Physics_Topic_4-6
Momentum is Always, Always, Always conserved in isolated systems (no outside forces acting).
REMEMBER THIS
Spring:
The applied force was non-conservative Energy (specifically Us) was added
Large k = stiff spring
stiff spring
average power
the amount of work done over a time interval
Elastic Potential Energy
the energy of stretched or compressed objects
When the spring is located at it maximum compressed position, -xmax,
the spring force is in the direction of the displacement, so positive work is being done. This will make the object move faster and faster.
Conservation of Energy
the total energy of an isolated system is conserved
Non-Conservative Force characteristic
the work done by a non-conservative force adds or removes mechanical energy from a system.
Change in potential energy
work done against a conservative force ΔU = -Wc
non-conservative system
some mechanical energy is added or removed: ΔK +ΔU = Wnc ≠ 0
Impulse
"How much force and for how long"
average force
(= ½ maximum force)
Center of Mass
*point where you could balance the object. *It represents the point where all the mass appears to be concentrated. *If a external force acts on the object, it will move as if the net force were applied directly to a single particle of mass M located at the center of mass. *This behavior is independent of other motions, such as rotation or vibration, or deformation of the object.
power old unit
1 horsepower (hp) = 746 W
momentum unit
= kg m/s = N.s
Kinetic Energy, K
=If there is a net force then there is acceleration =Acceleration means change in velocity
An arrow is drawn back so that 50 Joules of potential energy is stored in the stretched bow and string. When released, the arrow will have a kinetic energy of ______ Joules. A.50 B. more than 50 C. less than 50
A A drawn arrow has 50 J of stored energy due to the stretch of the bow and string. When released, this energy is converted into kinetic energy such that the arrow will have 50 J of kinetic energy upon being fired. Of course, this assumes no energy is lost to air resistance, friction or any other non-conservative forces and that the arrow is shot horizontally.
Bouncing
A ball that bounces when dropped on the floor has a larger change in momentum than a similar ball that does not. This in turn may translate to a larger force exerted by the floor on the ball (and vice versa). The larger force is not a given since the change in momentum is not equal to force, but to impulse - in other words, there could be a larger time involved, too.
Conservative Forces
A force is conservative if the work done by (or against) the force in moving an object is independent of the path of the object.
Potential Energy, U
Conservative forces Potential energy
Classify of the following forces as conservative or non-conservative forces. a)Air resistance. b)Elastic (spring) force. c)Friction forces. d)The force of gravity.
Conservative: B D Non-conservative: A C
Which of the following statements are true about conservative and non-conservative forces? Include all that apply. A force is regarded as a conservative force if it does work but does not remove mechanical energy from a system of objects. A force is regarded as a non-conservative force if it does not add mechanical energy to a system of objects. If a non-conservative force acts upon an object, then the object will either gain or lose mechanical energy. If the only forces which do work upon an object are conservative forces, then the object will conserve its mechanical energy. If the sum of an object's K and U is remaining constant, then non-conservative forces are NOT doing work. If work is NOT done on an object by a non-conservative force, then the object will experience a transformation of energy from kinetic to potential energy (or vice versa).
Answer: A(sort of) DE F(sort of) A. TRUE (sort of) - If a force does work, yet does not remove mechanical energy from an object, then it is definitely a conservative force. The sort of indicates that a force is also considered a conservative force if it does work and does not add mechanical energy to an object. B. FALSE - If a force does not add mechanical energy to a system of objects, then it is likely a conservative force (provided it doesn't remove mechanical energy either). Non-conservative forces are those which either add or remove energy from a system of objects. C. FALSE - Not only must the force act upon the object, it must also be doing work upon the object. As you sit in your chair, there is a non-conservative force (normal force) acting upon your body. But since it does not do work (it's being assumed that you are not sitting in one of those fancy lounge chairs that has more controls than a TV set), your mechanical energy is not changing. D. TRUE - This is a big principle. You must know this one! E. TRUE - Non conservative forces would alter the total mechanical energy; that is, the U + K would not be a constant value. F. TRUE (sort of) - This statement is true (sort of); when only conservative forces are doing work, an object has its kinetic energy transformed into potential energy (or vice versa) without the total amount of the two being altered. It would however be possible that work is not done by a non-conservative force and there be no transformation of energy at all; i.e., the object remains at rest. A conservative force must be doing work in order for there to be a transformation of energy.
Which of the following statements are true about power? Include all that apply. =Power is a time-based quantity. =Power refers to how fast work is done upon an object. =Powerful people or powerful machines are simply people or machines which always do a lot of work. =A force is exerted on an object to move it at a constant speed. The power delivered by this force is the magnitude of the force multiplied by the speed of the object. =The standard metric unit of power is the Watt. =If person A and person B do the same job but person B does it faster, then person A does more work but person B has more power. =The newton·meter is a unit of power.
