The student is expected to calculate the mechanical energy of, power generated within, impulse applied to, and momentum of a physical system.
A mass in motion has momentum. Momentum is equal to the product of mass and velocity.
Impulse is defined as the force applied to a system times the time interval over which the force is applied. The impulse equals the change in momentum.
In order to change the momentum of a physical system, a force must be applied.
Power is the rate of transferring energy and can be calculated as the rate at which work is done.
Mechanical energy is the sum of potential and kinetic energy.
Mechanical Energy
In the process of doing work, the object that is doing the work exchanges energy with the object upon which the work is done. When the work is done upon the object, that object gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy. The mechanical energy of an object is the sum of the energy of its motion (kinetic energy) and the energy of its position (potential energy).
Kinetic Energy: Mechanical energy can be the energy of motion that is possessed by an object due to its motion and is called kinetic energy (KE). Kinetic energy is a scalar quantity; it has no direction. The equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a two-fold increase in speed, the kinetic energy will increase by a factor of four. The formula for kinetic energy (measured in SI units of Joules) where m is mass and v is velocity is:
Formula for power
Potential Energy: Mechanical energy can also be the stored energy of position and is called potential energy (PE). One example is gravitational potential energy, which is gained when work is done to overcome the force of gravity (when something is raised to a higher level above a surface). The force required to lift an object is equal to the weight of the object, given by mg, where g is the acceleration due to gravity (approximately 9.8 m/s2 at Earth’s surface) and m is the mass of the object. The distance is the increase in vertical distance h, and the work done is the increase in potential energy:
Formula for Gravitational Potential Energy
Power
Any object that possesses mechanical energy - whether it is in the form of potential energy or kinetic energy - is able to do work. The rate at which that work is done is power. Power (P) is the rate of transferring energy and can be calculated as the rate at which work (W) is done on the physical system. The SI unit (International System of Unit) of power is the Watt. The more Watts, the more energy that is transformed. The heater in a house can be 1000 Watts, which means that 1000 Joules of energy will be transformed per second. An air conditioner (A/C) with 1500 Watts tells you how powerful it is.
Formula for power.
Momentum
Momentum (p) is the motion of a moving object. It is a quantity of motion that is based on collisions. Momentum is a vector quantity. It has the direction of the velocity. It can be calculated from the mass (m) and velocity of the physical system (v).
Formula for momentum.
Change in Momentum: In order to change the momentum of a physical system, a force must be applied. For the same object, the result of the momentum change leads to velocity change from v1 to v2. The external force (F) is the reason for this change.
Formula for the change in momentum.
Types of Collisions: From the view of energy, the work done by the force “F” makes the kinetic energy of the object change. In the point of view of momentum conservation, there are two types of collisions.
Elastic: An elastic collision is an encounter between objects in which the total kinetic energy of the objects before and after the collision is equal. In the elastic collision, the kinetic energy and the momentum are both conserved.
Inelastic: However, in another type of collision, inelastic collision, the kinetic energy is not conserved. An inelastic collision is an encounter between objects in which some of the kinetic energy is converted into other forms of energy.
Impulse
In classical mechanics, impulse is a force (F) exerted over a time interval (t) that causes a change in an object’s momentum. Impulse can be calculated from the period of time that a force is applied to a physical system that changes its momentum. As work can cause energy change, the mechanical energy change of a physical system can be calculated from the force that applies to change motion. How much work is done by the force is quantitatively equal to how much the mechanical energy changes.
Formula for impulse.