 cm = 0.03 m
Now,
The tension in the string is given by:
(1)
Also
T = m(g + a)
Thus eqn (1) can be written as:
Now, the speed is given by the third eqn of motion with initial velocity being zero:
where
u = initial velocity = 0
Thus
To solve this problem it is necessary to apply the concepts related to the conservation of energy, through the balance between the work done and its respective transformation from the gravitational potential energy.
Mathematically the conservation of these two energies can be given through
Where,
W = Work
Final gravitational Potential energy
Initial gravitational Potential energy
When the spacecraft of mass m is on the surface of the earth then the energy possessed by it
Where
M = mass of earth
m = Mass of spacecraft
R = Radius of earth
Let the spacecraft is now in an orbit whose attitude is then the energy possessed by the spacecraft is
Work needed to put it in orbit is the difference between the above two
Therefore the work required to launch a spacecraft from the surface of the Eart andplace it ina circularlow earth orbit is