Newton's Third Law

Newton's Third Law

Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

"to every action there is an equal and opposite reaction."

"action" force and "reaction" force are acting on different objects.

Newton's Second Law

Newton's Second Law of Motion

The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.

F (net) = m * a

In SI units, with the mass in kilograms, the unit of force is called the newton (N).

1N = 1 kg.m/s^2

Mass

Mass

Mass is a measure of the inertia of an object.

The more mass an object has, the greater the force needed to give it a particular acceleration.
It is harder to start it moving from rest, or to stop it when it is moving, or to change its velocity sideways out of a straight-line path.

In S.I units, the unit of mass is the kilogram (kg) .

Newton's First Law

Newton's First Law

Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

The tendency of an object to maintain its state of rest or of uniform motionin a straight line is called inertia. As a Nweton's first law is often called the law of inertia.

Dynamics: Newton's Laws of Motion (Chapter 4)

Objectives

1. Newton's three laws of motion
2. the term net force
3. Weight-the Force of Gravity; and the Normal Force
4. free body diagram locating each of the forces acting on an object or a system of objects.
5. free body diagrams and Newton's laws of motion to solve word problems.
6. Tension in a Flexible Cord
7. Firction, Inclines

Practiced Questions (Chapter 3)

1. If you drive west at 20 km/h for one hour, then drive east at 15 km/h for one hour, your net displacement will be

(A) 5 km east.
(B) 35 km west.
(C) 35 km east.
(D) 5 km west.


2. If the acceleration vector of a body is perpendicular to the velocity vector, which of the following must be true?

(A) The speed is changing.
(B) The direction is changing.
(C) Both the speed and the direction are changing.
(D) The direction is not changing.


3. A vector of magnitude 10 has an angle with the positive x-axis (east) of 120 degrees. What are its components?

(A) 5 and 8.7
(B) -5 and 8.7
(C) 5 and -8.7
(D) -5 and -8.7


4. A vector of magnitude 10 has an angle with the positive x-axis (east) of -60 degrees. What are its components?

(A) 5 and 8.7
(B) -5 and 8.7
(C) 5 and -8.7
(D) -5 and -8.7


5. A vector has components x = 6 m and y = 8 m. What is its magnitude and direction?

(A) 10 m and 30 degrees
(B) 14 m and 37 degrees
(C) 10 m and 53 degrees
(D) 14 m and 53 degrees


6. A vector has components x = -2 m and y = -2 m. What is its direction (angle with respect to east)?

(A) 45 degrees
(B) 135 degrees
(C) 225 degrees
(D) -45 degrees


7. Three vectors have components (x,y): A = (2,3), B = (4,-7) and C = (-6,-3). What is the magnitude of the resultant vector (D = A + B + C)?

(A) -7
(B) 17.7
(C) 15
(D) 7


8. Three vectors have components (x,y): A = (2,3), B = (4,-7) and C = (-6,-3). What is the magnitude of the resultant vector (D = A - B - C)?

(A) 13.6
(B) 15
(C) 52
(D) 7


9. Suppose that several projectiles are fired on level ground. Which one will be in the air longest?

(A) The one with the farthest range, R.
(B) The one with the highest maximum elevation, h.
(C) The one with the greatest initial velocity.


10. Which of the following does not affect the range of a projectile?

(A) V0 Initial Speed
(B) θ0 Launch Angle
(C) y0 Initial Height
(D) x0 Initial Horizontal Position


11. Which of the following must be zero for a projectile to achieve its maximum range?

(A) Vxf
(B) Vyf
(C) xf
(D) yf


12. Which of the following must be zero for a projectile to be at its maximum height?

(A) Vxf
(B) Vyf
(C) yf
(D) xf



13. Taking "up" as positive at the highest point, the acceleration of a projectile is

(A) -9.8 m/s2
(B) 0 m/s2
(C) +9.8 m/s2


14. If the sum of two vectors equals zero, the magnitude of their difference is

(A) equal to the magnitude of either one.
(B) equal to twice the magnitude of either one.
(C) less than twice the magnitude of either one.