Answer: ABDE a. TRUE - Power is a rate quantity and thus time-based. b. TRUE - This is the definition of power. c. FALSE - This is not always the case. A machine can do a lot of work but if it fails to do it rapidly, then it is not necessarily powerful. In fact two machines can do the same task (and therefore the same work), yet they can have drastically different power ratings. d. TRUE - An equation for computing work in constant speed situations is P=F•v. e. TRUE - Watt is the unit of power? Yes!! f. FALSE - Vice versa. If two people do the same job, then they're doing the same amount of work. The person who does it fastest generates more power. g. FALSE - A N•m is a Joule and that is a unit of work (not power). Think force (N) times distance (m); that's work (J).
Which of the following statements are true about collisions? Include all that apply. =Two colliding objects will exert equal forces upon each other even if their mass is significantly different. =During a collision, an object always encounters an impulse and a change in momentum. =During a collision, the impulse which an object experiences is equal to its velocity change. =The velocity change of two respective objects involved in a collision will always be equal. =In a collision, the two colliding objects could have different acceleration values. =Total momentum is always conserved between any two objects involved in a collision.
Answer: ABE a. TRUE - In any collision between two objects, the colliding objects exert equal and opposite force upon each other. This is simply Newton's law of action-reaction. b. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its momentum. c. FALSE - The impulse encountered by an object is equal to mass multiplied by velocity change - that is, momentum change. d. FALSE - Two colliding objects will only experience the same velocity change if they have the same mass and the collision occurs in an isolated system. However, their momentum changes will be equal if the system is isolated from external forces. e. TRUE - Two colliding objects will exert equal forces upon each other. If the objects have different masses, then these equal forces will produce different accelerations. f. FALSE - Total momentum is conserved only if the collision can be considered isolated from the influence of net external forces.
Which of the following statements are true about collisions? Include all that apply. =Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a continuum; where a particular collision lies along the continuum is dependent upon the amount kinetic energy which is conserved by the two objects. =Momentum is conserved in an elastic collision but not in an inelastic collision. =The kinetic energy of an object remains constant during an elastic collision. =A ball is dropped from rest and collides with the ground. The higher that the ball rises upon collision with the ground, the more elastic that the collision is. =The collision between a tennis ball and a tennis racket tends to be more elastic in nature than a collision between a halfback and linebacker in football.
Answer: ADE a. TRUE - A perfectly elastic collision is a collision in which the total kinetic energy of the system of colliding objects is conserved. Such collisions are typically characterized by bouncing or repelling from a distance. In a perfectly inelastic collision (as it is sometimes called), the two colliding objects stick together and move as a single unit after the collision. Such collisions are characterized by large losses in the kinetic energy of the system. b. FALSE - Momentum can be conserved in both elastic and inelastic collisions provided that the system of colliding objects is isolated from the influence of net external forces. It is kinetic energy that is conserved in a perfectly elastic collision. c. FALSE - In a perfectly elastic collision, in an individual object may gain or lose kinetic energy. It is the system of colliding objects which conserves kinetic energy. d. TRUE - If large amounts of kinetic energy are conserved when a ball collides with the ground, then the post-collision velocity is high compared to the pre-collision velocity. The ball will thus rise to a height which is nearer to its initial height. e. TRUE - There is significant bounce in the collision between a tennis racket and tennis ball. There is typically little bounce in the collision between a halfback and a linebacker (though there are certainly exceptions to this one). Thus, the ball-racket collision tends to be more elastic.
A platform diver weighs 500 N. She steps off a diving board that is elevated to a height of 10 meters above the water. The diver will possess ___ Joules of kinetic energy when she hits the water. A. 10 B. 500 C. 510 D. 5000 E. more than 5000
D The use of the work-energy theorem and a simple analysis will yield the solution to this problem. Initially, there is only U; finally, there is only K. Assuming negligible air resistance, the kinetic energy of the diver upon hitting the water is equal to the potential energy of the diver on top of the board. Ui = Kf m∙g∙hi = Kf Substituting 500 N for m∙g (500 N is the weight of the diver, not the mass) and 10 m for h will yield the answer of 5000 J.
Which of the following statements are true about momentum? Include all that apply. =Momentum is a vector quantity. =The standard unit on momentum is the Joule. =An object with mass will have momentum. =An object which is moving at a constant speed has momentum. =An object can be traveling eastward and slowing down; its momentum is westward. =Momentum is a conserved quantity; the momentum of an object is never changed. =The momentum of an object varies directly with the speed of the object. =A less massive object can never have more momentum than a more massive object.
