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Acceleration due to Gravity

Gravity is… acceleration of an object toward the center of the Earth The acceleration of an object toward the center of the Earth due to the gravitational attraction of the mass of the planet on the object. Free fall refers to only the force of gravity acting on an object. Gravity is a constant acceleration downward. It is a vector quantity.

All objects exert mutual gravitational attractive forces on each other. The reason the earth exerts such a large force is because it has such a large mass. When in free fall, objects have a constant downward acceleration of 9.8m/s 2 on the surface of the earth. …on Jupiter: 24.9 m/s 2 …on Mercury: 3.7 m/s 2

If we drop a full water bottle and an empty water bottle at the same time, which one will land first (or will they both land at the same time)? All objects fall with the same acceleration (if we neglect air resistance).

Gravity only does DOWN. Acceleration due to gravity (g) acts downward no matter whether the object is thrown upwards, dropped downwards, moving horizontally…no matter what! We choose to give g a positive or negative sign. We must be consistent within a problem when assigning direction.

Sample problem: A water droplet falls from an umbrella 3.60m from the ground. What is the velocity of the raindrop as it hits the ground? Assign down as positive d = 3.60m a = 9.8 m/s 2 Vf = ? Vi = 0m/s

D = 3.60m a = 9.8 m/s 2 Vf = ? Vi = 0m/s The raindrop had an initial speed of 0m/s. It fell 3.60m while accelerating at a rate of 9.8m/s 2. It reached a speed of -8.4m/s. Vf 2 = Vi 2 + 2ad Vf 2 = 0 2 + 2 (9.8)(3.60) Vf = - 8.4m/s or 8.4m/s

A person throws a ball upward into the air with an initial velocity of 15.0m/s. Calculate how high it goes and how long the ball is in the air before it comes back to his hand(we are not concerned with the throwing action). Downward is negative (-9.8m/s 2 ) Upward is positive (15.0m/s) For the upward motion: A = -9.8 m/s 2 Vi = 15 m/s Vf = 0 m/s Time to rise: A =  V  t -9.8 = 0-15  t  t = 1.53s Time to fall: A =  V  t -9.8 = -15-0  t  t = 1.53s Total time in the air: 3.06s Vf 2 = Vi 2 + 2ad 0 2 = 15 2 + 2(-9.8)d D = 11.5m high before falling Acceleration and velocity are not always in the same direction!

A person throws a ball upward into the air with an initial velocity of 15.0m/s. Calculate how high it goes and how long the ball is in the air before it comes back to his hand. The second part of this problem can be solved by using the displacement in the Distance formula. What is the displacement if the ball returns to the spot where it was released? Displacement= 0m D = Vit + ½at 2 0 = (15)t + ½(-9.8)t 2 0 = t(15 + 4.9t) Two answers: t = 0 15 + 4.9t = 0 t = 0s t = 3.06s

Terminal Velocity Air friction increases as falling objects accelerate. The force of air friction and force of acceleration due to gravity will eventually balance. After that point the object neither speeds up or slows down. The shape, density and orientation of an object affects its terminal velocity. Approximate terminal velocities: Large feather:0.4m/s Parachutist(chute open):7m/s no parachute:67m/s

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