motion of motor boat with current

Relative Velocity

http://www.physicsclassroom.com

Velocity is not absolute, it is dependant on the observer. That is why we say it is "relative" to the observer's state of motion.

formulas describing projectile motion

from http://www.mansfieldct.org/,

conceptual notions about projectiles

* a projectile is any object upon which the only force is gravity,

* projectiles travel with a parabolic trajectory due to the influence of gravity,

* there are no horizontal forces acting upon projectiles and thus no horizontal acceleration,

* the horizontal velocity of a projectile is constant (never changing in value),

* there is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down,

* the vertical velocity of a projectile changes by 9.8 m/s each second,

* the horizontal motion of a projectile is independent of its vertical motion.

Characteristics of a Projectile's Trajectory

From Physics Classroom, http://www.physicsclassroom.com/ ,

Concept of Projectile

From Physics Classroom , www.physicsclassroom.com

Projectile Motion

A projectile is an object upon which the only force acting is gravity.

A projectile is any object which once projected continues in motion by its own inertia and is influenced only by the downward force of gravity.

By definition, a projectile has only one force acting upon - the force of gravity

components of vector

Addition of 3 Vectors , 4 Vectors

Combining Vector Components

Polar Form Example

Example of Vector Components

Graphical Vector Addition

Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.

rectangular components

Components parallel to the axes of a rectangular system of axes are called rectangular components.
the horizontal axis X
the vertical axis Y

The direction of a vector is given as an angle counter-clockwise from the X-axis.

Method of components

The components of a vector are those vectors which, when added together, give the original vector.
The sum of the components of two vectors is equal to the sum of these two vectors.

A1, the component in an easterly direction, will have a magnitudeA1 = A cosQ.

A2, the component in a northerly direction, will have a magnitudeA2 = AsinQ

parallelogram method

Polygon Method

Addition of Vectors

Vectors and Scalars

Scalars are quantities which are fully described by a magnitude alone.
( for example: mass, time, temperature)

Vectors are quantities which are fully described by both a magnitude and a direction.
(for example: velocity)

Kinematics in Two Dimensions; Vectors (Chapter 3)

Kinematics in Two Dimensions; Vectors (Chapter 3)

Objectives:

1. The magnitude and direction of a vector .
2. Multiply or divide a vector quantity by a scalar quantity.
3. The methods of graphical analysis to determine the magnitude
and direction of the vector resultant in problems involving vector addition
or subtraction of two or more vector quantities.
The graphical methods to be used are the parallelogram method and
the tip to tail method.
4. The trigonometric component method to resolve a vector components in the x and y directions.
5. The trigonometric component method to determine the vector resultant in problems involving vector addition or subtraction of two or more vector quantities.
6. Two dimensional motion of projectiles.

Practice Questions (Chapter 2)

1. At t = 0 s

(A) Rider C is ahead of rider D.
(B) Rider D is ahead of rider C.
(C) Rider C and D are at the same position.

2. At t = 0 s

(A) C is moving, and D is at rest.
(B) D is moving, and C is at rest.
(C) C and D are both moving.
(D) C and D are both at rest.

3 . At t = 0 s

(A) C has a greater velocity than D.
(B) D has a greater velocity than C.
(C) C and D have the same velocity.
(D) C is accelerating.

4. At t = 10 s

(A) C and D are at the same position.
(B) C and D have the same velocity.
(C) The velocity of D is greater than the velocity of C.
(D) C is in front of D.

5. During the first 8 s

(A) C has decreasing velocity and D has increasing velocity.
(B) C and D both have decreasing velocities.
(C) C and D have the same velocity.
(D) C has the same average velocity as D.

6. During the first 8 s

(A) the magnitude of the acceleration of C is greater than the magnitude of D's acceleration.
(B) their accelerations are equal in magnitude but opposite in sign.
(C) their accelerations are equal in magnitude and equal in sign.

