The graph shows you three different projections of human population growth
1 answer:
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11)
12)
13) 50.0 m/s
14) 41.6 m/s
Explanation:
11)
The potential energy of an object is the energy possessed by the object due to its position relative to the ground. It is given by
where
m is the mass of the object
g is the acceleration due to gravity
h is the height relative to the ground
Here in this problem, when the train is at the top, we have:
m = 8325 kg (mass of the train + riders)
(acceleration due to gravity)
h = 127 m (height of the train at the top)
Substituting,
12)
According to the law of conservation of energy, the total mechanical energy of the train must be conserved (in absence of friction). So we can write:
where
is the kinetic energy at the top
is the potential energy at the top
is the kinetic energy at the bottom
is the potential energy at the bottom
The kinetic energy is the energy due to motion; since the train is at rest at the top, we have
Also, at the bottom the height is zero, so the potential energy is zero
Therefore, we find:
13)
The kinetic energy of an object is the energy of the object due to its motion. Mathematically, it is given by
where
m is the mass of the object
v is the speed of the object
From question 12), we know that the kinetic energy of the train at the bottom is
We also know that the mass is
m = 8325 kg
Therefore, we can calculate the speed of the train at the bottom:
14)
At the top of the second hill, the total mechanical energy of the train is still conserved.
Therefore, we can write again:
where
is the kinetic energy at the top of the 1st hill
is the potential energy at the top of the 1st hill
is the kinetic energy at the top of the 2nd hill
is the potential energy at the top of the 2nd hill
From the previous questions, we know that
and
The height of the second hill is
h = 39 m
So we can also find the potential energy at the second hill:
So, the kinetic energy at the second hill is
And so, the speed is
If the beam is in static equilibrium, meaning the Net Torque on it about the support is zero, the value of x₁ is 2.46m
Given the data in the question;
- Length of the massless beam;
- Distance of support from the left end;
- First mass;
- Distance of beam from the left end( m₁ is attached to );
- Second mass;
- Distance of beam from the right of the support( m₂ is attached to );
Now, since it is mentioned that the beam is in static equilibrium, the Net Torque on it about the support must be zero.
Hence,
we divide both sides by
Next, we make , the subject of the formula
We substitute in our given values
Therefore, If the beam is in static equilibrium, meaning the Net Torque on it about the support is zero, the value of x₁ is 2.46m
Learn more; brainly.com/question/3882839
