A.3. Work, Energy, and Power

Work is done when a force causes displacement.

W=F⃗⋅s=⃗ Fscos θ

Where:

● θ: Angle between force and displacement vectors

Work is the concept that quantifies the effect of a force acting over a distance. When you push or pull an object and it moves, you are doing work. The formula for work is W = F ⋅ s, which includes the force applied (F), the distance (s) the object moves, and the angle (θ) between the force direction and the direction of the movement. It shows that only the component of the force that acts in the direction of movement contributes to the work done.

Consider pushing a shopping cart down a grocery aisle. If you push it forward, you are doing work on the cart. However, if you push downwards while keeping the cart in place, you are not doing any work in terms of moving it forward. The effective force that moves the cart is the horizontal push, while the vertical force just helps in keeping the cart upright.

The energy possessed by a moving object.

Ek=12mv2

Kinetic energy refers to the energy an object possesses due to its motion. It is calculated using the formula Ek = 1/2 mv², where 'm' stands for mass and 'v' for velocity. This means that if an object has a large mass or is moving quickly, it has a significant amount of kinetic energy. The factor of 1/2 in the formula indicates that the energy increases with the square of the velocity, meaning that even small increases in speed result in a disproportionately large increase in kinetic energy.

Imagine riding a bicycle. When you pedal slowly, you have a small amount of kinetic energy. However, when you speed up, your kinetic energy increases quickly. If you hit a bump while going fast, you'll find it much harder to control the bike, which demonstrates why speed affects the energy involved in motion.

Energy due to an object's position in a gravitational field.

Ep=mgh

Gravitational potential energy is the energy stored in an object as it is positioned within a gravitational field. The formula to calculate gravitational potential energy is Ep = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'h' is the height above a reference point. This energy depends on the object's mass and height; the higher the object is raised, the more potential energy it has.

Think about a book placed on a high shelf. It has potential energy because of its height. If it falls off the shelf, that potential energy is converted into kinetic energy as it speeds up towards the ground. The energy was stored as long as the book was held at that height.

Energy stored in elastic materials when stretched or compressed.

Ee=12kx2

Where:

● k: Spring constant ● x: Displacement from equilibrium

Elastic potential energy is the energy stored in objects that can be stretched or compressed, such as springs or rubber bands. The formula is Ee = 1/2 kx², where 'k' represents the spring constant (indicating the stiffness of the spring) and 'x' is how far it is stretched or compressed from its rest position. This energy is released when the object returns to its original shape.

Consider a drawn bow. The more you pull on the string, the more energy is stored in the bow (elastic potential energy) as it bends. When you release the string, this stored energy quickly converts to kinetic energy, propelling the arrow forward. The bow's ability to store energy depends on how far you draw the string back.

Energy cannot be created or destroyed; it can only be transformed from one form to another.

Etotal, initial=Etotal, final

The law of conservation of energy states that the total energy in an isolated system remains constant. It emphasizes that energy can change forms but the total amount of energy never increases or decreases. For example, energy can transform from potential energy to kinetic energy, but the sum before and after the conversion will be equal.

Imagine a pendulum swinging. At the highest points of its swing, it has maximum potential energy and minimum kinetic energy. As it swings down, potential energy is converted into kinetic energy, reaching maximum kinetic energy at the lowest point. Throughout the swing, the total energy remains the same, just transformed between two forms.

The rate at which work is done or energy is transferred.

P=Wt=Et

Measured in watts (W), where 1 W=1 J/s.

Power measures how quickly work is done or energy is transferred. The formula P = W/t (where 'W' is work done, and 't' is time taken) tells us that if more work is done in less time, the power increases. Power is measured in watts (W), where one watt equals one joule of energy used per second. This measure helps quantify how efficient tasks are when work is performed.

Consider two people lifting the same box. If one person lifts it slowly, it takes a longer time compared to someone who lifts it swiftly. The person lifting quickly exhibits higher power because they do the same amount of work in less time. Just like a high-powered appliance like a microwave cooks food faster than a low-powered stove; both use energy but at different rates.

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