Question

What is meant by potential energy? Give an example of an object or material that possesses potential energy.

Short answer

Potential energy is the stored energy of an object or system due to its position or state, which can be converted into other forms of energy, such as kinetic energy. Two common types of potential energy are gravitational potential energy (\(PE = mgh\)) and elastic potential energy (\(PE = \frac{1}{2}kx^2\)). An example of an object possessing potential energy is a book placed on a high shelf, which has gravitational potential energy, or a stretched rubber band, which has elastic potential energy.

Step-by-step solution

Define Potential Energy

Potential energy is the stored energy of an object or system due to its position or state. It is a form of mechanical energy that depends on the relative positions of objects within a system or on the system's internal structure. Potential energy can be converted into other forms of energy, such as kinetic energy, when the object, or parts of the system, moves or changes its position.

Gravitational Potential Energy

One common example of potential energy is gravitational potential energy. Gravitational potential energy is possessed by an object due to its position in a gravitational field. An object that is higher in the gravitational field has more potential energy than an object closer to the ground. The formula for gravitational potential energy is \(PE = mgh\), where \(PE\) represents potential energy, \(m\) is the mass of the object, \(g\) is the acceleration due to gravity, and \(h\) is the height of the object above the reference point.

Elastic Potential Energy

Another common form of potential energy is elastic potential energy. Elastic potential energy is the energy stored in a system when an elastic object, such as a spring or rubber band, is deformed or stretched. The more the elastic object is deformed or stretched, the more potential energy it stores. The formula for elastic potential energy is \(PE = \frac{1}{2}kx^2\), where \(PE\) represents potential energy, \(k\) is the spring constant, and \(x\) is the amount of deformation or stretch.

Example of Potential Energy

A classic example of an object possessing potential energy is a book placed on a high shelf. The book has gravitational potential energy because it is elevated above the ground, and if it were to fall, this potential energy would be converted into kinetic energy. Another example is a stretched rubber band, which possesses elastic potential energy due to its deformation. As the rubber band is released, this potential energy is transformed into kinetic energy as the rubber band moves back to its original shape.

Key concepts

Gravitational Potential Energy

Gravitational potential energy is a type of energy that an object possesses because of its position in a gravitational field. Imagine an apple hanging from a tree; this apple has gravitational potential energy because of its height above the ground. If it falls, this stored energy converts into kinetic energy. Gravitational potential energy depends on three main factors:

• The mass of the object (

)

The height (

)

The value of gravitational acceleration (

)). The formula used to calculate it is: \( PE = mgh \), where \( m \) is mass, \( g \) is gravity (around 9.81 m/s² on Earth), and \( h \) is the height of the object above ground. Changing any of these variables will alter the amount of gravitational potential energy. For instance, increasing the height or mass of the object will increase its potential energy. In daily life, this concept is used to understand how energy can be stored and released, like when riding a roller coaster — ascending the height initially stores energy which then transforms into speed as the ride descends.

Elastic Potential Energy

Elastic potential energy is associated with objects that can be stretched, compressed, or twisted, such as rubber bands or springs. This energy is stored when such an object is deformed and is released when it returns to its original state. The more an object is stretched or compressed, the greater the elastic potential energy stored. The formula to determine elastic potential energy is \( PE = \frac{1}{2}kx^2 \), where \( k \) is the spring constant, reflecting the stiffness of the object, and \( x \) is the amount of deformation or stretch. Objects with a higher spring constant usually require more force to deform and thus can store more energy. Everyday examples include using a slingshot or the bounce of a pogo stick. In these situations, pulling or compressing stores energy which is rapidly released for motion. Understanding elastic potential energy helps in designing devices like shock absorbers, which utilize this stored energy to dampen impacts.

Mechanical Energy

Mechanical energy is the sum of potential and kinetic energy in a system. It is the energy associated with the motion and position of an object. In simpler terms, it’s a measure of how much work an object can do due to its movement and position. For instance, a swinging pendulum continuously converts its potential energy at the highest points into kinetic energy as it swings down, showcasing mechanical energy's transformation. To appreciate mechanical energy fully:

• Kinetic Energy is energy possessed due to movement. The faster an object moves, the more kinetic energy it has.
• Potential Energy exists due to the object’s position or condition (like height or elasticity).

Mechanical energy is vital in numerous fields such as engineering, where it's leveraged to design machines that efficiently convert stored energy into desired work performance. For instance, engines transform the stored chemical potential energy in fuel into motion, using the mechanical energy principle.