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Day 4 – May 13 – WBL 2.4-2.5 2.4 Kinematic Equations PC141 Intersession 2013Slide 1

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Day 4 – May 13 – WBL 2.4-2.5 2.4 Kinematic Equations PC141 Intersession 2013Slide 2

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Day 4 – May 13 – WBL 2.4-2.5 2.4 Kinematic Equations PC141 Intersession 2013Slide 3

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Day 4 – May 13 – WBL 2.4-2.5 Problem #1: Average Speed PC141 Intersession 2013Slide 4 An object accelerates uniformly from rest for t seconds. The object’s average speed for this time interval is A B C D WBL LP 2.15

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Day 4 – May 13 – WBL 2.4-2.5 Problem #2: From the Earth to the Moon PC141 Intersession 2013Slide 5 In his 1865 novel From the Earth to the Moon, Jules Verne proposed sending people to the moon via a rocket cannon that accelerates a capsule along a length of 220 m, attaining a final speed of 11.2 km/s. What acceleration would the passengers experience? Fun(ish) fact: 11.2 km/s is the “escape velocity” from Earth. An object must attain this velocity if it is to break free from the gravitational pull of Earth. Solution: In class

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Day 4 – May 13 – WBL 2.4-2.5 Problem #3: A Blow to the Head PC141 Intersession 2013Slide 6 A soccer ball is headed with and without the use of a helmet. In both cases, the acceleration of the player’s head is plotted as a function of time. At time t = 7 ms, what is the difference in the speed acquired by the bare head and the speed acquired by the helmeted head? Solution: In class

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Day 4 – May 13 – WBL 2.4-2.5 Problem #4: Sprinting PC141 Intersession 2013Slide 7 The current world record for the 100 m dash is 9.58 seconds, set by Usain Bolt in 2009. Analysis of that run shows that he reached his top speed around the 70 metre mark, at which point his speed was 12.42 m/s. What was his average speed during the race? Assuming that his acceleration was constant over the first 70 metres, what was the magnitude of his acceleration during that portion of the race? Solution: In class

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Day 4 – May 13 – WBL 2.4-2.5 Problem #5: Worst. Car. Ever. PC141 Intersession 2013Slide 8 The “slowest” car ever produced is the 2009 Tata Nano, which accelerates from 0 to 60 miles per hour in a blistering 29.4 seconds. What is the magnitude of this acceleration, assuming that it is constant over this duration? How much distance does it cover during this time? Solution: In class

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Day 4 – May 13 – WBL 2.4-2.5 Problem #6: Sprinter vs. Car PC141 Intersession 2013Slide 9 It seems that the 2009 Tata Nano has a much weaker acceleration that Usain Bolt. How much of a head start would the car require in order to “beat” Usain Bolt over 100 metres? Solution: In class

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Day 4 – May 13 – WBL 2.4-2.5 2.5 Free Fall PC141 Intersession 2013Slide 10

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Day 4 – May 13 – WBL 2.4-2.5 When an object’s motion is influenced only by g, we say that it is in free fall. Although this term seems to imply that the object is moving downward, it in fact refers to any motion that is subject only to g, even if it projected upward or at an angle (such as a drive of a golf ball). Remember, even when an object is traveling upward, it is still accelerating downward. This is what causes it to slow down, momentarily stop, then begin its downward journey. 2.5 Free Fall PC141 Intersession 2013Slide 11 Notice that g doesn’t depend on any properties (mass, shape…) of the moving object. This is only true in a vacuum. Otherwise, air resistance comes into play, and the object isn’t truly in free fall.

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Day 4 – May 13 – WBL 2.4-2.5 2.5 Free Fall PC141 Intersession 2013Slide 12

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Day 4 – May 13 – WBL 2.4-2.5 Here are a few facts about free fall motion for an object thrown vertically upward. These may be of benefit in solving more difficult problems later on… 1.If the object returns to its original elevation, the upward and downward portions of the journey take the same time. 2.If the object returns to its original elevation, it does so with the same speed as that at which it was launched. The velocity isn’t the same, since the direction has changed. This concept will be beneficial when we study kinetic and potential energy. 3.At the top of the object’s trajectory, its velocity is momentarily zero. 2.5 Free Fall PC141 Intersession 2013Slide 13

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Day 4 – May 13 – WBL 2.4-2.5 Problem #7: Dropping Rocks PC141 Intersession 2013Slide 14 You drop a rock off a bridge. When the rock has fallen 4 m, you drop a second rock. As the two rocks continue to fall, what happens to their separation? A The separation increases as they fall B The separation stays constant at 4 m C The separation decreases as they fall D It is impossible to answer without more information

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Day 4 – May 13 – WBL 2.4-2.5 Problem #8: Your Idiot Upstairs Neighbour PC141 Intersession 2013Slide 15 A particular apartment building has floors which are vertically separated by 4.0 m. Somebody from an upper floor drops an apple from their window. A resident on the 1 st floor measures the time that the apple takes to pass across his entire window, which measures 1.35 m vertically. From what floor was the apple dropped? Solution: In class WBL EX 2.73

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Day 4 – May 13 – WBL 2.4-2.5 Problem #9: Vertical Rocket PC141 Intersession 2013Slide 16 A model rocket is fired vertically upward, with a constant acceleration of 12.0 m/s 2. When it reaches a height of 1000 m, the engines immediately cut off, leaving the model rocket in free fall. What is the rocket’s speed at the moment the engines cut off? What is the maximum altitude of the rocket? What is the time it takes to reach this maximum altitude, measured from the moment of launch from the ground? Solution: In class WBL EX 2.75

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