Forces, work, energy and power

Forces, work, energy and power
POSTED IN O/A Level PHYSICS, MECHANICS

Forces

Forces are vectors, they have both a size (magnitude) and a direction. By adding up all the forces on an object like vectors you can find the resultant force which will tell you what will happen to the object.

Forces can cause objects to accelerate and it makes logical sense that an object with more mass will accelerate less than an object with less mass when the same force is applied. This gives rise to an important equation:

Where F is the force, m is the mass and a is the acceleration. This can be arranged to be more helpful:

Work done

Work is done when a force is used to move an object. If the direction of movement is the same as the direction of the force then work done can be calculated as:

Where W is the work done, F the force and  is the change in displacement

Work is measured in joules with 1J being equal to a force of 1 Newton moving an object 1 metre, therefore 1J = 1Nm (newton metre)

Work done at an angle

The work done at an angle involves the use of trigonometry:

Where W is the work done, F the force and  is the change in displacement

Energy

Kinetic energy

An object that is in motion has kinetic energy, defined by the equation:

Where E_K is the kinetic energy in joules, m is the mass and v is the velocity of the object.

You can do work to an object to change its kinetic energy. The work done is equal to the change in the kinetic energy:

Where F is the net force,  is the change in the displacement, m is the mass of the object, v is the initial velocity and u is the final velocity

Gravitational potential energy

The gravitational potential energy of the object is the work that gravity can do to an object if it was to fall. The gravitational potential of an object is defined by the equation:

Where E_p is the potential energy in joules, m is the mass of the object, g is the acceleration due to gravity (9.81ms^-2) and h is the height of the object against gravity

Conservation of energy

An object's mechanical energy is the sum of that object's kinetic and gravitational potential energy:

Assuming no energy is lost (e.g. as heat or sound) mechanical energy is conserved. For example if a ball has 100J of mechanical energy which is all gravitational potential energy when it is dropped the gravitational potential energy is converted to kinetic energy, when the ball hits the ground it has 100J of kinetic energy and no gravitational potential energy.

Power

Power is the rate of transfer of energy or rate of work (as work is a transfer of energy). Power is therefore calculated as:

Where P is the power, measured in Watts (1W = 1J per second),  is the energy transferred (work done) and t is the time taken in seconds.

Since  is equal to  (work done):

And since distance over time is equal to average speed...