Answer:
Explanation:
Calculating the exit temperature for K = 1.4
The value of is determined via the expression:
where ;
R = universal gas constant =
k = constant = 1.4
The derived expression from mass and energy rate balances reduce for the isothermal process of ideal gas is :
------ equation(1)
we can rewrite the above equation as :
where:
Thus, the exit temperature = 402.36 K
The exit pressure is determined by using the relation:
Therefore, the exit pressure is 17.79 bar
Answer:
a) The average friction force exerted on the toboggan is 653.125 newtons, b) The rough region reduced the kinetic energy of the toboggan in 92.889 %, c) The speed of the toboggan is reduced in 73.333 %.
Explanation:
a) Given the existence of non-conservative forces (friction between toboggan and ground), the motion must be modelled by means of the Principle of Energy Conservation and the Work-Energy Theorem, since toboggan decrease its speed (associated with due to the action of friction. Changes in gravitational potential energy can be neglected due to the inclination of the ground. Then:
Where:
,
are the initial and final translational kinetic energies of the tobbogan, measured in joules.
- Dissipated work due to friction, measured in joules.
By applying definitions of translation kinetic energy and work, the expression described above is now expanded and simplified:
Where:
- Friction force, measured in newtons.
- Distance travelled by the toboggan in the rough region, measured in meters.
- Mass of the toboggan, measured in kilograms.
,
- Initial and final speed of the toboggan, measured in meters per second.
The friction force is cleared:
If ,
,
and
, then:
The average friction force exerted on the toboggan is 653.125 newtons.
b) The percentage lost by the kinetic energy of the tobbogan due to friction is given by the following expression, which is expanded and simplified afterwards:
If and
, then:
The rough region reduced the kinetic energy of the toboggan in 92.889 %.
c) The percentage lost by the speed of the tobbogan due to friction is given by the following expression:
If and
, then:
The speed of the toboggan is reduced in 73.333 %.
One of the components that affect the period is gravity (the other is length). This gravity is basically the value of the effective acceleration that acts on the body due to gravity. When the elevator is over free fall, the effective gravity becomes zero. Mathematically this can be visualized as,
Since this value is zero, the period would tend to be infinite,
Therefore the frequency that is inversely proportional to the period would be defined as
In this way there is no frequency on the body which will not generate any oscillation on the body
Answer:
Explanation:
(a) Just as one-dimensional numbers add on a number line by putting them end-to-end, so two-dimensional numbers add on a coordinate plane the same way.
Here, we choose to let the positive y-axis represent North, and the positive x-axis, East. This is the way a map is conventionally oriented. The velocity of the plane is represented by a vector pointing north (up). Its length represents the magnitude of the velocity. Likewise, the wind is represented by a vector of length 15 pointing east (right). The sum of these is the hypotenuse of the triangle they form.
The magnitude of the sum can be found here using the Pythagorean theorem, but for the purpose of this question, you're not asked to find that.
Instead, you're asked to estimate whether it is more or less than 25 (m/s).
Your knowledge of the triangle inequality will tell you that the hypotenuse (resultant) must be shorter than the sum of the lengths of the sides of the triangle, hence must be less than 10+15 = 25.
__
(b) The triangle inequality says the resultant is less than the sum of the other two sides of the triangle.
__
(c) Since the wind is blowing the plane toward the east, but the plane is traveling toward the north, the resulting direction is somewhere between north and east.
__
(d) "Somewhere between north and east" can be expressed as the inequality ...
0° < angle < 90°
