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Falling objects accelerate down at agravity g 32 ft/sec2 9.8 m/sec2 more precisely: at sea level 9.80621 m/sec2 32.1725 ft/sec2 16.0 km (10 miles) above earth’s surface agravity drops to about 9.75 m/sec2 even skydivers experience a 9.8 m/sec2 32.5 km (20 miles) above earth’s surface agravity drops to about 9.70 m/sec2 even commercial jet carriers experience agravity only 1% under the value at sea level! North Pole San Francisco Denver agravity = 9.832 agravity = 9.800 agravity = 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. If you drop an object (assuming air resistance is negligible) it accelerates down at g=9.8 m/sec2. If instead you throw it upward, its acceleration the moment after you release it is A. B. C. <g =g >g If you drop an object (assuming air resistance is negligible) it accelerates down at g=9.8 m/sec2. If instead you throw it downward, its acceleration after release is A. B. C. <g =g >g 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! Inclined Plane A ball rolling down an inclined plane has constant acceleration 12 22 32 42 52 Is the acceleration of the ball down the ramp 9.8 m/s2? A) yes B) 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! 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/s2 (at every moment). 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? m 1 sec = 9.8 m/sec 9.8 2 sec How fast is an object moving at the end of a three second fall? m 3 sec = 29.4 m/sec 9.8 2 sec 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 How far does an object in freefall drop in one second? In 8 seconds? Your grade school mnenomic distance = rate time We qualify this slightly with current = starting point + rate time position x x0 v t position at t = 0 Since a falling object’s velocity is constantly increasing, maybe we should use: rate time = (average velocity) time vmin + vmax average velocity = 2 v0 + v = 2 starting velocity at time=0 current velocity at the present time x x0 vavg t position at t = 0 average velocity = starting velocity at time=0 v0 + v 2 current velocity at the present time built up by accelerating over the time t v v0 at x x0 x x0 v0 ( v0 at ) 2 2v0 at 2 t x x0 v0t at 1 2 2 t How far does an object in freefall drop in one second? In 8 seconds? x x0 v0t at 1 2 distance fallen 2 x x0 v0t at 1 2 0 from rest In 1 second: d at 9.8m / s (1s) 1 2 2 2 1 2 = 4.9 m In 8 seconds: d 9.8m / s (8s) 1 2 2 = 313.6 m 2 2 2 We all saw: 150 100 3 sec 50 1 sec downhill: vavg=25 cm/sec final speed: v =150 cm/3sec 2 sec downhill: 1.5 sec vavg=50 cm/sec final speed: v =100 cm/sec 3 sec 1 sec downhill: vavg=225 cm/3sec final speed: v =150 cm/sec Which we can check out: 150 100 3 sec 50 1 sec downhill: vavg=25 cm/sec 25 is the average of 0+50. final speed: To build up to final speed of 50cm/sec in 1 sec took an accleration = 50cm/sec2. v =150 cm/3sec So along this ramp the ball accelerates this fast! 2 sec downhill: 1.5 sec Accelerating for 2 seconds should allow The ball to build to a speed of (50cm/sec2)(2 sec) = 100 cm/sec… exactly the final speed we observed! vavg=50 cm/sec final speed: v =100 cm/sec 3 sec 1 sec downhill: vavg=225 cm/3sec Accelerating for 3 seconds should mean a final speed of (50cm/sec2)(3 sec) = 150 cm/sec… final speed: Also note, the average speed down v =150 cm/sec the ramp now is (0 + 150)/2 = 75 cm/sec which equals our measured 225/3 = 75 cm/sec Some Answers Question 1 Question 3 B. = g Question 2 B. = g C) both have the same acceleration 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! Question 4 Question 5 B) no 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! C) v = 0, but a At the highest point in its path, the ball momentarily comes to a stop, and so its velocity is zero. 0 However, since the ball is in free fall, its acceleration is g = 9.8 m/s2 (at every moment). Question 6 A) TRUE vt. Question 7 A) TRUE vt. Question 8 B) FALSE Question 9 B) FALSE 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!