Answer: ADG a. TRUE - Momentum is a vector quantity. Like all vector quantities, the momentum of an object is not fully described until the direction of the momentum is identified. Momentum, like other vector quantities, is subject to the rules of vector operations. b. FALSE - The Joule is the unit of work and energy. The kg m/s is the standard unit of momentum. c. FALSE - An object has momentum if it is moving. Having mass gives an object inertia. When that inertia is in motion, the object has momentum. d. TRUE - This is true. However, one should be quick to note that the object does not have to have a constant speed in order to have momentum. e. FALSE - The direction of an object's momentum vector is in the direction that the object is moving. If an object is traveling eastward, then it has an eastward momentum. If the object is slowing down, its momentum is still eastward. Only its acceleration would be westward. f. FALSE - To say that momentum is a conserved quantity is to say that if a system of objects can be considered to be isolated from the impact of net external forces, then the total momentum of that system is conserved. In the absence of external forces, the total momentum of a system is not altered by a collision. However, the momentum of an individual object is altered as momentum is transferred between colliding objects. g. TRUE - Momentum is calculated as the product of mass and velocity. As the speed of an object increases, so does its velocity. As a result, an increasing speed leads to an increasing momentum - a direct relationship. h. FALSE - A less massive object would have a greater momentum owing to a velocity which is greater than that of the more massive object. Momentum depends upon two quantities * mass and velocity. Both are equally important.
Which of the following statements are true about work? Include all that apply. =The force of friction acts upon a softball player as she makes a headfirst dive into third base. This is an example of work being done. =An eraser is tied to a string; a person holds the string and applies a tension force as the eraser is moved in a circle at constant speed. This is an example of work being done. =A force acts upon an object at a 90-degree angle to the direction that it is moving. This force is doing negative work upon the object. =An individual force does NOT do positive work upon an object if the object is moving at constant speed. =An object is moving to the right. A force acts leftward upon it. This force is doing negative work. =A non-conservative force is doing work on an object; it is the only force doing work. Therefore, the object will either gain or lose mechanical energy.
Answer: AEF A. TRUE - There is a force and a displacement; the force acts in the opposite direction as the displacement and so this force does negative work. B. FALSE - For uniform circular motion, the force acts perpendicular to the direction of the motion and so the force never does any work upon the object. C. FALSE - If a force acts at a 90-degree angle to the direction of motion, then the force does not do any work at all. Negative work is done when there is a component of force opposite the direction of motion. D. FALSE - There are many instances in which an individual force does positive work and yet the object maintains a constant speed. Consider a force applied to lift an object at constant speed. The force does positive work. Consider a car moving at constant speed along a level surface. The force of the road on the tires does positive work while air resistance does and equal amount of negative work. E. TRUE - A force which acts in a direction opposite the motion of an object will do negative work. F. TRUE - When non-conservative forces do work upon an object, the object will either gain or lose mechanical energy. Mechanical energy is conserved (neither gained nor lost) only when conservative forces do work upon objects.
Which of the following statements are true about mechanical energy? Include all that apply. The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy. Heat is a form of mechanical energy. The mechanical energy of an object is always conserved. When non-conservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved. When a friction force does work on an object , the total mechanical energy of that object is changed. The total mechanical energy of an object remains constant if the only forces doing work on the object are conservative forces. If an object gains mechanical energy, then one can be certain that a non-conservative force is doing work.
Answer: AEFG A. TRUE - This is the definition of mechanical energy. B. FALSE - Heat or thermal energy is a non-mechanical form of energy. Potential and kinetic energy are the only forms of mechanical energy. C. FALSE - The mechanical energy of an object is only conserved if non-conservative forces do not do work upon the object. D. FALSE- If a non-conservative force does work upon an object, then the total mechanical energy of that object is changed. Energy will not be conserved. E. TRUE - Friction is a non-conservative force and thus alters the total mechanical energy of an object. F. TRUE - This is the conservation of energy principle and one that you need to firmly understand. G. TRUE - If there is any change in the total mechanical energy of an object (whether a gain or a loss), then you know for certain that there is a non-conservative force doing work.
Which of the following statements are true about potential energy? Include all that apply. =Moving objects cannot have potential energy. =Potential energy is the energy stored in an object due to its position. =Both gravitational and elastic potential energy are dependent upon the mass of an object. =If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well. =Gravitational potential energy is lost as objects free-fall to the ground. =The higher that an object is, the more potential energy which it will have. =The unit of measurement for potential energy is the Joule.
