Chapter 1: Physical Quantities and Vectors

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2 Chapter 1: Physical Quantities and Vectors Chapter 2: Linear Motion Chapter 3: Curvilinear Motion

3 Physics the science that deals with matter, energy, motion and force. Branches of Physics (1) Thermodynamics (5) Quantum Physics (2) Optics (6) Nuclear Physics (3) Mechanics (7) Magnetism (4) Acoustics (8) Electricity

4 Physical Quantities Scalar Quantity quantities specified by magnitude only Ex. Time, Mass, Speed, Distance, Temperature, Volume, Area, Work, Energy. Vector Quantity quantities specified by both magnitude and directions. Ex. Velocity, Displacement, Acceleration, Force, Weight, Momentum, Impulse.

5 Forces are analyzed in a number of ways; it is common approach to establish a coordinate system to quantify the forces and their effects in a system or body. Since it is customary to assign the axes, the analysis may be coplanar (two-dimensional) or non-coplanar (three-dimensional).

6 A system of forces may be represented by a resultant force which has the same effect as the system. Forces on an object Equivalent Resultant Force 2N 1N 3N 2N 6N The resultant force, much like any other force, has magnitude and direction. The geometric sum of the forces will yield the resultant. 4N Resultant =0 6N 3N 3N

7 Coplanar Force Systems analyze forces acting on a body by taking their components along two designated axes. A force system can be identified into two main types: concurrent non-concurrent.

8 The resultant of concurrent forces must be defined by magnitude and direction. Magnitude represents the length of the vector while the direction is referred from the defined axis. Resultant Force

9 The equilibrant of the forces is a single vector that can balance two or more vectors - it is equal in magnitude as the resultant - opposite the direction of the resultant - acting along the same line of action as the resultant Resultant Force Equilibrant

10 Solutions to Vectors Problems: (1) Graphical Method (with the aid of ruler and protractor) (a) Parallelogram (b) Triangle Method (Tip-to-Tail Method) (c) Polygon Method (2) Analytical/Mathematical Method (a) Use of Pythagorean Theorem (b) Use of Sine/Cosine Law (c) Component Method

11 Example 1: Given: A = 150 lbs, 60ᵒ N of E B = 200 lbs, 20ᵒ S of E Find the resultant and its direction using graphical and analytical method.

12 Example 2: Given: A = 100 lbs, NE B = 150 lbs, 30ᵒ N of W C = 200 lbs, Due South Find the resultant and its direction using graphical and analytical method.

13 Example 3: In the final game of last year s regular season, south was playing New Greer Academy for the Conference Championship. In the last play of the game, star quarterback Avery took a snap from scrimmage and scooted backwards (northwards) 8.0 yards. He then ran sideways (westward out of the pocket for 12.0 yard before finally throwing a 34.0 yard pass directly downfield (southward) to Kendall for the game-winning touchdown. Determine the magnitude and direction of the ball s displacement.

14 Example 4: Four forces act concurrently at a point. Force A has a magnitude of 70 lb and is directed 30ᵒ N of E; force B has a magnitude of 60 lb and is directed westward; force C has a magnitude of 50 lb and is directed southward; and force D has a magnitude of 40 lb and is directed 20ᵒ E of S. (a) What is the x-component and y-component of the resultant of the four forces? (b) What are the magnitude and direction of a fifth force will produce equilibrium at the point?

15 Example 5: A group of physics students, after three days of hiking, are 30 km north of their starting position. On the first day they hiked 20 km east. On the second day they hiked 30 km in a direction 53ᵒ north of west. Using the component method: (a) Find the x-component and y-component of their displacement vector on the third day. (b) Find the magnitude and direction of their displacement vector on the third day.

16 Example 6: A man walks one morning from his house to a store that is 5000 m N40 o E from his house. He started covering 1200 m NE; then goes 1000 m 10 o S of E; then saw a friend who is 800 m 30 o E of N from where he is. Determine: (a) How far and in what direction was his friend from his house? (b) If he continued with his journey, how far and in what direction was his displacement from where his friend was to finally get to the store? (c) From the store, he first went to another friend s house before going back home. This friend s house is 950 m N50 o W form the store. How far and in what direction from his house is his second friend s house? (Solve graphically or analytically)

17 Example 7: The force vector A has a magnitude of 20 lb and points 25ᵒ east of north. The force vector B has a magnitude of 35 lb and points 24ᵒ north of west. The force vector C has a magnitude of 10 lb and points south. Assuming that the force vectors are coplanar and concurrent: (a) Find the magnitude and direction of A+B + C. (b) Find the magnitude and direction of 3A 2B C. (c) Find the magnitude and direction of 2A B+3C.

18 Example 8: A boy scout continues walking 10 m SW from a campsite, then 15 m 40 o S of W, then saw a baby ape 9m S from where he is, and walks toward it. Use graphical or analytical method to answer the following questions, but use only one method to answer both. (a) How far and in what direction was the baby ape from the campsite? (b) He then left the ape started to walk away from it to a tree for some rest. When he reached the tree, his position is now 20m S 30 o E from the campsite. Determine the magnitude and the direction of the last displacement covered to get to the tree.

19 Example 9: X, Y, and Z are coplanar, concurrent forces. If X = 150 lb, 35ᵒ W of S; Y = 220 lb, 21.5ᵒ N of W; and X + Y + Z = 200lb, W: (a) What is the magnitude and direction of Z? (b) What is the magnitude of X 2Y + Z? (c) What is the direction of X 2Y + Z?