Lab6 - Dr. Gelman PDF

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Dr. Gelman...

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Lab #6: Acceleration Due to Gravity PHYS 1.2 L Section: D705 Instructor: Dr. Gelman Date: 10/15/13 Lab partners names: Emmanuel, Peter

Jonathan Santana

Objectives In this experiment you will verify that the displacement of a freely falling body from rest is directly proportional to the square of the falling time and the acceleration due to gravity does not depend on mass.

Learning Outcomes 

Determine the acceleration due to gravity.

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Explore the relationship between position, velocity, and acceleration for a freely falling object.

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Analyze the graphs of position versus square of time and velocity versus time for a freely falling object.

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Determine the instantaneous velocity and acceleration of a freely falling object.

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Explain how the slope of the graph relates to the acceleration due to gravity.

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Understand that the acceleration due to gravity is independent of the mass of the falling object.

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Use Excel for analysis and find the equations of the trend lines.

Theoretical Background The most familiar example of motion with constant acceleration is an object falling towards the Earth. The motion of a falling object under the influence of the Earth's gravity is called free fall. If we allow an object to fall in vacuum, so that air resistance does not affect its motion, we find a remarkable fact: all bodies, regardless of their size, shape, or composition, fall with the same acceleration at the same point near the Earth's surface. I he acceleration Of a freely Balling called the acceleration due to gravity or the acceleration of free fall, and its magnitude is denoted by the symbol g. At or near the Earth's surface, the magnitude of g is approximately 9.81 m/s' = 981 cm/s'. This is the standard value for g, the direction of the free fall acceleration at any point establishes what we mean by the word "down" at that point. Although we speak of falling objects, objects in upward motion experience the same free fall acceleration, both in magnitude and direction. That is, no matter whether the velocity of the object is up or down, the direction of its acceleration under the influence of the Earth's gravity is always down. The exact value of the free fall acceleration varies with latitude and altitude, there are also significant variations caused by the differences in the local density of the Earth's crust. The demonstration of a freely falling body performed by the Apollo astronauts in 1971 on the surface of the Moon was seen by millions of people on television. One of the astronauts dropped

a feather and a hammer simultaneously and millions saw them fall at the same rate. Remember that there is no atmosphere on the Moon. Hence, neglecting air resistance, all freely falling bodies accelerate downward at the same rate regardless of their masses. When an object falls through the air, the air exerts a retarding or drag force that tends to reduce the speed of the object. The force of air resistance acting on the falling object depends primarily on two things. First, it depends on the size of the falling object Second it depends on the speed of the falling object relative to the air. To the speed of the object, for higher speeds, it is more nearly of the speed of the object. When the object is dropped near the surface of the Earth that object is squared experiences the constant acceleration g. Since the acceleration due to gravity is constant near the surface.

g Verus m 10 9.95

G (m/s^2)

9.9

f(x) = − 0 x + 9.95

9.85 9.8 9.75 9.7 9.65

5

10

15

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25

30

m (g)

Questions 1. What kind of information is indicated by the graph of the acceleration due to gravity versus balls mass if the slope of the curve is zero? It is indicating that inertial mass and gravitational mass are the same property of matter. 2. A ball is dropped from the roof of a building. The ball strikes the ground after 6 seconds. (a) How tall, in meters is the building? Initial velocity=0

Time = 6 seconds Acceleration= 9.81 (down is positive) d= displacement d= vi*t + 1/2a(t^2) d=0(6)+1/2(9.81)(6^2) d=176.58 (b) What is the magnitude of the ball's velocity just before it reaches the ground? Initial velocity=0 a=9.81 t=6s Acceleration= velocity final- velocity initial/time 9.81= vf-0/6 vf=58.86 m/s 3. A student throws a ball vertically downward from the top of a building. The ball leaves the thrower's hand with a speed of 10 m/s. (a) What is its speed after falling for 1s? 2s? 3s? v(1) = 10m/s + 9.8m/s/s x 1s = 19.8m/s, v(2) = 29.6m/s, v(3) = 39.4m/s (b) How far does it fall in 1s? 2s? 3s? distance = v0 t + 1/2 gt^2 distance after 1s = 10m/s x 1s + 4.9m/s/s x 1s = 14.9m, 2s = 10m/s x 2s + 4.9m/s/s (4s^2) = 39.6m , similarly for t=3s (b) What is the magnitude of its velocity after falling 10m? use vf^2=v0^2 + 2ad vf^2 = 10^2 + 2 x 9.8*10 = 17.2m/s 4. A ball is thrown straight up in the air. What is its acceleration at the instant it reaches its highest point? Does the acceleration due to gravity change ether in magnitude or in direction, when the velocity of the ball changes direction? Ignore air resistance. Acceleration => Vy^2=Vx^2 - 2a (y1-y0) and acceleration due to gravity is usually 9.81m/s^2 on earth, but it can change if you go to a different planet. So it depends on masses and distance. But for the ball on earth the gravity is 9.81 down. 5. What are some examples of falling objects in which it would be unreasonable to neglect air resistance? A feather, a parachute, a towel, a paper air plane... anything that is relatively light weight compared to its size and is not aerodynamically shaped usually works when considering long distances.

Conclusion To sum it all up, in this laboratory we verified that the displacement of a freely falling body from rest is directly proportional to the square of the falling time and the acceleration due to gravity, does not depend on mass....