2. a gravity  g Falling objects accelerate down at  32 ft/sec 2 9.8 m/sec 2 more precisely: at sea level9.80621 m/sec 2 32.1725 ft/sec 2 16.0 km (  10 miles) above earth’s surface a gravity drops to about 9.75 m/sec 2 32.5 km (  20 miles) above earth’s surface a gravity drops to about 9.70 m/sec 2 even skydivers experience a  9.8 m/sec 2 even commercial jet carriers experience a gravity only 1% under the value at sea level!

3. North Pole a gravity = 9.832 San Franciscoa gravity = 9.800 Denver a gravity = 9.796 The gravitational force on an object decreases by about a millionth for every 3 meter (~10 feet) gain in elevation. An individual with a 50 kilogram mass weighs 490 Newtons (110 pounds) in New York City; but ~0.25 newton (1 ounce) less in mile-high Denver.

4. If you drop an object (assuming air resistance is negligible) it accelerates down at g=9.8 m/sec 2. If instead you throw it downward, its acceleration after release is A.<g B.=g C.>g If you drop an object (assuming air resistance is negligible) it accelerates down at g=9.8 m/sec 2. If instead you throw it upward, its acceleration the moment after you release it is A.<g B.=g C.>g

5. A ball is dropped from rest, and a bullet shot out of a gun, straight down. Neglecting air resistance, which has the greater acceleration just before hitting the ground? A) the ball B) the bullet C) both have the same acceleration The acceleration of gravity does not depend on the mass or the speed of the object in free fall!

6. Inclined Plane 1212 2 3232 4242 5252 A ball rolling down an inclined plane has constant acceleration Is the acceleration of the ball down the ramp 9.8 m/s 2 ? A) yesB) no No! This ball is not in free fall. Gravity alone does not act on it. The inclined plane provides a force of support which affects the motion!

7. A ball is thrown straight up and falls back to the ground. Which of the following is true about its velocity v and its acceleration a at the highest point in its path? A) v = 0 and a = 0 B) v  0, but a = 0 C) v = 0, but a  0 D) v  0 and a  0 E) cannot be determined At the highest point in its path, the ball momentarily comes to a stop, and so its velocity is zero. However, since the ball is in free fall, its acceleration is g = 9.8 m/s 2 (at every moment).

8. The maximum velocity, v, an object reaches falling freely from rest, is directly proportional to the time, t, of its fall: v  t. A) TRUE B) FALSE How fast is an object moving at the end of a one second fall? 9.8 m sec 2  1 sec = 9.8 m/sec How fast is an object moving at the end of a three second fall? 9.8 m sec 2  3 sec = 29.4 m/sec

9. A ball is in free fall for 8 seconds. Its speed after 4 seconds is half the speed it will reach by 8 seconds. A) TRUE B) FALSE The distance it travels in the first 4 seconds equals the distance it will travel in the last 4 seconds. A) TRUE B) FALSE For objects in freefall, the distance fallen, d, is directly proportional to the time, t, spent falling: d  t. A) TRUE B) FALSE

10. How far does an object in freefall drop in one second? In 8 seconds? distance = rate  time Your grade school mnenomic We qualify this slightly with = starting point + rate  time current position position at t = 0 Since a falling object’s velocity is constantly increasing, maybe we should use: rate  time = (average velocity)  time average velocity = v min + v max 2 = v 0 + v 2 starting velocity at time=0 current velocity at the present time

11. position at t = 0 average velocity = v 0 + v 2 starting velocity at time=0 current velocity at the present time built up by accelerating over the time t

12. How far does an object in freefall drop in one second? In 8 seconds? distance fallen from rest 0 = 4.9 m In 1 second: = 313.6 m In 8 seconds:

13. 15010050 We all saw: 25100225 1 sec3 sec 2 sec 1.5 sec 3 sec 1 sec downhill: v avg =25 cm/sec final speed: v =150 cm/3sec downhill: v avg =50 cm/sec final speed: v =100 cm/sec downhill: v avg =225 cm/3sec final speed: v =150 cm/sec

14. 15010050 Which we can check out: 25100225 1 sec3 sec 2 sec 1.5 sec 3 sec 1 sec downhill: v avg =25 cm/sec final speed: v =150 cm/3sec downhill: v avg =50 cm/sec final speed: v =100 cm/sec downhill: v avg =225 cm/3sec final speed: v =150 cm/sec 25 is the average of 0+50. To build up to final speed of 50cm/sec in 1 sec took an accleration = 50cm/sec 2. So along this ramp the ball accelerates this fast! Accelerating for 2 seconds should allow The ball to build to a speed of (50cm/sec 2 )  (2 sec) = 100 cm/sec… exactly the final speed we observed! Accelerating for 3 seconds should mean a final speed of (50cm/sec 2 )  (3 sec) = 150 cm/sec… Also note, the average speed down the ramp now is (0 + 150)/2 = 75 cm/sec which equals our measured 225/3 = 75 cm/sec

15. Question 1 B. = g Question 2 B. = g C) both have the same acceleration Question 3 Whenever an object is freed of constraints – a ball released from your grip, a bullet escaping from its barrel, an arrow loosed from its bowstring – whatever forces were supplied under those constraints (the driving push of your hand, the pressure of expanding gases from exploding gunpowder, the tension of a bowstring) vanish. In all the above cases, the ONLY force acting on the objects (after release) is gravity! A ball on a ramp is not in free fall. Gravity alone does not act on it. The inclined plane provides a force of support which affects the motion! Question 4 B) no C) v = 0, but a  0 Question 5 At the highest point in its path, the ball momentarily comes to a stop, and so its velocity is zero. However, since the ball is in free fall, its acceleration is g = 9.8 m/s 2 (at every moment). A) TRUE v  t. Question 6 Question 7 A) TRUE v  t. B) FALSE Question 8 B) FALSE Question 9 Distance fallen is NOT proportional to time falling. Initially, as you build speed from 0, your speeds are modest (you may not get very far each second). But as you build speed you travel greater distances in the same interval of time! Some Answers