7.Based on all the graphical information

(A) they meet at the same position at t = 8 s.
(B) they will meet at the same position, at t = 10 s.
(C) they will never meet at the same position.
(D) not enough information is given to decide if they meet.

8. Which graph represents an object at rest?


(A)

(B)

(C)

(D)

9 . How is motion in the negative x direction represented on an x vs. t plot?

(A) By a curve to the left of the origin.
(B) By a curve below the horizontal axis.
(C) By a downward sloping curve.
(D) Such a motion cannot be shown on a simple x vs. t graph.

10. What is the meaning of a horizontal line on a plot of v vs. t?

(A) The object is at rest.
(B) The object is moving at constant speed.
(C) The object is speeding up at a constant rate.
(D) The object is accelerating at a constant non-zero rate.

11. If a car accelerates from rest in the positive direction

(A) its final velocity is zero.
(B) its initial position is zero.
(C) its initial velocity is zero.
(D) its acceleration is negative.

12. A car accelerating from rest at 2.0 m/s2 for 5 s

(A) covers a distance of 10 m.
(B) has a final speed of 10 m/s.
(C) covers a distance of 50 m.
(D) has an average velocity of 10 m/s.

13. In this problem "up" is taken to be positive.
A ball is dropped off a high cliff

(A) and its initial velocity is zero.
(B) and its final velocity is positive.
(C) and its acceleration is 9.8 m/s2.
(D) and its acceleration is -9.8 m/s.

14. In this problem "up" is taken to be positive.
A ball is thrown straight up in the air; at the very top its

(A) velocity is negative.
(B) acceleration is zero.
(C) its acceleration is 9.8 m/s2.
(D) its acceleration is -9.8 m/s2.

15. In this problem "up" is taken to be positive.
A vertically upward thrown rock has a

(A) positive initial velocity.
(B) positive final velocity.
(C) positive acceleration.
(D) positive final height.

16. In this problem "up" is taken to be positive.
A falling object has

(A) positive acceleration and positive velocity.
(B) negative acceleration and negative velocity.
(C) positive acceleration and negative velocity.
(D) negative acceleration and positive velocity.

17 . In this problem "up" is taken to be positive.
An object moving upward under the influence of gravity has

(A) positive acceleration and positive velocity.
(B) negative acceleration and negative velocity.
(C) positive acceleration and negative velocity.
(D) negative acceleration and positive velocity.

18. In this problem "up" is taken to be positive.
A ball thrown vertically upward with an initial velocity of 19.6 m/s, after 5 s has a final velocity of

(A) 19.6 m/s.
(B) -19.6 m/s.
(C) 29.4 m/s.
(D) -29.4 m/s.

19 . An object is shot upward at 34.3 m/s. How high does it go?

(A) 60.0 meters
(B) 180.1 meters
(C) 102.9

20 . Ball A is thrown vertically upward with a speed of 19.6 m/s from the topedge of a high building. As it passes the edge on the way down, a second ball, B, is thrown downward at 19.6 m/s. Which of the following is correct?

(A) Ball A hits the ground before B.
(B) The two balls hit the ground at the same time.
(C) Ball B hits the ground before A.

21. A car moving right to left applies the brakes. Its

(A) velocity and acceleration are both positive.
(B) velocity and acceleration are both negative.
(C) velocity is negative and its acceleration is positive.
(D) velocity is positive and its acceleration is negative.

22. A ball is dropped off a ledge. How far does it fall in the 2nd second?

(A) 4.9 meters
(B) 9.8 meters
(C) 14.7 meters
(D) 19.6 meters

23. Ball A is thrown upward at the same time as ball B and with half the speed of ball B. Which of the following is true?

(A) They will hit the ground at the same time.
(B) A will hit before B.
(C) B will hit before A.

24.Ball A is thrown upward at the same time as ball B and with half the speed of ball B. How much higher does B go than A?

(A) 8 times.
(B) 4 times.
(C) 2 times.
(D) Not enough information is given to answer this question.