Fundamental Principles of Energy, Motion, and Fluids
Topic 5: Energy
Energy is the property of materials, bodies, or systems that allows for the production of transformations such as work and/or heat.
- 1 J = 0.24 cal
- 1 kJ = 103 J
- 1 cal = 4.18 J
- 1 kcal = 103 cal
Mechanical energy (Em) is the energy linked to the position or movement of bodies. There are two types of Em, and Em = Ec + Ep
Ec: This is the energy that moving bodies possess. Its value depends on the mass and velocity of the body.
Ep: This is the energy that certain bodies possess due to their position. Its value depends on the medium in which the body is found. We can distinguish between:
Gravitational Ep: This is the energy that bodies possess due to being at a certain height above the Earth’s surface. The gravitational Ep of a body is considered to be zero when it is on the Earth’s surface.
Elastic Ep: This is the energy that bodies undergoing deformation possess. Its value depends on the body’s elasticity constant and the extent of deformation.
Work is the transfer of energy from one body (or system) to another by means of a force that causes displacement. It is equal to the product of the force in the direction of movement multiplied by the distance traveled.
Work-Energy Theorem
When a body experiences a force that causes displacement in its own direction, the work done corresponds to the variation in the body’s kinetic energy.
When a force acts on a body in a vertical direction, causing it to move in the same direction with constant velocity, the work done coincides with the variation in the body’s potential energy.
When a force acts on a body, causing changes in both its position and velocity, the work done by the force is equal to the change in the body’s mechanical energy.
Principle of Conservation of Mechanical Energy
If the only force doing work on a body is its own weight, its mechanical energy remains constant.
Power
Power (P) is the physical quantity that relates the work done (or energy exchanged) to the time taken to do it.
Power is measured in watts (W).
A watt is the power of a machine that can do a job of 1 joule in 1 second.
- 1 kW = 1000 W
- 1 CV = 736 W
1 kilowatt multiplied by an hour is a unit of work, not power.
Topic 3: Kepler’s Laws
1st Law: Planets move around the Sun in elliptical orbits, with the Sun at one of the foci of the ellipse.
2nd Law: Planets move with constant areal velocity, meaning that the line connecting the planet to the Sun sweeps out equal areas in equal times.
3rd Law: For all planets, there is a relationship between the mean distance to the Sun and the orbital period.
Weight
Weight is the force of gravitational attraction that the Earth exerts on bodies in its proximity.
P = mg
- M = mass of the Earth
- m = mass of the body
- R = Earth’s radius
- g = acceleration due to gravity
Topic 4: Fluids
A fluid is a body whose particles change position easily (liquids and gases).
Archimedes’ Principle
When we submerge a body in water, its weight decreases by an amount equal to the weight of the water it displaces. When a body is introduced into a liquid:
- A volume of liquid is displaced equal to the volume of the submerged body.
- The body’s weight decreases while it is inside the liquid.
Thrust: The upward force that counteracts the weight of the body.
Thrust = Real weight – Apparent weight
A body totally or partially submerged in a fluid experiences a vertical upward force called thrust, which is equal to the weight of the volume of fluid displaced.
- If P > thrust, the body sinks.
- If P < thrust, the body floats.
- If P = thrust, the body remains in equilibrium.
Pressure in the Interior of a Fluid
A body submerged in a fluid is subjected to a force that acts perpendicularly to the body in any direction.
The greater the depth at which it is found, the greater the value of the force.
The pressure at a point in a fluid is directly proportional to the density of the fluid and its depth.
Pressure: A unit of force per surface area. It is a scalar quantity, defined by a number and a unit.
Hydrostatic pressure: The pressure exerted on a body submerged in a fluid depends on the column of fluid above the body.
Two points submerged in a liquid at the same height are subjected to the same pressure.
Atmospheric Pressure – Torricelli’s Experiment
A tube of mercury is placed in a container with mercury, and it empties until it reaches 760 mm.
1 atmosphere is the pressure that the atmosphere exerts at sea level, and it is equivalent to the pressure exerted by a column of mercury 760 mm high.
Atmospheric pressure varies with altitude. P = dgh
Pascal’s Principle
The pressure exerted at a point in a liquid is transmitted integrally to all other points in the liquid.
The hydraulic press is used to lift large weights.