Momentum And Energy Review BRYCE TOWLE EDCI 270 Click this Home Button to return to the main menu at anytime. Use this to switch from momentum to energy, or to restart a section! Click it now!

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Momentum  First, we will start with the definition of momentum in words. This will help us to derive the equation in a second.  Choose the best definition of momentum from the list below: 1. An Object of Mass M being accelerated by a Force F 2. The amount of force that an object is carrying whilst moving 3. A measure of velocity per unit of time

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Oops! Go Back!

Great!  Excellent Job! An easier way the think about momentum is how much force that one object can exert on another!  Next we’ll work on finding a mathematical formula to use! Click Here to Continue

Deriving Momentum NEXT

Based on the Previous Information:  With the same velocity but a different mass, the baseball provided enough force to break the window, while the much lighter table tennis ball did not.  What can we say about the relationship of mass to momentum?  Click on to the correct relationship between momentum and mass Or

Oops! Sorry, but that’s not quite the right answer! Go back and try again! If a more massive object breaks a window, but less massive object does not, shouldn’t there be more momentum with more mass? Go Back!

Correct!  Momentum is Directly Proportional to mass!  This means that as the mass of the object increases, the momentum increases linearly.  Click Next to Continue finding the Formula for Momentum! NEXT

Deriving Momentum NEXT

Based on the Previous Information:  Two bowling balls of equal mass are rolled towards an arrangement of pins with different velocities. The ball with a higher velocity knocks down all the pins, while the ball thrown at the slower speed does not.  So what can we say about the effect of velocity on momentum?  Click on the correct relationship between momentum and velocity Or

Oops! Sorry, but that’s not quite the right answer! Go back and try again! Both balls have the same mass, but the faster ball knocks down all of the pins. How should momentum be affected by velocity? Go Back!

So Our Final Formula is:  Combining the past information given to us provides: NEXT

Remember: NEXT

Practice Questions 1. What is the momentum of a 2 kg ball traveling at 12 m/s? ANSWER: 24 kgm/s 2. A 2000 kg car travels 90 kilometers in one hour. What is the momentum of the car? ANSWER: 50,000 kgm/s HINT:Remember to change units when finding velocity NEXT

Conservation of Momentum and Collisions

Conservation of Momentum  When there is no net force on a system of objects, the total momentum of the system: Click the correct answer  Does not Change  Changes as Velocity  Is Always Zero

Oops! Sorry, but that’s not quite the right answer! Go back and try again! With no net force to act on the object, there’s no acceleration. Acceleration is the change in velocity, so with no acceleration, there is no change in velocity Go Back!

Oops! Sorry, but that’s not quite the right answer! Go back and try again! Just because there’s no net force, doesn’t mean that momentum is equal to zero. Go Back!

Right!  Whenever we have a system of two or more objects that has no net force being applied on it, the total momentum does not change.  What about when there is a force?  We call this change in momentum (∆P) an Impulse, or a force applied on an object over a small period of time: NEXT

Impulse  A force always acts perpendicularly on an object traveling in the x- direction. How does the particle act?  Click on the letter corresponding to the correct path the particle follows: x y AB

Oops! Sorry, but that’s not quite the right answer! Go back and try again! At every point, the force is perpendicular to the motion. So when traveling to the right, the force is down. To the left, the force is up. Go Back!

Quick Recap.. NEXT

Momentum Quiz Question 1  What is the momentum of a 2 kg baseball traveling at 18 m/s?  36 kg m/s  54 kg m/s  24 kg m/s

Sorry, That is Incorrect NEXT

Correct!  Excellent Job! NEXT

Momentum Quiz: Question 2  A 1500 kg car is traveling at a constant 60 mph. If 1 mph is 0.45 m/s, what is the momentum of the traveling vehicle in kg m/s?  90,000 kg m/s  40,500 kg m/s  200,000 kg m/s

Sorry, That is Incorrect. NEXT

Sorry, That is Incorrect  You were close, but made one error. Your units don’t quite cancel.  Instead of dividing by the conversion factor, if we multiply, we end up getting our units to cancel and end up with the correct units: kg m/s.  By plugging in these values, we end up with 40,500 kg m/s, which is the correct answer. NEXT

That Is Correct!  By correctly canceling your units, you were able to find the correct answer!  Continue on to the next in question NEXT

Momentum Quiz Question 3  Two pool balls of mass 1.5 kg are at play on a table. One ball roles at 2.2 m/s toward the other. Once the two collide head-on, the first ball continues to roll at 0.2 m/s. What is the velocity of the second ball after the collision?  2.4 m/s  1.7 m/s  2 m/s

Sorry, That is Incorrect NEXT

That is Correct!  Excellent job!  Note that since the masses the same for both the balls, we can factor out the mass; it makes no difference what the mass of the objects are!  Had the masses been different, we would not have been able to do this. NEXT

Momentum Quiz Question 4  One train car of mass 200 kg is moving at 9 m/s toward another train car of mass 150 kg at rest. When the two train cars collide, they stick together. What is the velocity of the combined train cars?  5.14 m/s  12 m/s  9 m/s

