Physics_Topic_2-6

Associative-vector

(A + B) + C = A + (B + C)

Distributive-scalar

(c + d) · A = c · A + d · A

Associative- scalar

(c · d) · A = c · (d · A)

Multiplicative Zero - scalar

0 · A = 0

Multiplicative Identity- scalar

1 · A = A

Which of the following statements are true of vector addition, vector subtraction, and vector addition diagrams? List all that apply. =Vectors A, B, and C are added together as A + B + C. If the order in which they are added is changed to C + B + A, then the result would be different. =Vectors A, B, and C are added together as A + B + C. If the order in which they are added is reversed to C + B + A, then the result would be a vector with the same magnitude but the opposite direction. =When constructing a vector diagram for A + B + C, it is not necessary that vectors B and C use the same scale that is used by vector A. =The resultant in a vector addition diagram always extends from the head of the last vector to the tail of the first vector. =*If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is greater than the magnitudes of either one of the individual vectors A and B. =*If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is less than the arithmetic sum of the magnitudes of A and B. =Vector addition diagrams cannot be used to determine the resultant when there is a vector subtraction operation.

=No, vector addition is commutative =No, same direction, i.e. the same result. =If you want a realistic diagram for which you can actually estimate the answer, the scales must be the same. =Opposite: From the tail of the first to the head of the last. =The resultant is the hypotenuse =The resultant is the hypotenuse =You just add the negative vector

Effect of Air Resistance

=Slow down the horizontal motion (ax < 0) =Reduce the vertical height and the time in the air =Shorter range =Not a parabolic trajectory

changes in a particle's motion may produce an acceleration:

=The magnitude of the velocity vector may change. =The direction of the velocity vector may change. =Even if the magnitude remains constant =Both may change simultaneously

Projectile Motion

=The motions in each direction are independent =The horizontal and vertical parts can be treated as straight-line motions.

A rightward applied force is used to displace a television set to the right. A)o B. 90o C. 180o D. 270°

A

Additive Inverse- vector

A + (-A) = 0

Additive Identity - vector

A + 0 = 0 + A = A

Commutative- vector

A + B = B + A

Subtraction-vector

A - B = A + (-1)·B

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.

Vector Addition

A sum of vectors is called a resultant.

The vertical motion

Acceleration due to gravity: ay = -10.m/s2 Initial vertical speed: voy = vo·sinθo Changing speed: vy = voy - (10.m/s2) t Distance: Δy = voy·t - ½·(10.m/s2) t2

A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, its acceleration is _______. (Neglect the effects of air resistance.) =entirely vertical =entirely horizontal =both vertical and horizontal =not enough information given to know

Answer: A As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. At the peak and everywhere throughout the trajectory, there is a vertical (downward) acceleration. In fact, a projectile is an object upon which the only force is gravity. This force causes an acceleration which is in the same direction as the force - downward.

Two projectiles are fired at equal speeds but different angles. One is fired at angle of 30°and the other at 60°. The projectile to hit the ground first will be the one fired at (neglect air resistance) ____. 30 degrees 60 degrees both hit at the same time

Answer: A For projectiles launched at angles, a launch angle of 45 degrees will provide the largest horizontal displacement. Launch angles greater than 45 degrees result in large vertical components of velocity; these stay in the air longer and rise to higher heights. Launch angles less than 45 degrees result in small vertical components of velocity; these do not rise as high and end up falling to the ground in shorter times.

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.

Answer: ACDH 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.

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 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.

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.

A projectile is launched at an angle of 15° above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance? 30 degrees. 45 degrees. 50 degrees. 75 degrees 90 degrees.

Answer: D For projectiles launched at angles, a launch angle of 45 degrees will provide the largest horizontal displacement. Any two launch angles which are separated from 45 degrees by the same amount (for example, 40 degrees and 50 degrees, 30 degrees and 60 degrees and 15 degrees and 75 degrees) will provide the same horizontal displacement.

At what point in its path is the horizontal component of the velocity (vx) of a projectile the smallest? a)The instant it is thrown. d) As it nears the top. b)Halfway to the top. e) It is the same throughout the path c)At the top.

Answer: E As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. Having a constant horizontal velocity, there is no point along the trajectory where the vx value is smaller than at other points.

