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Energy2.notebook
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February 05, 2019
Topic 2: Work, Energy and PowerEnergy is the ability to do work. Energy is a scalar quantity. When work is done on or by a system, the total energy of the system is changed. Energy is common in many forms.
Terms you may have heard: Potential, Kinetic, Thermal(heat), Nuclear, etc...
(Energy will be discussed in greater detail soon)
WORK
Work is the transfer of energy to an object when object moves due to the application of a force. Work is a scalar quantity. The amount of Work done on an object, W, is the product of the force, F, along the direction of the displacement, and the displacement,d, of the object. The work done on the object produces a change in the object's total energy.
W = F * d
"Work makes you mad!'
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Examples: 1. A 2.3 kg block rests on a horizontal surface. A constant force with a magnitude of 5N is applied to the block at an angle of 30 degrees to the horizontal. Calculate the work done in moving the block 6m to the right along the surface.
2. how much work is done by the person on the block?
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PowerThe rate at which work is done is a scalar quantity called power.
A 7.8 * 102 N man does 8.58 * 103 J of work in 12.3 seconds running up three flights of stairs to a landing vertically above his starting point. Calculate the power developed by the man.
A constant horizontal force of 6N to the left is applied to a box on a counter to overcome friction. Calculate the power dissipated in moving the box 3 meters to the left in 1.5 seconds.
In raising an object vertically at a constant speed of 2 meters per second, the power developed is 18 watts. Calculate the weight of the object.
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How much work is done by the lifter?
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Forms of EnergyEnergy has many forms, including thermal, nuclear, chemical, electromagnetic, sound, and mechanical. Whatever its form, energy is measured by the amount of work it can do.
Thermal Energy(heat) is a measure of the total kinetic energy of individual particles in a system.
Internal Energy total potential and kinetic energy possessed by the particles that make up an object, but excludes the potential and kinetic energies of the system as a whole.
Nuclear Energy is the energy released by nuclear fission or nuclear fusion.
Electromagnetic energy energy present in electric or magnetic fields. Ex: Visible Light, microwaves,and radio waves
Devices for converting energy:
photocell
generator
motor
battery
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Potential EnergyThe energy possessed by an object due to its position or condition. If NO energy if lost due to friction then the work done to bring an object to a different position or condition from its original condition or position is equal to the objects change in potential energy.
Gravitational Potential Energy(GPE):
Energy an object possess due to its position above the earth's surface or relative to some starting position.
PE = mg h
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Example:
Calculate the gravitational potential energy with respect to the floor gained by a 2kg object as a result of being lifted from the floor to the top of a .92 meter high table.
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Do now:
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Elastic Potential Energy
The energy stored in a spring, when work is done in elongating or compressing the spring is called the elastic potential energy.
Hooke's Law
In order to discuss elastic potential energy we must first discuss the spring force. A force a spring exerts is known as a restorative force, the spring pushes against the applied force because the spring always wants to return to its original rest (equilibrium) position. When a force is applied on a spring it will displace until it reaches a new equilibrium.
Remember equilibrium means net force equals 0N.
Fs = kx
Fs > is the force of the spring
k > spring constant
x > displacement of the spring
The spring constant "k" is a measure of the hardness of a spring, every spring has a unique spring constant. One must be careful when elongating or compressing a spring, too much displacement can exceed the spring limit and break the spring.
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Examples
1. A mass of 3kg hangs from a spring and causes the spring to displace 2cm from its rest position. determine the spring constant of the spring.
Hanging masses from springs.
Replace the 3kg block with a 10kg block and determine the new displacement.
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Bonus:Two equal forces of 10N are pulling an object upward at constant speed. How much work is done in lifting the object 5 meters?
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Bonus:
Two ropes pull a boat across the water at a constant speed. Both ropes are exerting an equal force of 10N. How much work is done moving the boat directly to the right 30 meters?
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Elastic Potential Energy
By compressing/elongating the spring we increase the spring's potential energy.
PEs = 1/2 kx2
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A force of 30N causes a spring to compress 0.5 meters. Determine the potential energy of the spring.
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Kinetic Energy energy in motion
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Examples
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ExamplesA force of 60N acts on a block initially at rest on a horizontal frictionless surface for a distance of 3m. If the block has a mass of 4kg, determine the blocks change in kinetic energy. How fast is the block moving after traveling the three meters.
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Total Work The work energy relationship
Recall that the work done on an object causes the objects energy to change. But what kind of energy!? It depends on how the question is worded.
W = Change in Energy
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ExampleA 70kg runner runs up a hill at constant speed. At the top of the hill the runner is at a height of 30 meters . If the runner does 800J of work against friction, what is the total work done by the runner?
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A 70kg runner runs up a hill. at the bottom of the hill her initial velocity is 3m/s, at the top of the hill her speed is 5m/s. At the top of the hill the runner is at a height of 30 meters. If the runner does 800J of work against friction, what is the total work done by the runner?
Example
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Example500J of work is used to lift a 4kg block ,attached to a rope through a pulley, 10 meters vertically at constant speed . Determine the amount of work done against friction.
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ExamplesDetermine the amount of work required to move a 5kg block initially at rest to a speed of 4 m/s in 6 meters, horizontally across a surface if the kinetic friction between the block and surface is 15N.
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Conservation of EnergyThe first law of thermodynamics, also known as Law of Conservation of Energy, states that energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another.
What happens to the energy of an object when it is thrown upwards?
What happens to the energy of an object when it is dropped?
How do most roller coasters work?
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For our purposes when investigating conservation of energy we will be looking at a closed system that loses no energy to friction or as heat. Therefore total mechanical energy will remain the same throughout.
Total mechanical Energy = Kinetic Energy + Potential Energy
Lets look at an example we had in the beginning of the year.
A 1kg ball is thrown upwards with a speed of 10 m/s. How high does it go?
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A 5kg box initially at rest is allowed to slide down a frictionless ramp 2 meters above the ground. If the ramp has an incline of 15 degrees determine the speed of the cart at the bottom of the incline.
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A 4kg box slides across a frictionless surface at 2 meters per second. The box slides onto an incline angled at 20 degrees. How high above the ground does the object go? How far up the incline does the object go?
If the angle of the incline were to be increased to 30 degrees how high and how far would the object go compared to the 15 degree incline.(no math)
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SEMESTER 2 DAY 1 Remember, energy cannot be created nor destroyed but can be transferred
A 100kg snowboarder slides down a frictionless ramp. Determine the snwbrdrs kinetic energy at the bottom of the ramp.
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Kinetic energy and elastic potential energy.
A 2kg block slides along a frictionless surface at 2m/s. The block collides with a spring and it compresses the spring until the block comes to a full stop. Determine how much potential energy will be in the spring.
If the spring has a constant of 20 N/m, how much does the spring compress?
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A .1kg arrow is knocked on a bow and drawn .2m from a rest position. If the bowstring has a spring constant of 100N/m, determine the speed the arrow leaves the bow.
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ex. At the bottom of its swing a 3kg mass has a speed of 5m/s. Determine the height the mass will reach
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At a position of 12 cm above the starting rest position a bob attached has equivalent potential and kinetic energies. Determine how fast the bob is moving at the position.
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Ballastic PendulumA tool used to measure the energy stored in a bullet. Used to determine speeds of moving projectiles. Ballastic pendulum combines the concepts of conservation of energy and conservation of momentum.
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A .01 kg bullet moving at 300m/s is fired into a 3kg block attached to a pendulum. The bullet lodges itself into the block and proceeds to swing the pendulum. How high above the ground will the pendulum swing?
