Mechanical or Electrical Load and Work
Mechanical and electrical loads refer to the forces and demands placed on systems that convert energy into work. In mechanical systems, loads can be categorized as axial (tension and compression), transverse, or torsional, impacting how structures like elevators operate. These systems utilize simple machines, such as levers and wheels, to amplify human effort, enabling significant work output with minimal input. Electrical systems, on the other hand, rely on principles like voltage, current, and resistance to manage electrical loads, with Ohm's law providing foundational relationships among these elements.
Work, defined as the force applied over a distance, occurs in both mechanical and electrical contexts. For instance, in an elevator, the electric motor must perform sufficient electrical work to counteract the gravitational load of the elevator car. This interaction between mechanical and electrical forces is crucial, as seen in applications ranging from household appliances to advanced robotics, where efficiency and structural integrity are paramount. Understanding these concepts is essential for designing systems that effectively combine mechanical strength with electrical performance.
Mechanical or Electrical Load and Work
FIELDS OF STUDY: Classical Mechanics; Electronics
ABSTRACT: Mechanical and electrical systems are designed to perform work functions either to augment human effort or to perform work that humans are not physically capable of performing. Both electrical and mechanical systems perform work by acting on a load that opposes the work being done. Both depend on different aspects of material properties such as compressive strength and electrical resistance. Advanced applications include biomechanics and robotics.
PRINCIPAL TERMS
- compressive strength: the ability of a material to resist deformation or structural failure when experiencing a force of compression (squeezing).
- demand: the load on an electrical supply system over time.
- dummy load: a device applied to an electrical circuit or other system in order to provide a corresponding load without performing an output function.
- impedance: the opposition to electrical current flow produced by a voltage.
- mechanical advantage: the ratio of the output work done by a system or machine to the input work required for a function to be carried out.
- tensile strength: the ability of a material to resist structural failure when experiencing a force of tension (pulling).
- work: a force successfully moving an object, or the successful transfer of energy. The International System of Units unit of work is the joule.
Work, Energy, and Load
Mechanical and electrical systems are designed to perform work. Mechanical systems typically provide a large mechanical advantage compared to human effort alone. Simple machines such as levers and wheels are the central components of most machines. The work delivered as the output of levers and wheels can be many orders of magnitude greater than the work input. An elevator is a good example of mechanical advantage. The operator presses a button and machine actions then carry out the work of raising or lowering large weights a certain distance. The machinery that carries out the function of an elevator is both electrical and mechanical. The cables that lift the elevator car must have enough tensile strength that they will not break under the weight of the elevator. The structural components that support the elevator must have enough compressive strength that they will not fail under the crushing weight of the elevator. Tension (pulling) and compression (squeezing) are examples of an axial load, since they function in a direction parallel to the central axis of a component.
A load that is applied across the central axis is called a transverse load. A load applies a twisting movement to a component about its axis is called a torsional load. The electrical systems that supply voltage and current to the electric motors and other devices required for the operation of the elevator must be able to meet the demand placed on them when the machinery is in operation. All such systems are designed to perform physical work.
Electrical and Mechanical Work
Work is defined in physics as the operation of a force over a distance. In the elevator example, the lifting force of the machinery displaces the elevator by a certain distance, and the output work can be easily calculated using the force, the displacement of the object, and the cosine of the angle between the direction of the force and the direction of the displacement.
Electricity is defined as the movement of electrons through a conductor. The force that moves the electrons through the system is called the electromotive force (emf), or the applied voltage. A 12-volt battery, for example, supplies an emf of 12 volts over the length of an electrical system. The output performance of batteries and other electrical systems can be tested by the use of a dummy load. A dummy load applies a normal load to the system to test its potential output without actually performing any of the work functions of the system. A battery provides a constant voltage or emf to produce a constant flow of electrons, or a direct current (DC), in only one direction. Components of the system provide load by resisting the flow of electrons through them.
Most electrical systems rely on alternating current (AC). In AC, the electrons travel in one direction for a short time and then travel in the opposite direction for a longer period of time. AC is produced by an emf that varies in a sinusoidal manner, typically at 50 to 60 hertz (1 hertz = 1 cycle per second). AC moves through a maximum positive value and a maximum negative value. Therefore, AC has a value of zero twice in each cycle. The resistance provided by components in an AC system also varies in a cyclic manner as a result. This resistance is called the impedance. Current, voltage, and resistance values determine the electrical power of the devices, the rate at which the device performs work. The power consumed by any device is defined as the product of its resistance and the square of the current passing through the device.
Electrical work is converted into mechanical work by a motor. The electrical power required to operate the motor depends on the mechanical resistance that it experiences in the conversion of electrical work to mechanical work. In the elevator example above, the electric motor that supplies the mechanical power to raise the car against the force of gravity has to do more electrical work when there are more people in the elevator. Similarly, the cables and other mechanical components have to resist a greater force when there is more weight in the elevator car. The elevator car is thus a load acting in opposition to both the electrical and mechanical work performed in the system.
Voltage, Current, and Power
Electrical systems function when an applied voltage drives a current through a load resistance. The three are related by Ohm’s law. Georg Simon Ohm (1787–1854) discovered their relationship in 1827. Ohm’s law states that the voltage (E) applied to a system is equal to the product of the resistance (R) and the current (I) flowing in the system, or
E = IR
The power (P) produced by the system is the product of the resistance and the squared value of the current, or
P = I2R
These simple formulas are fundamental to the design of electrical systems and have their mechanical counterparts in classical mechanics. Voltage corresponds to force in mechanical systems. Resistance corresponds to friction and other factors that act against the movement of a mechanical component. Current may correspond to the number of mechanical components that function in the system between the work input and a specific work output. By this analogy, the force required to achieve a specific mechanical result would be the product of the number of components and the resistive factors of each component.
Sample Problem
An electric stove operates at 1,500 watts, an air conditioner operates at 1,000 watts, and four lightbulbs operate at 60 watts each. Calculate the individual resistances of these devices and the load on the electrical system of the home in which they operate. (Standard operating voltage for stoves is 220 volts and 110 volts for the other devices.)
Answer:
The load on the electrical system is the sum of the individual loads. In this case,
1,500 + 1,000 + (4 × 60) = 2,740 watts
The resistances are found using the two formulas E = IR and P = I2R, and rearranging them to solve for R as
R = E/I
I2 = P/R
Set the equations equal to one another:
(E/R)2 = P/R
E2/R2 = P/R
E2 = PR
R = E2/P
Therefore,
- the resistance of the stove is (220)2/(1,500) = 32.27 Ω (Ω or omega is the standard symbol for ohms)
- the resistance of the air conditioner is (110)2/1,000 = 12.1 Ω
- the resistance of each lightbulb is (110)2/60 = 201.67 Ω
Note that a calculation of the combined resistance of these devices is complicated because it depends on whether they are connected in series or in parallel with each other and their impedance rather than their resistance.
Applied Electromechanics
Perhaps the most fascinating application of electrical and mechanical loading is biomechanical engineering, including robotics. Industrial robots are relatively simple mechanical systems that function using electrical and hydraulic power systems. They are designed to carry out a programmed set of precise movements using specified spatial coordinates. Therefore, they cannot vary from that pattern unless reprogrammed. Biomechanics, however, is based on the principle that muscles function as motors and bones function as structural elements. The challenge that this poses is to construct artificial devices or prosthetics that permit functioning with the same range and type of motion as the limbs or organs that they replace. This requires an unequaled amount of design calculation to specify electrical and mechanical components with structural and performance capabilities comparable to those of the actual living system in which they function.
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