Vanessa, Rochelle, Melinda

Work Definition: Work is a force applied through a distance. It is the product of the force exerted on an object and the distance the object moves in the direction of the force.

Calculating Work/Force/Displacement:
- work can be calculated by multiplying the force by the distance
- measured in joules (J)
equation: W = Fd

Work/Force/Displacement Examples:
1. How much work is done when a waiter carries a 250N tray up 4m of stairs?
W = Fd
W = 250N x 4m
W = 1,000J

2. 148J lifts box A 0.800m. How much does box A weigh?
W = Fd
F = W/d
F = 148J x 0.800m
F = 185N
The box weight 185N.

Power Definition: Power is the rate of doing work, or the rate at which energy is transferred. It is measured in watts (W).

Calculating Power/Work/Time
- power is work done divided by the time it takes
equation: P = W/t

Power/Work/Time Examples
1. How much power, in kW, does an elevator use to lift a 9.0 x 10^3kg elevator up 33m in 12s?
F = ma
F = (9.0 x 10^3) (9.8)
F = 88200N

W = Fd
W = 88200N x 33m
W = 2910600J

P = W/t
P = 2910600J/12s
P = 242550W
= 242.5kW

2. In order to ride a bike 20km in 1 hour, 5kW of power is used. If we assume that the rider supplied a constant force over this time, calculate the magnitude of the force.
P = W/t
W = P x t
W = 5000W x 3600s
W = 1.8 x 10^7

W = Fd
F = W/d
F = (1.8 x 10^7)/(20000m)
F = 900N
Efficiency Definition: Efficiency is the ratio of output work to input work, where the work output is the work done by the machine and the work input is the work done by the person to operate the machine. An ideal machine has equal output and input work, therefore W0/Wi = 1 and the efficiency is 100%. Efficiency is expressed in terms of the mechanical advantage (MA) and the ideal mechanical advantage (IMA). The equation = W0/Wi x 100%, or MA/IMA x 100%.

Efficiency Examples:
1. Wile E. Coyote raises a 750kg boulder to a heigh of 10m using an ACME pulley system. The pulley system has an 80% efficiency rating. How far will Wile E. need to pull the rope if 392N of force is needed to use the pulley system?

E = W0/Wi x 100%
80 = (75) (9.8) (10) / (392) (d)
d = 234m

2. A student uses the bicycle wheel with gear radius 4.00cm and wheel radius 35.6 cm. When a force of 155 N is exerted on the chain, the wheel rim moves 14 cm. Due to friction, its efficiency is 95%. What is the IMA and MA of the wheel and gear?
4cm/35.6cm = 0.112

MA = efficiency x (IMA/100%)
= (95%) (0.112) / 100%
= 0.107
Energy Definition: Energy is the capacity of a physical system to perform work. Energy exists in several forms such as heat, kinetic or mechanical energy, light, potential energy, electrical, or other forms.

Gravitational Potential Energy Definition: The energy gained by an object as its height above ground level increases. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be a constant at about 9.8m/s^2

Energy Examples:

2. A baseball is thrown up in the air with an initial velocity v0. What is the highest point it reaches?

The initial kinetic energy of the baseball is

external image Chapter765.gif

At its highest point the velocity of the baseball is zero, and therefore its kinetic energy is equal to zero. The work done on the baseball by the gravitational force can be obtained:

W = Kf - Ki = - Ki

In this case the direction of the displacement of the ball is opposite to the direction of the gravitational force. Suppose the baseball reaches a height h. At that point the work done on the baseball is

W = - m g h

The maximum height h can now be calculated:
external image Chapter766.gif
external image Chapter767.gif

Kinetic Energy Definition: The energy of a mass in motion.

The following steps of information was obtained from the website: It is very helpful with providing steps and examples and covers a range of topics under work and kinetic energy.

An object is moving with a certain velocity indicates that at some time in the past work must have been done on it. Suppose our object has mass (m) and is moving with velocity (v). Its current velocity is the result of a force (F). For a given force F we can obtain the acceleration of our object:
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Assuming that the object was at rest at time t = 0 we can obtain the velocity at any later time:
external image Chapter754.gif
Therefore the time at which the mass reaches a velocity v can be calculated:
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1. A 46.0kg child cycles up a large hill to a point that is a vertical distance of 5.25 m above the starting position. Find:

a) the change in the child's gravitional potential energy
potential energy = mgh
= (46 kg) x (9.8 m/s) x (5.25m)
= 2366.7 J

b) the amount of work done by the child against the gravity
W = force x distance

Force = mass x accleration
= (46 kg) (9.8 m/s)
= 450.8 N

Now that the force is calculated, it can be plugged into the previous equation of:
Work Formula:
=force x distance
=(450.8 N) x (5.25 m)
= 2366.7 J

    • After these calculations we notice that the answers from part a and b are the same! This proves that work = change in potential energy.

Temperature: The measure of the heat of an object from a scale.

Thermal energy: The total kinetic and potential energy of the motion of particles within an object.

Specific heat capacity: The quantity of energy that is needed to raise the temperature of a unit mass by one temperature unit.

-Specific heat capacity can be determined by using the equation: Q= CM ∆T (Q= heat added, C=specific heat, M=mass, ∆T=change in temperature).

-The following link provides a detailed representation of specific heat capacity:

-The mass of an object greatly effects thermal energy and the specific heat capacity. When determining the specific heat capacity of an object, mass must be determined in order to solve the equation (Q= CM ∆T).

-The specific heat capacity varies depending on the material or substance of an object. In general, certain materials such as metal have a higher heat capacity in comparison to water or air.

-A change in temperature also depends on the material and composition of an object. An example of a good conductor of heat would be metal because of the compositions of particles within it. The change in temperature of an object relies on the movement of particles (atoms) within the object. Given that the particles in metal are close to each other, they consequently vibrate at a fast pace which causes a rapid change in temperature. Since metals are a great conductor of heat, it is able to increase in temperature at a faster rate than a material such as rubber.

-The following link shows the thermal conductivity of numerous metals, proving that metal are great conductors of heat and that they are sensitive to changes in temperature.

-Work can be determined by the quantity of force multiplied by the distance (W=F×D). Work involves the energy transformation of an object and there are numerous types of energy involved in the movement of an object. For example, when lifting a box, there is potential energy before the box is lifted. This energy is transformed into mechanical energy of the hands lifted the box. Mechanical energy converts into kinetic energy as it is being moved. All of these energy transformations are involved (in work) to move the box.

Law of Conservation: Energy can change its form within a closed and isolated system; however the total amount of energy remains constant.

-The following link demonstrates the Law of Conservation through the movement of a pendulum. As the pendulum its changes its form of energy from potential to kinetic energy however, the total amount of energy stays constant.

-The following link also uses a pendulum to describe the law of conservation. Using the information from the example, the potential energy of the pendulum is 19.6 joules and the kinetic energy is 0 joules (at the initial position). Halfway through the movement of the pendulum, kinetic energy reaches a maximum of 19.6 joules while potential energy reaches 0 joules. Finally, the pendulum has a maximum potential energy of 19.6 joules again while kinetic energy is 0 joules. This change in energy continues as the pendulum swings, yet the total amount of energy is always constant. This essentially causes the pendulum to consistently swing back and forth until friction slows it down. Therefore (according to the Law of Conservation), when there are changes in energy (gravitational, potential, kinetic, and thermal) of an object, the total amount of energy always remains constant.