Answer: BDEFG a. FALSE - Potential energy has nothing to do with speed; an object could be moving at an elevated position. It is this elevation above zero level which gives an object potential energy. b. TRUE - This is the definition of potential energy. c. FALSE - Gravitational potential energy is dependent upon the mass of the object (PEgrav = m•g•h) but elastic potential energy is dependent upon the spring constant and the compression or stretch length of the spring (PEelastic = 0.5•k•x2). d. TRUE - The equation states that PEgrav = m•g•h; if the h is doubled, then the PE will be doubled as well. e. TRUE - As objects free-fall, the height (h) decreases; subsequently, the PE decreases. f. TRUE - The equation states that PEgrav = m•g•h; PE is directly related to height. g. TRUE - The Joule (abbrev. J) is the standard metric unit of energy - all forms of energy.
Examples of Uses of the Law of Conservation of Mechanical Energy
Dropping an object Throwing a ball off the edge of cliff Rolling down a ramp Pendulum Roller coaster Mass bouncing on a spring
Which of the following statements are true about impulse? Include all that apply. =Impulse is a force. =Impulse is a vector quantity. =An object which is traveling east would experience a westward directed impulse in a collision. =Objects involved in collisions encounter impulses. =The Newton is the unit for impulse. =The kg·m/s ( N·s ) is equivalent to the units on impulse. =An object which experiences a net impulse will definitely experience a momentum change. =In a collision, the net impulse experienced by an object is equal to its momentum change.
Answer: BDFGHI a. FALSE - Impulse is NOT a force. Impulse is a quantity which depends upon both force and time to change the momentum of an object. Impulse is a force acting over time. b. TRUE - Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it. c. FALSE - An object which is traveling east could encounter a collision from the side, from behind (by a faster-moving object) or from the front. The direction of the impulse is dependent upon the direction of the force exerted upon the object. In each of these scenarios, the direction of the force would be different. d. TRUE - In a collision, there is a collision force which endures for some amount of time. The combination of force and time is what is referred to as an impulse. e. FALSE - The Newton is the unit of force. The standard metric unit of impulse is the N•s. f. TRUE - The N•s is the unit of momentum. The Newton can be written as a kg•m/s^2. When substituted into the N•s expression, the result is the kg m/s. g. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse. This impulse acts upon the object to change its velocity and thus its momentum. h. TRUE - Yes!!! This is the impulse-momentum change theorem. The impulse encountered by an object in a collision causes and is equal to the momentum change experienced by that object.
Which of the following statements are true about kinetic energy? Include all that apply. -Kinetic energy is the form of mechanical energy which depends upon the position of an object. -If an object is at rest, then it does not have any kinetic energy. -If an object is on the ground, then it does not have any kinetic energy. -The kinetic energy of an object is dependent upon the weight and the speed of an object. -Faster moving objects always have a greater kinetic energy. -More massive objects always have a greater kinetic energy. -Kinetic energy is a scalar quantity.
Answer: BG a. FALSE - Kinetic energy depends upon the speed of the object; potential energy depends upon the position of the object. b. TRUE - Kinetic energy depends upon speed. If there is no speed (the object is at rest), then there is no kinetic energy. c. FALSE - If an object is on the ground, then it does not have potential energy (relative to the ground). d. FALSE (sort of) - Kinetic energy depends upon mass and speed. Two objects of the same mass could have different weights if in a different gravitational field; so it is not appropriate to say that kinetic energy depends upon weight. e. FALSE - Faster moving objects would have more kinetic energy than other objects of the same mass. However, another object could have less speed and make up for this lack of speed in terms of a greater mass. f. FALSE - More massive objects would have more kinetic energy than other objects with the same speed. However, another object could have less mass and make up for this lack of mass in terms of a greater speed. g. TRUE - Kinetic energy does not have a direction associated with it; it is a scalar quantity.
Which of the following statements are true about kinetic energy? Include all that apply. =Kinetic energy is the form of mechanical energy which depends upon the position of an object. =If an object is at rest, then it does not have any kinetic energy. =if an object is on the ground, then it does not have any kinetic energy. =The kinetic energy of an object is dependent upon the weight and the speed of an object. =Faster moving objects always have a greater kinetic energy. =More massive objects always have a greater kinetic energy. =Kinetic energy is a scalar quantity.