Sorry, That is Incorrect NEXT

That is Correct!  Nice Job!  Remember that, when dealing with inelastic collisions, the masses are added together and can be thought of as a single mass with a single momentum.  When dealing with elastic collisions, the masses must be thought of and treated individually. NEXT

How to Interpret Your Results  Got them all right?  Excellent! You appear to be well prepared for the test!  Missed One?  Good Job, but it might be a good idea to go over your notes one more time.  Missed two?  Perhaps you should go through the notes and come back here. Try through this again and if you don’t do better, come see me.  Missed three or four?  Come talk to me and we’ll try working through this assignment together. Back to Main Menu

Work And Energy  Choose the best definition for Work:  1. The amount of force applied to an object over a distance  2. The distance a particle travels after a change in momentum  3. The amount of energy per second lost in a system

Oops! Sorry, but that’s not quite the right answer! Go back and try again! Work changes the energy of a system. Think about which definition would apply to that way of thinking. Go Back!

Oops! Sorry, but that’s not quite the right answer! Go back and try again! Work changes the energy of a system. Think about which definition would apply to that way of thinking. Go Back!

Excellent!

Oops! Sorry, but that’s not quite the right answer! Go back and try again! If work is inversely proportional to the distance the force is applied, then more distance means less work. Does this seem reasonable? Go Back!

Oops! Sorry, but that’s not quite the right answer! Go back and try again! If work is inversely proportional to the force applied on an object, then more force means less work. Does this seem reasonable? Go Back!

Good!  Now we have a fundamental formula to find work  Notice that we are using the magnitude of the force, not the vector.  A magnitude of a vector is a scalar, so work is a scalar quantity NEXT

Potential Energy  The energy that describes how much energy that a two-object system can have at any point.  Potential Energy can be changed by doing Work on the system.  Now, we’ll look at deriving the equation to find the change in Potential Energy. NEXT

Deriving Potential Energy NEXT

Deriving Kinetic Energy NEXT

Deriving Kinetic Energy NEXT

Total Energy NEXT

Practice Problems  A 200 kg rollercoaster is at the top of a 20 m high hill. What is the potential energy of the coaster?  Answer: 40,000 J  What is the Kinetic Energy at the bottom of the hill?  Answer: 40,000 J  At what speed is the coaster traveling at the bottom of the hill?  Answer: 20 m/s  HINT: You know the kinetic energy, so solve the kinetic energy equation for velocity NEXT

Work and Energy Quiz Problem 1  While out with your friends, your car unfortunately runs out of gas 380 m from the nearest gas station. You and two of your friends push you 600 kg car with a force of 1200 N. What is the work done pushing your car to the gas station?  J  380,000 J  228,000,000 J

Sorry, That is Incorrect  Remember, W = F*∆x  The mass given is simply extra information! We don’t need it to solve the problem! NEXT

That is Correct!  Good Work!  Work is just the net force multiplied by the distance over which the force is applied.  The mass given is simply extra information! We don’t need it to solve the problem! NEXT

Work and Energy Quiz Problem 2  An 83 kg skydiver is in his airplane at 1020 m above the ground. What is his potential energy?  84,660 J  624,000 J  846,600 J

Sorry, That is Incorrect  Remember: PE = mgh  An easy way to remember the equation is by remembering work and Newton’s Second Law.  W = F* x  F = ma  This gives us 846,600 J NEXT

That is Correct!  Well Done!  Remember: PE = mgh  An easy way to remember the equation is by remembering work and Newton’s Second Law.  W = F* x  F = ma NEXT

Work and Energy Quiz Problem 3  The 83 kg skydiver now pulls his paracheute very close to the ground (so assume that h is zero. He’s alright though). At what speed is he traveling just before he pulls his ‘cheute?  101 m/s  86 m/s  142 m/s

Sorry, That is Incorrect  We are assuming that all of the energy is now Kinetic Energy (i.e. Potential Energy is zero).  Therefore, the total energy (Answer to the last Problem) is now the kinetic energy.  Solve the Kinetic Energy Equation for velocity to get 142 m/s. NEXT

That is Correct!  Now that there is no Potential Energy, all of the energy from problem 2 is now Kinetic Energy.  Solving the Kinetic Energy equation for velocity, you were able to obtain the correct answer. NEXT

Work and Energy Quiz Question 4  When the skydiver is at 400 m above the ground, he has both Kinetic and Potential energies. What is the Potential Energy and velocity of the skydiver at this point?  PE = 332,000 J, v = 124 m/s  PE = 514,600 J, v = 97.2 m/s  PE = 332,000 J, v = m/s

Sorry, That is Incorrect  Knowing the height, we can simply plug into the Potential Energy formula to find PE = 332,000 J.  We know that the total energy doesn’t change, so the Kinetic Energy is E – PE = 514,600 J.  Solve the kinetic energy for velocity and plug in the values to get v = m/s. NEXT

That is Correct!  Good Work!  Knowing the height, we can simply plug into the Potential Energy formula to find PE = 332,000 J.  We know that the total energy doesn’t change, so the Kinetic Energy is E – PE = 514,600 J.  Solve the kinetic energy for velocity and plug in the values to get v = m/s. NEXT

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