a gravity  g Falling objects accelerate down at  32 ft/sec m/sec 2 more precisely: at sea level m/sec ft/sec km (  10 miles) above earth’s surface a gravity drops to about 9.75 m/sec 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!

North Pole a gravity = San Franciscoa gravity = Denver a gravity = 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/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

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 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!

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).

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

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? 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

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

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: = m In 8 seconds:

Last time we saw: 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

A rocket test projectile is launched skyward at 88 m/sec (198 mi/hr). How high does it go? v o = ? v final = ? a = ? time to reach peak, t = ? height reached, x = ? When does it peak? What has happened by that point? v = 0 = 9 sec So = 792m – 396.9m = 395 m (1/4 mile)  9.8 m/sec 2  8 m/sec

A ball is thrown straight upward and caught when it returns to the height from which it was released. 1. At its peak position, the ball’s A. instantaneous velocity is maximum. B. instantaneous velocity is zero. C. instantaneous acceleration is zero. D. both B & C are true. 2. The time to fall back from its peak position is A. greater than B. equal to C. less than the time it took to climb that high. 3. The speed it builds up to downward by the moment it is caught is A. greater than B. equal to C. less than the speed it was thrown upward with.

For objects for which air friction is negligible, time up = time down speed down = speed up

Two spheres of identical mass are Released when the mechanism above Is triggered. One sphere is launched Horizontally by a spring, the other is simultaneously dropped from rest. A. The launched sphere will reach the ground first. B. Both spheres touch ground at the same time. C. The dropped sphere reaches the ground first.

Galileo’s critics argued that if the earth moved:

A stone is flung horizontally at 8 m/sec from a point 1100 meters above the base of a cliff. How far away from the cliff does it land? or +1100m m/s Careful!!! Actually a y =  9.8m/s 2 a x = ? 0 VERTICALLY t = 15 sec HORIZONTALLY  x = 120 m Its y-component of motion is like dropping from rest!

WeightSupport (floor)

Adding all these supporting forces together some pull left, some pull right, some pull forward, some pull back all tend to pull UP! (a tug-of-war balancing)

Styrofoam bridge weighted at center Pressure applied to rigid glass bar

Launched vertically, when the spring is released, from this fast moving cart, the ball will A. still be caught by the barrel from which it was fired. B. land out in front of the cart since it carried the cart’s forward motion before it was fired. C. land behind the cart which will have moved out from beneath it.