Answer: BG a. FALSE - Kinetic energy depends upon the speed of the object; potential energy depends upon the position of the object. b. TRUE - Kinetic energy depends upon speed. If there is no speed (the object is at rest), then there is no kinetic energy. c. FALSE - If an object is on the ground, then it does not have potential energy (relative to the ground). d. FALSE (sort of) - Kinetic energy depends upon mass and speed. Two objects of the same mass could have different weights if in a different gravitational field; so it is not appropriate to say that kinetic energy depends upon weight. e. FALSE - Faster moving objects would have more kinetic energy than other objects of the same mass. However, another object could have less speed and make up for this lack of speed in terms of a greater mass. f. FALSE - More massive objects would have more kinetic energy than other objects with the same speed. However, another object could have less mass and make up for this lack of mass in terms of a greater speed. g. TRUE - Kinetic energy does not have a direction associated with it; it is a scalar quantity.
Luke Autbeloe stands on the edge of a roof throws a ball downward. It strikes the ground with 100 J of kinetic energy. Luke now throws another identical ball upward with the same initial speed, and this too falls to the ground. Neglecting air resistance, the second ball hits the ground with a kinetic energy of ____ J. A. less than 100 B. 100 C. 200 D. more than 200 E. none of these
B. Quite surprisingly to many, each ball would hit the ground with the same speed. In each case, the U + K of the balls immediately after being thrown is the same (they are thrown with the same speed from the same height). Upon hitting the ground, they must also have the same U + K. Since the U is zero (on the ground) for each ball, it stands to reason that their K is also the same. That's a little physics and a lot of logic - and try not to avoid the logic part by trying to memorize the answer.
Inelastic collision examples:
Explosion or dispersive collision, where one object breaks up into two or more objects - a maximum amount of energy is gained.
Inelastic collision examples:
Implosion or sticky collision, where two or more objects stick together and become one - a maximum amount of energy is lost.
Consider firing a bullet out of the barrel of a rifle in terms of
Impulse and momentum Work and energy
Consider the braking (slowing down) of a car in terms of
Impulse and momentum Work and energy
Conservation of Mechanical Energy
In a conservative system the sum of all types of kinetic and potential energy is conserved. K + U = Ko+ Uo or ΔK + ΔU = 0
isolated system
In an isolated system the total momentum is conserved (unchanged). system: object or group of objects Isolated: No external forces acting upon the system.
Total Elastic Collision:
Kinetic energy conserved - no sound or heat is generated - touchless collision, using magnets or other field forces, like gravity or electrostatic fields.
Total Inelastic Collision:
Kinetic energy is not conserved
impulse unit
N s =kg*m/s
Free Fall:
The force of gravity is conservative Energy was conserved (Ug changed to KE)
Hooke's Law (for springs)
The force of the spring depends on the position: fs=-k delta x =-k(x-x0)
Braking:
The friction force was non-conservative. Energy (specifically K) was removed
Drone:
The lifting force was non-conservative Energy (both K and Ug) was added
Collisions in 2-D
The momentum is conserved in all directions.
Power
The rate at which energy (E) is transferred
power unit :
Watts (W)
Non-conservative force:
Work depends on path Example: Friction forces
Conservative Forces
Work does not depend on the path Examples: Force of gravity Spring forces
Which of the following statements are true about work? Include all that apply. =Work is a form of energy. =A Watt is the standard metric unit of work. =Units of work would be equivalent to a Newton times a meter. =A kg•m2/s2 would be a unit of work. =Work is a time-based quantity; it is dependent upon how fast a force displaces an object. =Superman applies a force on a truck to prevent it from moving down a hill. This is an example of work being done. =An upward force is applied to a bucket as it is carried 20 m across the yard. This is an example of work being done. =A force is applied by a chain to a roller coaster car to carry it up the hill of the first drop of the Shockwave ride. This is an example of work being done.
a. TRUE - Work is a form of energy, and in fact it has units of energy. b. FALSE - Watt is the standard metric unit of power; Joule is the standard metric unit of energy. c. TRUE - A N•m is equal to a Joule. d. TRUE - A kg•m2/s2 is a mass unit times a speed squared unit, making it a kinetic energy unit and equivalent to a Joule. e. FALSE - Work is not dependent on how rapidly the force displaces an object; power is time-based and calculated by force multiplied by speed. f. FALSE - Since Superman does not cause a displacement, no work is done; he is merely holding the car to prevent its descent down the hill. g. FALSE - The upward force does not cause the horizontal displacement so this is a NON-example of work. h. TRUE - There is a component of force in the direction of displacement and so this is an example of work.
Impulse-Momentum Theorem
change in momentum *impulse not equal to momentum * impulse not equal to impact force
Momentum
how difficult it is to stop an object or the potential to cause a force.
Impulse formula
impulse = average force x time
momentum formula
momentum = mass x velocity
Compressing a Spring
non-constant force - spring force called Hooke's law, Fs = -kx î
Small k = soft spring
soft spring