Projectile -

Any object moving only under the influence of gravity

A waiter uses an applied force to balance the weight of a tray of plates as he carries the tray across the room. A.0o B. 90o C. 180o D. 270°

B

The force of air resistance acts upon a vertically-falling skydiver. A.0o B. 90o C. 180o D. 270°

C

The force of friction acts upon a baseball player as he slides into third base. A.0o B. 90o C. 180o D. 270°

C

The force of friction acts upon a rightward-moving car to bring it to a stop. A.0 B. 90o C. 180o D. 270°

C

At what point in its path is the vertical component of the velocity (vy) of a projectile the smallest? a)The instant it is thrown. d) As it nears the top. b)Halfway to the top. e) It is the same throughout the path c)At the top.

C As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. During the upward portion of its trajectory, the vy continuously decreases until it becomes 0 m/s at the peak. Thus, the vy is as small as it will ever be when it is at the peak of the trajectory.

Potential Energy

Change in potential energy = work done against a conservative force ΔU = -Wc

Hooke's Law Equation

Fs= -k delta x =-k(x-x0_ * k is constant*

Hooke examples

If you pull (or push) twice as hard, then the stretch (or compression) is twice as great.

The horizontal motion

No acceleration: ax = 0 Constant speed: vx = vox = vo·cosθo Distance: Δx = vox·t

Classify of the following forces as conservative or non-conservative forces. =Air resistance. =Elastic (spring) force. =Friction forces. =The force of gravity.

Nonconservative Conservative Nonconservative Conservative

Kinematics

Study of motion (kínisi - motion in Greek)

Range

The horizontal distance from starting position to where the projectile lands

Trajectory

The path of a projectile.

Parabolic

The shape of the trajectory

thermal energy

The total energy of motion in the particles of a substance

work-energy theorem

The work done on an object equals the change in kinetic energy of the object

angles between 90° and 270°

These are forces with components against the direction of the displacement. These force perform negative work. So, when you lift a box, you are doing positive work, while gravity is doing negative work and what you will learn is that this negative work is transformed into gravitational potential energy.

θ = 90°

This means that carrying box down a hallway is not work!!! The normal force of holding the object is vertical and the displacement is horizontal, so the angle is 90° and the cos90° is zero.

Non-conservative force

Work depends on path Example: Friction forces

Conservative force

Work does not depend on the path Examples: !Force of gravity !Spring forces

An object moves 4 m east, then 7 m west, and finally 5 m east. What is the total displacement?

a) 15 m, east b*) 2 m, east c) 16 m, east d) 2 m, west

An object moves 4 m east, then 7 m west, and finally 5 m east. What is the total distance traveled?

a) 2 m b) 9 m c*) 16 m d) 7 m e) 0 m

Which of the following statements are true of the horizontal motion of projectiles? List all that apply. =A projectile does not have a horizontal velocity. =A projectile with a rightward component of motion will have a rightward component of acceleration. =The horizontal velocity of a projectile changes by 9.8 m/s each second. =A projectile with a horizontal component of motion will have a constant horizontal velocity. =The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory. =The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other. =The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity. =The final horizontal velocity of a projectile is always equal to the initial horizontal velocity. =As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will decrease.

a. FALSE - Many projectiles are moving from left to right and from right to left as they simultaneously free fall. Such projectiles have a horizontal motion. While a projectile can have a horizontal motion, it cannot have a horizontal acceleration. Whatever motion which it has in the horizontal dimension, must be motion with a constant velocity. b. FALSE - A projectile with a rightward motion (in addition to a vertical motion) will have a constant velocity in the rightward direction. This is to say that it has no horizontal acceleration. c. FALSE - A projectile has a constant horizontal velocity. The vertical velocity will change by 9.8 m/s each second. d. TRUE - Absolutely true! Projectiles are objects being acted upon by gravity alone. As such, there is a vertical acceleration but no horizontal acceleration. The horizontal velocity of a projectile is either zero or a constant nonzero value. e. FALSE - The vertical velocity of a projectile is 0 m/s at the peak of its trajectory; but the horizontal component of the velocity at the peak is whatever the value was when first launched. f. TRUE - For any two dimensional motion (whether projectile motion or riverboat problems or ...), perpendicular components of the motion are independent of each other. Any alteration in a vertical component will not effect the horizontal components of motion. g. TRUE - The horizontal displacement (x) can be calculated with the formula x = vox • t, where vox is the initial horizontal velocity and t is the time. These are the two variables which effect the horizontal displacement of a projectile. h. TRUE - Since there is no horizontal acceleration for a projectile, the initial horizontal velocity is equal to the final horizontal velocity. i. FALSE - This is a true description for the vertical component of the velocity. The horizontal velocity is unchanging throughout the trajectory of a projectile.

