Download The work done on an object by an external force is given by the

Work
The work done on an object by an external force is given by the formula
Wdone = force displacement
Work is our first example of a scalar product or dot product. A dot product occurs when
two vectors are multiplied together in such a way as to produce a scalar value.
Technically, the above definition for work can be calculated with the equation
Wdone = ||F|| * ||s|| cos(θ)
where : ||F|| represents the magnitude or the length of vector F, ||s|| represents the
magnitude or the length of vector s, θ represents the magnitude of the angle between F
and s. Or, it can equivalently be evaluated with the formula: Wdone = Fx * sx + Fy * sy
Where: the x- and y-components of F and s are multiplied and then added together.
Kinetic Energy
Energy is defined as the ability to do work and is a scalar quantity. Energy has no
direction, only magnitude. Mechanical energy comes in two varieties: kinetic energy
(KE) and potential energy (PE).
Kinetic energy represents the energy caused by an object's motion: KE = ½mv2
kg (m/s)2 = kg m2/s2 is called a joule (J).
Gravitational potencial energy
This type of potential energy represents the energy an object possesses by virtue of its
location in a gravitational field.
PE = mgh
where: h is the height above an arbitrary zero level that is convenient for the solution of
the problem. For instance, the zero level might be assigned as the base of a cliff for a
projectile being thrown from the top of the cliff or the zero level might be the floor for a
marble rolling off a table onto the ground.
The expression mg represents the objects weight or the force of gravitational attraction
between the earth and the object. Forces are measured in newtons. Thus the expression
Nm also equals a joule (J).
The work-energy theorem states that the net work done on an object equals the change
in its kinetic energy. That is, when an external force moves an object through a distance
it does work on the object which is evidenced by a change in its velocity or its kinetic
energy, KE = ½mv2.
Wdone = ∆KE
Suppose a constant net force Fnet acts on an object of mass m over some distance .
Newton's Second Law tells us that the object will have an acceleration a = Fnet/m. If the
object's initial velocity was vo and its final velocity is v, kinematics tells us that:
Multiplying both sides of this equation by the object's mass, m, gives:
Rearranging:
Since Fnet = ma (Newton's Second Law), we can substitute:
then divide both sides of the equation by 2:
1. A force of 50 N, applied at an angle of 37º to the horizontal, is required to drag a
block across the table at a constant velocity of 0.7 m/sec.
a. If the coefficient of friction between the block and the table is 0.20, what is the
mass of the block?
b. If the block is pulled for a total of 3 seconds, how much work was done by the
applied force
2. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m.
What is the average net force on the truck?
3. A force of 6.0 N is used to accelerate a mass of 1.0 kg from rest for a distance of
12m. The force is applied along the direction of travel. The coefficient of kinetic friction
is 0.30. What is the
a. Work done by the applied force?
b. Work done by friction?
c. Kinetic energy at the 12-m mark?
4. A 0.600-kg particle has speed of 2.00 m/s at point A and kinetic energy of 7.50 J at
point B. What is
a. Its kinetic energy at A?
b. Its speed at B?
c. The total work done on the particle as it moves from A to B?
Conservation of energy
There is a relationship between work and mechanical energy change. Whenever work is
done upon an object by an external or nonconservative force, there will be a change in
the total mechanical energy of the object. If only internal forces are doing work (no
work done by external forces), there is no change in total mechanical energy; the total
mechanical energy is said to be "conserved." The quantitative relationship between
work and the two forms of mechanical energy is expressed by the following equation:
KEi + PEi + Wext = KEf + PEf
Forces can be categorized as internal forces or external forces. There are many
sophisticated and worthy ways of explaining and distinguishing between internal and
external forces. Many of these ways are commonly discussed at great length in physics
textbooks. For our purposes, we will simply say that external forces include the applied
force, normal force, tension force, friction force, and air resistance force. And for our
purposes, the internal forces include the gravity forces, magnetic force, electrical force,
and spring force.