When we lift an object vertically upwards, such as raising a book from a table, we are actually doing work against the force of gravity. This force, exerted by the Earth, pulls objects toward its surface. As we lift the object, we counteract this gravitational force, and the work done in doing so can be calculated using specific formulas.
The work done in lifting the object against gravity can be calculated using the formula:
Here, the variables stand for:
W: Work done
m: Mass of the object
g: Acceleration due to gravity
h: Vertical distance through which the object is lifted
In many cases, the motion of an object is not in the exact direction of the applied force. For instance, when a child pulls a toy car with a string, the car moves horizontally on the ground, but the force applied by the child is at an angle to the ground due to the string's orientation. This means that the whole force is not contributing to the object's movement; only the horizontal component of the force is effective in moving the object.
In such instances, the formula W = F × s cannot be directly used, as the distance moved 's' is not parallel to the applied force 'F'. Instead, the effective force component along the direction of motion needs to be considered. This effective force is represented by 'F cos θ', where 'θ' is the angle between the direction of force and the direction of motion.
The formula for calculating work done when a body moves at an angle 'θ' to the direction of force is derived as follows:
Here:
W: Work done
F: Applied force
θ: Angle between force direction and motion direction
s: Distance moved
When a force acts at right angles (90^{o}) to the direction of motion, no work is done, as the effective force component becomes zero.
Similarly, if a force acts opposite to the direction of motion (180^{o}), the work done is negative. In the latter case, the work is calculated as:
Work (W) = -F × s
This means that the force is opposing the motion, leading to negative work.
The concept of positive, negative, and zero work is crucial in understanding how different forces impact the motion of objects.
Positive Work: When a force acts in the same direction as the motion of an object, the work done is considered positive. In this scenario, the force contributes to increasing the speed and energy of the object. For example, if a football is kicked while lying on the ground, the force of the kick acts in the direction of the football's motion. As a result, the work done on the football is positive, causing it to accelerate and gain speed.
Negative Work: Negative work occurs when a force acts in the opposite direction to the motion of an object. In this case, the force acts to slow down or oppose the object's movement. For instance, when a moving football experiences friction with the ground, the force of friction acts against the direction of motion, resulting in negative work. This force reduces the object's speed and kinetic energy.
Zero Work: Zero work is observed when a force acts perpendicular to the direction of motion of an object. In this situation, the force doesn't influence the object's speed, and its energy remains unchanged. An example of zero work is the gravitational force acting on a satellite moving in a circular orbit around the Earth. The gravitational force acts at right angles to the direction of motion, causing no change in the satellite's kinetic energy.
In some cases, multiple forces may be acting on an object. The net work done by these forces will be the sum of their individual work contributions.
Energy is a fundamental concept that refers to the ability of a system to perform work. Work is done when a force is applied to an object, causing it to move a certain distance. Energy is what enables this process of performing work and bringing about changes in the physical world.
Energy manifests in various forms, each playing a distinct role in the physical world. Some of the primary forms of energy include:
Kinetic energy is a fundamental concept in physics that describes the energy associated with the motion of an object. It's a type of mechanical energy that arises from the movement of an object and its speed. In simpler terms, kinetic energy is the energy that an object possesses due to its motion.
Formula for Kinetic Energy: The kinetic energy (K.E.) of an object with mass 'm' and velocity 'v' is given by the formula:
In terms of momentum (p = mv), Kinetic energy can be quantified as:
Key Points about Kinetic Energy
Motion and Speed: Kinetic energy is only relevant when an object is in motion. An object at rest has no kinetic energy, regardless of its mass.
Dependence of Kinetic Energy on Mass and Speed:
Energy Transfer: When a moving object collides with another object or interacts with it, it can transfer some of its kinetic energy. This energy transfer can lead to changes in the motion or behaviour of the objects involved.
Units: The SI unit of kinetic energy is the joule (J), which is the same unit used for work. The kinetic energy of an object can be measured in joules.
Conservation of Energy: In isolated systems (where no external forces are acting), the total mechanical energy, including both kinetic and potential energy, is conserved. This principle is known as the conservation of mechanical energy.
