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Physics I 95.141 LECTURE 3 9/13/10

Physics I 95.141 LECTURE 3 9/13/10. Exam Prep Question. 2 cars are racing. Car A begins accelerating ( a A =4m/s 2 ), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of a B =5m/s 2 .

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Physics I 95.141 LECTURE 3 9/13/10

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  1. Physics I95.141LECTURE 39/13/10

  2. Exam Prep Question • 2 cars are racing. Car A begins accelerating (aA=4m/s2), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of aB=5m/s2. (a) (5pts) What is the speed of Car A when Car B finally starts moving? (b) (5pts) What is the head start (in m) that Car A gets? • (10 pts) How long (in s) until Car B catches up to Car B? • (10 pts) What is the minimum length of the race track required for Car B to win the race?

  3. Exam Prep Question • 2 cars are racing. Car A begins accelerating (aA=4m/s2), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of aB=5m/s2. • Draw Diagram/Coord. System • Knowns and unknowns

  4. Exam Prep Question • 2 cars are racing. Car A begins accelerating (aA=4m/s2), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of aB=5m/s2. • (a) (5pts) What is the speed of Car A when Car B finally starts moving? • (b) (5pts) What is the head start (in m) that Car A gets?

  5. Exam Prep Question • 2 cars are racing. Car A begins accelerating (aA=4m/s2), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of aB=5m/s2. • (10 pts) How long (in s) until Car B catches up to Car B?

  6. Exam Prep Question • 2 cars are racing. Car A begins accelerating (aA=4m/s2), but Car B stalls. After 5s, Car A thinks it has won and stops accelerating, while Car B finally starts and accelerates at a rate of aB=5m/s2. • (d) (10 pts) What is the minimum length of the race track required for Car B to win the race?

  7. Outline • Freely Falling Body Problems • Vectors and Scalars • Addition of vectors (Graphical) • Adding Vectors by Components • Unit Vectors • What Do We Know? • Units/Measurement/Estimation • Displacement/Distance • Velocity (avg. & inst.), speed • Acceleration

  8. Review of Lecture 2 • Last Lecture (2) we discussed how to describe the position and motion of an object • Reference Frames • Position • Velocity • Acceleration • Constant Acceleration

  9. Freely falling Bodies • Most common example of constant acceleration is a freely falling body. • The acceleration due to gravity at the Earth’s surface is basically constant and the same for ALL OBJECTS (Galileo Galilei)

  10. Example Problem • Batman launches his grappling bat-hook upwards, if the beam it attaches to is 50m above Batman’s Batbelt, at what bat-velocity must the hook be launched at in order to make it to the beam? (Ignore the mass of the cord and air resisitance) 1) Choose coordinate system 2) Knowns and unknowns 3) Choose equation(s)

  11. Example Problem • Batman launches his grappling bat-hook upwards, if the beam it attaches to is 50m above Batman’s Batbelt, at what bat-velocity must the hook be launched at in order to make it to the beam? (Ignore the mass of the cord and air resisitance) 3) Choose equation(s) 4) Solve

  12. Vectors and Scalars • A quantity that has both direction and magnitude, is known as a vector. • Velocity, acceleration, displacement, Force, momentum • In text, we represent vector quantities as • Quantities with no direction associated with them are known as scalars • Speed, temperature, mass, time

  13. Vectors and Scalars • In the previous chapter we dealt with motion in a straight line • For horizontal motion (+/- x) • For vertical motion (+/- y) • Velocity, displacement, acceleration were still vectors, but direction was indicated by the sign (+/-). • We will first understand how to work with vectors graphically

  14. Vectors • Graphically, we can depict a vector as an arrow • Arrows have both length (magnitude) and direction.

  15. Addition of vectors • In one dimension • If the vectors are in the same direction • But if the vectors are in the opposite direction

  16. Addition of Vectors (2D) • In two dimensions, things are more complicated

  17. Addition of Vectors • “Tip to tail” method • Draw first vector • Draw second vector, placing tail at tip of first vector • Arrow from tail of 1st vector to tip of 2nd vector is

  18. Commutative property of vectors • “Tip to tail” method works in either order • Draw first vector • Draw second vector, placing tail at tip of first vector • Arrow from tail of 1st vector to tip of 2nd vector is

  19. Three or more vectors • Can use “tip to tail” for more than 2 vectors = + +

  20. Subtraction of vectors • For a given vector the negative of the vector is a vector with the same magnitude in the opposite direction. = + - • Difference between two vectors is equal to the sum of the first vector and the negative of the second vector

  21. Adding vectors by components • Adding vectors graphically is useful to understand the concept of vectors, but it is inherently slow (not to mention next to impossible in 3D!!) • Any 2D vector can be decomposed into components

  22. Determining vector components • So in 2D, we can always write any vector as the sum of a vector in the x-direction, and one in the y-direction. • Given V(V,θ), we can find Vx and Vy

  23. Determining vector components • Or, given Vx and Vy, we can find V(V,θ).

  24. Example • A vector is given by its vector components: • Write the vector in terms of magnitude and direction

  25. Adding vectors by components • Given V1 and V2, how can we find V= V1 + V2? V2 V V1

  26. 3D Vectors • Adding vectors vectors by components is especially helpful for 3D vectors. • Also, much easier for subtraction

  27. Multiplying a vector by a scalar • You can also multiply a vector by a scalar • When you do this, you don’t change the direction of the vector, only its magnitude c=2 c=4 c=-2

  28. Unit Vectors • Up to this point, we have written vectors in terms of their components as follows: • There is an easier way to do this, and this is how we will write vectors for the remainder of the course:

  29. Unit Vectors • What are unit vectors? • Unit vectors have a magnitude of 1 and point along major axes of our coordinate system • Writing a vector with unit vectors is equivalent to multiplying each unit vector by a scalar

  30. Unit Vectors • For a vector with components: • Write this in unit vector notation

  31. Example: Vector Addition/Subtraction • Displacement • A hiker traces her movement along a trail. The first leg of her hike brings her to the foot of the mountain: • On the second leg, she ascends the mountain, which she figures to be a displacement of: • On the third, she walks along a plateau. • Then she falls of a cliff • What is the hiker’s final displacement?

  32. Example: Vector Addition/Subtraction

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