In accordance with the definition of density as r = m/V, in order to determine the density of
matter, the mass and the volume of the sample must be known.
The determination of mass can be performed directly using a weighing instrument.
The determination of volume generally cannot be performed directly. Exceptions to this rule
include
· cases where the accuracy is not required to be very high, and
· measurements performed on geometric bodies, such as cubes, cuboids or cylinders, the volume
of which can easily be determined from dimensions such as length, height and diameter.
· The volume of a liquid can be measured in a graduated cylinder or in a pipette; the volume of
solids can be determined by immersing the sample in a cylinder filled with water and then
measuring the rise in the water level.
Because of the difficulty of determining volume with precision, especially when the sample has a
highly irregular shape, a "detour" is often taken when determining the density, by making use of the
Archimedean Principle, which describes the relation between forces (or masses), volumes and
densities of solid samples immersed in liquid:
From everyday experience, everyone is familiar with the effect that an object or body appears to
be lighter than in air – just like your own body in a swimming pool.
Figure 3: The force exerted by a body on a spring scale in air (left) and in water (right)
The particle has constant acceleration according to
Its velocity at time 
is
Then the particle has position at time according to
At at the point (3, 6, 9), i.e. when 
, it has speed 8, so that
We know that at some time 
, the particle is at the point (5, 2, 7), which tells us
and in particular we see that
and
Then
That is, there are two possible initial velocities for which the particle can travel between (3, 6, 9) and (5, 2, 7) with the given acceleration vector and given that it starts with a speed of 8. Then there are two possible solutions for its position vector; one of them is
Answer: 4.8 s
Explanation:
We have the following data:
the mass of the raft
the force applied by Sawyer
the raft's final speed
the raft's initial speed (assuming it starts from rest)
We have to find the time
Well, according to Newton's second law of motion we have:
(1)
Where 
is the acceleration, which can be expressed as:
(2)
Substituting (2) in (1):
(3)
Where 
Isolating from (3):
(4)
Finally:
An object can be at rest and still be in motion because the earth is always in motion.
In order to answer these questions, we need to know the charges on
the electron and proton, and then we need to know the electron's mass.
I'm beginning to get the creepy feeling that, in return for the generous
5 points, you also want me to go and look these up so I can use them
in calculations ... go and collect my own straw to make the bricks with,
as it were.
Ok, Rameses:
Elementary charge . . . . . 1.6 x 10⁻¹⁹ coulomb
negative on the electron
plussitive on the proton
Electron rest-mass . . . . . 9.11 x 10⁻³¹ kg
a). The force between two charges is
F = (9 x 10⁹) Q₁ Q₂ / R²
= (9 x 10⁹ m/farad) (-1.6 x 10⁻¹⁹C) (1.6 x 10⁻¹⁹C) / (5.35 x 10⁻¹¹m)²
= ( -2.304 x 10⁻²⁸) / (5.35 x 10⁻¹¹)²
= 8.05 x 10⁻⁸ Newton .
b). Centripetal acceleration =
v² / r .
A = (2.03 x 10⁶)² / (5.35 x 10⁻¹¹)
= 7.7 x 10²² m/s² .
That's an enormous acceleration ... about 7.85 x 10²¹ G's !
More than enough to cause the poor electron to lose its lunch.
It would be so easy to check this work of mine ...
First I calculated the force, then I calculated the centripetal acceleration.
I didn't use either answer to find the other one, and I didn't use " F = MA "
either.
I could just take the ' F ' that I found, and the 'A' that I found, and the
electron mass that I looked up, and mash the numbers together to see
whether F = M A .
I'm going to leave that step for you. Good luck !
