Work Energy And Power Example Problems
Concepts
Work

Definition: Work is done when a force causes an object to move in the direction of the force. Mathematically, work is calculated as the dot product of the force and the displacement.

Positive and negative work: Work is done by a constant force in the direction of the force is taken to be positive and against the direction of the force as negative.

Units of work: The SI unit of work is the joule (J), which is defined as the work done when a force of one newton (N) is applied over a distance of one meter (m) in the direction of the force.
Energy:

Definition: Energy is the ability to do work or cause change. It is a scalar quantity.

Various forms of energy: There are many different forms of energy, including kinetic energy (the energy of motion), potential energy (the energy stored in a system due to its position or configuration), thermal energy (the energy associated with the random motion of particles), and electrical energy (the energy associated with the movement of electric charges).

Units of energy: The SI unit of energy is the joule (J), which is the same unit used to measure work.
Power:

Definition: Power is the rate at which work is done or energy is transferred. Mathematically, power is calculated as the scalar product of the force and the velocity of the object.

Scalar quantity: Power is a scalar quantity, meaning it has only magnitude and no direction.

Relationship between work, energy, and power: Power is related to work and energy by the equation:
Power = Work / Time
Energy = Work done = Power x Time
 Units of power: The SI unit of power is the watt (W), which is defined as one joule per second (1 W = 1 J/s).
Example Problems
Calculating the work done by a force acting on an object over a distance
A force of 10 N is applied to an object, causing the object to move a distance of 5 meters in the direction of the force. Calculate the work done.
Solution:
Using the definition of work, we have:
Work = Force x Displacement x cosθ
Work = 10 N x 5 m x cos 0°
Work = 50 J
Therefore, the work done by the force is 50 J.
Determining the kinetic energy of an object based on its mass and velocity
An object with a mass of 10 kg is moving at a velocity of 5 m/s. Calculate the kinetic energy of the object.
Solution:
Using the formula for kinetic energy, we have:
Kinetic energy = (1 / 2) mv^2
Kinetic energy = (1 / 2) x 10 kg x (5 m/s)^2
Kinetic energy = 125 J
Therefore, the kinetic energy of the object is 125 J.
Calculating the potential energy of an object based on its mass, height, and acceleration due to gravity
An object with a mass of 20 kg is 10 meters above the ground. Calculate the potential energy of the object due to its position in the Earth’s gravitational field (acceleration due to gravity = 9.8 m/s2).
Solution:
Using the formula for potential energy, we have:
Potential energy = mgh
Potential energy = 20 kg x 9.8 m/s2 x 10 m
Potential energy = 1960 J
Therefore, the potential energy of the object due to its position is 1960 J.
Calculating the power required to lift an object at a certain speed against the force of gravity
A force of 500 N is required to lift an object a height of 10 meters in 2 seconds. Calculate the power required to perform this task against gravity.
Solution:
Using the definition of power, we have:
Power = Work done / Time
First, calculate the work done by the force:
Work done = Force x Displacement x cos θ
Work done = 500 N x 10 m x cos 0° = 5000 J
Then, substitute work and time into the power equation:
Power = Work done / Time
Power = 5000 J / 2 s = 2500 W
Therefore, the power required to lift the object is 2500 W.