Energy, Kepler’s Laws, and Fluid Dynamics: Key Concepts
ITEM 5: Energy
Energy is a property of bodies or material systems that produces changes in how people work and/or heat.
- 1 J = 0.24 cal
- 1 J = 103 kJ
- 1 cal = 4.18 J
- 1 kcal = 103 cal
Mechanical energy (EM) is the energy linked to the position or the movement of bodies. There are two types of EM:
EM = Ec + Ep
Ec: The energy that bodies have due to the fact of being in motion. Its value depends on body mass and speed.
Ep: The energy that bodies have because they occupy a certain position. Depending on the body and the environment, we can distinguish between:
Gravitational Ep: The energy that bodies have due to being in a particular place on the ground. Considering the gravity of a body, Ep is 0 when this is over the surface of the Earth.
Elastic Ep: The energy that bodies have when they have been deformed. Its value depends on the elastic constant of the body and how much it has been deformed.
Work is the energy that is transferred from one body (or system) to another through a force that causes a displacement, and equals the product of the force made in the direction of motion times the distance traveled.
The work of the friction force
When a force acting on a body causes a displacement in the same direction, the work developed coincides with the change in kinetic energy experienced by the body.
When a vertical force acts on a body, making it move in the same direction with constant velocity, the work developed coincides with the variation of potential energy experienced by the body.
When a force acting on a body causes changes in its speed and its position, the work of that force is equal to the change in mechanical energy experienced by the body.
Principle of conservation of mechanical energy: If only gravitational forces and/or elastic forces act on a body or system, its mechanical energy is preserved.
The power (P) is a physical quantity that relates the work done (or energy value) over the time it is used in:
Power is measured in watts (W).
One watt is the power of a machine that can perform work of one joule in one second.
- 1 kW = 1000 W
- 1 HP = 736 W
1 kW per hour is a power unit multiplied by time, therefore it is a work unit.
ITEM 3: Kepler’s Laws
1st Law: All planets move around the Sun in elliptical orbits. The Sun is one focus of the ellipse.
2nd Law: The planets move at a constant sector velocity, that is, the line joining each planet to the Sun sweeps out equal areas in equal time.
3rd Law: For all the planets:
d3/T2 = constant
Where d is the average distance to the Sun, and T is the period.
Weight: Gravitational attraction that the Earth exerts on the bodies that are in their vicinity.
P = m * g
Where M = mass of Earth, m = mass of the body, R = radius of Earth
Acceleration of gravity
ITEM 4: Fluids
Fluid: A body whose particles change position easily (liquids and gases).
Archimedes’ Principle
When a body is immersed in water, its weight decreases by an amount that matches the weight of the water it displaces.
When you submerge a body in a liquid:
- It displaces a volume of liquid equal to the volume of the submerged body.
- The body weighs less when it is in the liquid.
Thrust: The force that pushes the body upward and counteracts the weight of the body.
Fthrust = Apparent weight – Actual weight
Any body wholly or partially submerged in a fluid experiences a vertically upward force called thrust that is equal to the weight of the volume of fluid displaced.
- If weight is greater than the thrust, it sinks. P > E
- If the weight is less than the thrust, the body rises. P < E
- If the weight is equal to the thrust, the body stays in balance. P = E
Forces within a Fluid: Pressure
A body immersed in a fluid is subjected to a force acting in any direction perpendicular to the body.
The value of the force will be greater the greater the depth at which it is.
The pressure at a point in a fluid is directly proportional to fluid density and depth.
Pressure: Measures the force per unit area. It is a scalar, as it is perfectly defined by a number and its unit.
Hydrostatic pressure: The pressure exerted on a body immersed in a fluid depends on the fluid column that is on the body.
Two points that are submerged in a liquid at the same height shall be subject to the same pressure.
Atmospheric Pressure: Torricelli
Mercury tube in a bucket of mercury, emptied until 760 mm.
1 atmosphere: Pressure of the atmosphere at sea level. It is equivalent to the pressure of a column of mercury 760 mm high.
The atmospheric pressure varies with altitude. P = d * g * h
Pascal’s Principle
The pressure at a point of a liquid is transmitted in full to all points of it.
Hydraulic Press
It is used to lift large weights.