Work and Kinetic Energy

                 

 FORCE 

               

                       A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force.

Force is basically the component that causes a change in the motion of a body. Like a how a body at rest moves when a force is given.

F = m*a

Force = mass * acceleration

Sample Problem

1.What is the tiger's weight if its mass is 100 kg

mass*gravity= weight

(100kg)(9.8m/s^2)=980 kg m/s^2 or 980N (Newton)

WORK

                Work is the transfer of energy from one object to another, especially in order to make the second object move in a certain direction. Work is equal to the amount of force multiplied by the distance over which it is applied.

Work done is the measurement of force over some distance. Work done helps us understand how much force is used(either given or acquired) in an event. The difference is that work done is a measure of force. Force is the driving component of motion of a body.

W= F*d = m*a*d

 W = work
F = force
d = distance
m = mass
a = acceleration

 Work= mass*acceleration*distance

Example:

 A 10 kg object experiences a horizontal force which causes it to accelerate at 5 m/s^2, moving it a distance of 20 m, horizontally. How much work is done by the force?

mass*acceleration*distance

(10 kg)(5 m/s^2)(20 m)

1000 kg m^2/ s^2 1000 J (Joules)

KINETIC ENERGY

                     Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

KE = 0.5 • m • v 2

m = mass of object

v = speed of object

Example:  Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.

 KE = 0.5*m*v2

KE = (0.5) * (625 kg) * (18.3 m/s)2

KE = 1.05 x105 Joules

 A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr.

KE = 80 000 J The KE is directly related to the square of the speed. If the speed is reduced by a factor of 2 (as in from 60 mi/hr to 30 mi/hr) then the KE will be reduced by a factor of 4. Thus, the new KE is (320 000 J)/4 or 80 000 J. POTENTIAL ENERGY                          An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.

PEgrav = mass • g • height

PEgrav = m *• g • h

Example
 A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

PE = m*g*h

PE = (3 kg ) * (9.8 m/s/s) * (0.45 m)

PE = 13.2 J

 If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart?

  W = F * d * cos θ(if the force is inclined)

W = 14.7 N * 0.9 m * cos (0 degrees)

W = 13.2 J

MECHANICAL ENERGY

                     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.

Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position). A moving car possesses mechanical energy due to its motion (kinetic energy)

TME  = PE + KE

M.E = K. E + P.E
M.E = ½ mv2 + mgh

TME = TOTAL MECHANICAL ENERGY

PE= POTENTIAL ENERGY

KE = KINETIC ENERGY

Example 1

A person is sitting on a building of height 10m and the mass of the person is 50kg, determine the mechanical energy.

Solution:

Given parameters are,

m = 50 kg

h = 10m

the person is not moving, therefore, K. E = 0

Mechanical energy formula is given by,

1. E = 1 / 2mv2 + mgh

Since K.E is 0, the equation becomes,
M.E = mgh
    = 50 ×9.81 ×10
    = 4905 J

Example 2
Determine the mechanical energy of a 20 kg object which is moving with a speed of 10m/s.

Solution:
Given parameters are,
m = 20kg
v = 10m/s
the person is moving, therefore P. E = 0
Mechanical energy formula is given by

1. E = 1 / 2 mv2 + mgh

Since P.E is 0, the equation becomes,
M.E = 1 / 2mv2
= 1 / 2 × 20 ×102

= 1000 J

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