Answer:
Explanation:
According to Newton's law of Gravitation for the first case:
(1)
Where:
is the gravitational force
is the Gravitational Constant
is the mass of each container
is the distance between both containers
Now, for the second case the mass of the first container is and the second
:
(2)
Finally:
To solve this problem we will apply the concepts related to the principle of archimedes. for which we will summarize that the bearing force must be equivalent to the mass of the individual and the mass of the way. Said mass of wood will be expressed in terms of density and volume. Finally with the values found we will proceed to find the Volume of the wood and thus find the mass.
For the relation between density and Volume we have that,
Where given that,
Mass of woman,
If the density of the wood is 60% the density of the water we will have to
Density of water,
And density of wood is
Now the mass of the man can be expressed as
Mass of wood required is given by,
Therefore the minimum mass necessary to support a 70kg Woman is 105Kg.
Answer:
4 x 10⁷m/s
Explanation:
When a charged particle moves in a curved path in a magnetic field, it experiences some magnetic force, and in the absence of any other force, which supplies the centripetal force needed to keep the particle in balance.
Let the magnetic force be
Let the centripetal force be
=> =
--------------(i)
We know that;
= qvBsinθ
Where;
q = charge on the particle
v = speed of the particle
B = magnetic field intensity
θ = angle between the speed and magnetic field vectors
Also;
=
Where;
m = mass of the particle
v = velocity/speed of the particle
r = radius of the circular path of motion.
From equation (i)
qvBsinθ = [divide both sides by v]
qBsinθ = [make v subject of the formula]
v = qrBsinθ / m --------------------(ii)
From the question;
B = 1.0T
r = 0.4m
θ = 90° [since magnetic field is always perpendicular to velocity]
q = 1.6 x 10⁻¹⁹C [charge of a proton]
m = 1.6 x 10⁻²⁷kg [mass of a proton]
Substitute these values into equation(ii) as follows;
v = (1.6 x 10⁻¹⁹ x 0.4 x 1.0 x sin90°) / (1.6 x 10⁻²⁷)
v = 4 x 10⁷ m/s
Therefore the speed of the proton is 4 x 10⁷m/s