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**Section 3: Falling Objects**

Chapter 2 Section 3: Falling Objects

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**Free Fall acceleration:**

An object dropped or thrown near the surface of the Earth experiences a constant acceleration directed toward the center of the earth. This acceleration is called the free- fall acceleration, or the acceleration due to gravity. Free fall acceleration is the same for all objects, regardless of mass.

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**Free fall acceleration:**

The value we will use for free fall acceleration is: agravity = g = m/s2 This is the average value near the surface of the Earth. It is different at other locations, such as on the Moon. We consider the direction of free fall to be negative because it is toward the Earth (down), so we assign a negative value to the acceleration vector (the object accelerates toward earth)

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**Free fall acceleration:**

9.8 m/s 19.6 m/s 29.4 m/s 39.2 m/s 49.0 m/s

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**Free fall acceleration:**

All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall. Vertical velocity at the top of the arc is 0

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**Free fall acceleration:**

If 2 objects of different masses are dropped from the same height, they will accelerate at the same rate, and hit the ground at the same time (not counting air resistance)

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**Ignore Air Resistance (unless instructed otherwise)**

If there is air resistance, the object will be slowed down The more surface area, the more air resistance. An object with the same mass and more surface area will be slower than an object with less surface area. (ex. A wadded piece of paper and a flat piece of paper.) When there is no air resistance, (such as in a vacuum) no matter what the surface area of the object is, it will fall and hit the ground at the same time as all other objects. Unless told otherwise, you can ignore air resistance when working free-fall problems

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Formulas Acceleration = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 − 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 = 𝑣 𝑓 − 𝑣 𝑖 ∆𝑡 (from previous unit) Acceleration = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 − 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 2 (𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡) = 𝑣 𝑓 2 − 𝑣 𝑖 ∆𝑑

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**Equations for Free-Fall Acceleration**

When vi = 0 m/s When vi = 0 m/s ∆𝑑 = 𝑣 𝑓 2 − 𝑣 𝑖 𝑎

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**Formulas (continued) For constant velocity, For accelerated motion,**

Displacement (d) = 𝑣 ∆𝑡 (from previous unit) For accelerated motion, 𝑑= 𝑣 𝑖 ∆𝑡 𝑎 𝑡 2 For zero initial velocity (for example, free-fall from a drop), 𝑑= 𝑣 𝑖 ∆𝑡 𝑎 𝑡 2 = 0 ∙ ∆𝑡 𝑎 𝑡 2 = 1 2 𝑎 𝑡 2

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**Class assignment / Homework**

1. A gumdrop is released from rest at the top of the Empire State Building, which is 381 m tall. Disregarding air resistance, calculate the displacement of the gumdrop after 1.00, 2.00, and 3.00 s. 2. A small sandbag is dropped from rest from a hovering hot-air balloon. After 2.0 s, how far below the balloon is the sand bag? 3. A physics student throws a softball straight up into the air with a speed of 17.5 m/s. The ball is in the air for a total of 3.60 s before it is caught at its original position. How high does the ball rise? (Hint: The time to max height is ½ total time.)

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**Average velocity : (slope of the line)**

Displacement : x position x as a function of time t x2 x x1 t t1 t2 t Average velocity : (slope of the line)

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9.2 Calculating Acceleration

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