Which of the following statements are true of the time of flight for a projectile? List all that apply. =The time that a projectile is in the air is dependent upon the horizontal component of the initial velocity. =The time that a projectile is in the air is dependent upon the vertical component of the initial velocity. =For a projectile which lands at the same height that it is projected from, the time to rise to the peak is equal to the time to fall from its peak to the original height. =For the same upward launch angles, projectiles will stay in the air longer if the initial velocity is increased. =Assume that a kicked ball in football is a projectile. If the ball takes 3 seconds to rise to the peak of its trajectory, then it will take 6 seconds to fall from the peak of its trajectory to the ground.

a. FALSE - The time for a projectile to rise vertically to its peak (and subsequently fall back to the ground) is dependent upon the initial vertical velocity. Alteration in the horizontal velocity will only cause the projectile to have a greater horizontal displacement (x). b. TRUE - Absolutely true. Projectiles with a greater vertical component of initial velocity will be in the air for longer amount of times (assuming that the direction of viy is upward). An alteration in the viy value will alter the time of flight of the projectile, regardless of the direction of viy. c. TRUE - For projectiles launched at upward angles and landing at the original height, the time to the rise to the peak equals the time to fall from the peak. If it takes 3 seconds to rise upward, it will take 3 seconds to fall. d. TRUE - For a constant launch angle, an increase in the initial velocity (vi) will increase the vertical velocity (viy). This results in an increased time for the projectile to decelerate to 0 m/s as it rises towards its peak. So the projectile takes longer to get to the peak, longer to fall from the peak and overall is in the air for a longer time. e. FALSE - Close, but very false. If it takes 3 seconds to rise to the peak, then it takes 3 seconds to fall from the peak; The 6 seconds is the total time of flight of the projectile.

Which of the following statements are true of the vertical motion of projectiles? List all that apply. =The vertical component of a projectile's velocity is a constant value of 9.8 m/s. =The vertical component of a projectile's velocity is constant. =The vertical component of a projectile's velocity is changing. =The vertical component of a projectile's velocity is changing at a constant rate. =A projectile with an upward component of motion will have a upward component of acceleration. =A projectile with an downward component of motion will have a downward component of acceleration. =The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second. =The vertical velocity of a projectile is 0 m/s at the peak of its trajectory. =The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other. =The final vertical velocity of a projectile is always equal to the initial vertical velocity. =The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity.

a. FALSE - The vertical component of a projectile's velocity is constantly changing. It is the acceleration which has a value of 9.8 m/s/s. b. FALSE - Projectiles are objects being acted upon by gravity alone. As such, there is a vertical acceleration; the vertical velocity is not constant, but changing. c. TRUE - See part b above. d. TRUE - A projectile has a vertical acceleration of 9.8 m/s/s throughout the entire trajectory. This acceleration value is constant. This means that the vertical velocity changes by the same amount - 9.8 m/s - during each second of its motion. There is a change in the vertical velocity by a constant amount. e. FALSE - All projectiles experience a downward acceleration, whether they are moving upward or downward. The upward-moving projectiles have an upward velocity, but the actual velocity values are getting smaller; that is, the projectile is slowing down on the way to its peak. f. TRUE - This is a true statement. It could also be said that a projectile with an upward component of motion also has a downward acceleration. All projectiles accelerate in the downward direction. Period. g. TRUE - This is absolutely true . h. TRUE - At the peak of its trajectory, a projectile is in the process of changing directions. The vertical velocity must change from a positive value (+ for upward) to a negative value (- for downward). This transition means that the value for the vertical velocity must at sometime be in between a + and - number. The in-between number is 0 m/s and this occurs at the peak. i. TRUE - For any two dimensional motion (whether projectile motion or riverboat problems or ...), perpendicular components of the motion are independent of each other. Any alteration in a vertical component will not effect the horizontal components of motion. j. FALSE - A projectile launched at an angle forms a parabolic trajectory. Suppose that one were to trace a projectile's motion forward in time from the peak and backwards in time from the peak. If done, one would find that the vertical velocity value has the same magnitude for equal amounts of times traced forward and backward from the peak. So for the same time before and after the peak, a projectile has the same speed. However, some projectiles are not launched from the same height at which they land. The final height is not the same as the initial height and as such the time to rise to the peak is not equal to the time to fall from the peak. In such instances, the initial vertical velocity is not equal to the final vertical velocity. k. TRUE - The initial vertical velocity has an effect on the time taken by a projectile to rise towards its peak. It also effects the average speed of the projectile as it rises towards its peak. As a result, any alteration in the vertical velocity will alter the peak height of the projectile.