Work-Energy Theorem: The Work-Energy Theorem is a fundamental concept in physics that relates the work done on an object to its change in kinetic energy. When work is done on an object, it can change the object's kinetic energy.
The Work-Energy Theorem states that the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be written as:
This means that the work done on an object by the applied force causes a change in its kinetic energy. If the work done is positive (force and displacement are in the same direction), the kinetic energy of the object increases. If the work done is negative (force and displacement are in opposite directions), the kinetic energy decreases.
If the object starts from rest (initial velocity, u = 0), the theorem simplifies to:
Potential energy is a form of energy associated with the position or configuration of an object relative to other objects or forces. It is the energy an object possesses due to its location within a gravitational field or due to changes in its shape or configuration. In simpler terms, potential energy is the energy that an object has stored within it, ready to be converted into other forms of energy when certain conditions are met.
Types of Potential Energy
Where:
P.E. is the gravitational potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the height above a reference point
Key Points about Potential Energy
Power is the rate at which work is done or energy is transferred or converted. It measures how quickly energy is used or produced. Mathematically, power is defined as the amount of work done (or energy transferred) per unit of time. It is a measure of how quickly a task can be completed or how fast energy is being used or produced. Power is a scalar quantity; it has magnitude but no direction.
Formula for Power: The formula for calculating power is given by:
Where:
P is the power,
W is the work done or energy transferred
t is the time taken to do the work or transfer the energy.
Units of Power: The SI unit of power is the watt (W), named after James Watt, the inventor and engineer. One watt is equal to one joule of work done (or energy transferred) per second. In other words, it's the power required to do one joule of work in one second. Mathematically:
1 watt = 1 joule/second
Larger units of power are also commonly used:
Relation Between Power and Energy: Power and energy are related concepts. Power is the rate of energy transfer or conversion. Energy is the total amount of work done or transferred. The relationship between power, energy, and time is given by:
Where:
E is the energy (work done or transferred)
P is the power
t is the time.
Commercial Unit of Energy: The commercial unit of energy used for billing purposes is the kilowatt-hour (kWh). One kilowatt-hour is the amount of energy consumed when using a device with a power rating of one kilowatt for one hour. It's equivalent to 3.6 million joules.
1 kWh = 3.6 × 10^{6} J
This conversion allows us to relate energy usage in everyday terms to the standard SI unit of energy, the joule.
Energy transformation refers to the process where energy changes from one form to another. This happens constantly in various systems and processes. Some examples of energy transformation are:
The law of conservation of energy states that energy cannot be created or destroyed; it can only be transferred or converted from one form to another. In a closed system, the total amount of energy remains constant over time. This law is a fundamental principle of physics and is applicable to all types of energy, including mechanical, thermal, chemical, electromagnetic, and more.
Learn more about Magnetic Effects of Electric Current |
The law of conservation of energy has profound implications in various scientific and practical contexts:
Learn more about Sources of Energy |
1. How is energy related to work?
Energy is the ability to do tasks. When work is performed on an item, energy is moved to or from it, resulting in a change in its energy state.
2. Under what conditions is no work done, even if a force is applied to an object?
No work is done if:
i. The force applied does not cause any displacement (e.g., pushing against a wall).
ii. The displacement is perpendicular to the direction of the applied force (e.g., carrying a book horizontally without lifting or lowering it).
3. How does energy transformation occur in an electric motor?
In an electric motor, electrical energy is transformed into mechanical energy. When an electric current flows through the motor, it creates a magnetic field that interacts with the motor's components, causing motion.
4. How does the Law of Conservation of Energy apply to a roller coaster?
At the highest point of a roller coaster, the car has maximum potential energy and minimal kinetic energy. As the car descends, potential energy is transformed into kinetic energy, increasing its speed. At the lowest point, kinetic energy is at its maximum. The total mechanical energy (potential + kinetic) remains constant throughout the ride, ignoring friction.
5. In real-world scenarios, why do we observe a loss of mechanical energy, even though the Law of Conservation of Energy holds?
In real-world scenarios, mechanical energy appears to be "lost" due to the transformation into other forms of energy like heat, sound, or light, often because of friction or air resistance. While mechanical energy decreases, the total energy of the system remains constant.
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