Which of the following descriptions of moving objects accurately portray a projectile? List all that apply. =an object which is moving through the air and not touching any surface =a falling skydiver with an open parachute =any object upon which air resistance is negligible =a free-falling object =an object upon which the only significant force is the force of gravity =a falling feather =a falling feather in a vacuum chamber =a falling feather in a falling vacuum chamber.

a. NO - A plane moves through the air and is not touching any surface. Yet, a plane is clearly not a projectile. b. NO - A falling skydiver typically experiences considerable air resistance. It is popular to describe such skydivers as being in free fall. This is an erroneous use of the term. c. NO - As you sit in your chair, air resistance is negligible. You are certainly not a projectile (at least, we hope not). d. YES - A projectile is an object in free fall. e. YES - An object upon which the only significant force is gravity fits the definition of a projectile (provided that significant means "having an influence"). f. NO - Falling feathers encounter air resistance which impedes the downward acceleration and causes the feather to fall at nearly a constant velocity. g. YES - When a feather is allowed to fall in a vacuum, air resistance is eliminated and the feather can free fall. h. YES - When a feather is allowed to fall in a vacuum and the vacuum is free-falling as well, air resistance is eliminated and an observer would notice that both the vacuum chamber and the feather are in free fall.

Which of the following statements are true of projectiles? List all that apply. =A projectile is a free-falling object. =A projectile experiences negligible or no air resistance. =A projectile must be moving in the downward direction. =A projectile must be accelerating in the downward direction. =A projectile does not have to have horizontal motion. =A projectile could begin its projectile motion with a downward velocity. =A projectile does not need to be "falling."

a. TRUE - Free-falling objects, like projectiles, are objects upon which the only significant force is gravity. b. TRUE - The only force on a projectile is gravity; air resistance must not be present or must not have an influence upon the motion of the projectile. c. FALSE - Projectiles can be moving either upward or downward or at an angle to the vertical. They must however be accelerating downward, consistent with gravity's effect on an object. d. TRUE - The force of gravity acts directly downwards upon an object, causing a downward acceleration. Any projectile must be accelerating downwards regardless of other features of its motion. e. TRUE - A projectile could be moving strictly in a vertical direction with no horizontal motion. A ball thrown straight up in the air would be such a case. f. TRUE - There is no rule about which direction a projectile must be moving at the instant it is projected. It could begin its motion with a initial downward velocity. g. TRUE - The word "falling" can mean different things to different people. If "falling" involves moving in the downward direction at all instants in time, then a projectile does not need to be "falling." To many, "falling" means being pulled downward by gravity's force. In this case, a projectile must be "falling." This will be explored further in T2L4 Preview 'From Projectile to Satellite'.

Potential Energy, U

associated with conservative forces only. Gravity & force of spring

When adding vector B to vector A geometrically (or graphically) using the head to tail method, the resultant is drawn from ____ to the ____. a)head of A, tail of B c) head of B, tail of A b)tail of A, head of B d) tail of B, head of A

b

Which of the following quantities are vectors? Select all that apply. a)distance traveled d) average velocity b)displacement e) instantaneous velocity c)average speed f ) acceleration

b,d,e,f,

Distributive- scalar

c · (A + B) = c · A + c · B

Hooke's Law (for springs)

force of the spring depends on the position.

instantaneous velocity

limit of the average velocity as Δt approaches zero.

Motion in two dimensions

modeled as two independent motions in each of the two perpendicular directions associated with the x- and y-axes. *Any influence in the y-direction does not affect the motion in the x-direction. *The motion in the x-direction is constant (linear), while the motion in the y-direction is parabolic.

Average velocity

the displacement vector divided by a scalar, time, so the directions are the same.

Instantaneous acceleration

the limit as the time interval approaches zero of the change in velocity over change in time.

Non-conservative characteristic

the work done by a non-conservative force adds or removes mechanical energy from a system.

Force parallel to the displacement in the same direction

theta = 0 degrees

Parallel to displacement in the same direction

w= |F||deltar|cos0degrees =F . delta r

x-direction ( 𝑖 ̂ )

y-direction ( 𝑗 ̂ )

Magnitude- scalar

||c · A|| = |c| · ||A||