2.1. One way to measure gravitational acceleration is to simply drop an object and measure its time of flight, i.e. the time it is in air before landing. Suppose you drop an object from height h = 2 m. To minimize the effect of drag (air resistance), suppose the object is aerodynamic in shape, and has a small cross-sectional area but a large mass. Under these conditions, drag will be negligible. You will measure the time of flight using a stopwatch. 2.1.1. Suppose you measure the time of flight to be 0.639 s. Use the kinematic equations to calculate g: What is the percent difference between this value and the expected value of 9.8 m/s²? 2.1.2. Suppose you repeat the measurement to verify your results. When you repeat the measurement, you find the time of flight to be 0.739 s. Use the kinematic equations to calculate g: What is the percent difference between this value and the expected value of 9.8 m/s? The human reaction time is approximately 0.2 seconds.10 This is the minimum time required to respond to a stimulus, such as an object hitting the ground. Notice that a difference of only 0.1 seconds between the flight times – less than the human reaction time – makes a large difference in your result. This is clearly - - not a good method for measuring gravitational acceleration. 2.2. A better way to measure gravitational acceleration is to use a video camera. A video camera takes a fixed number of photographs per second. Knowing this number, you can calculate the time of flight much more accurately than a stopwatch. 2.2.1. Traditional movie cameras record video at a rate of 24 frames per second (fps). This means that 24 photographs are recorded each second. Recently, some directors choose to use cameras with higher frame rates for a "heightened sense of reality."11 Suppose you plan to use a camera with a frame rate of 40 fps. How long (in seconds) does each photograph take? In other words, what is the time interval (in seconds) between two consecutive frames?
2.1. One way to measure gravitational acceleration is to simply drop an object and measure its time of flight, i.e. the time it is in air before landing. Suppose you drop an object from height h = 2 m. To minimize the effect of drag (air resistance), suppose the object is aerodynamic in shape, and has a small cross-sectional area but a large mass. Under these conditions, drag will be negligible. You will measure the time of flight using a stopwatch. 2.1.1. Suppose you measure the time of flight to be 0.639 s. Use the kinematic equations to calculate g: What is the percent difference between this value and the expected value of 9.8 m/s²? 2.1.2. Suppose you repeat the measurement to verify your results. When you repeat the measurement, you find the time of flight to be 0.739 s. Use the kinematic equations to calculate g: What is the percent difference between this value and the expected value of 9.8 m/s? The human reaction time is approximately 0.2 seconds.10 This is the minimum time required to respond to a stimulus, such as an object hitting the ground. Notice that a difference of only 0.1 seconds between the flight times – less than the human reaction time – makes a large difference in your result. This is clearly - - not a good method for measuring gravitational acceleration. 2.2. A better way to measure gravitational acceleration is to use a video camera. A video camera takes a fixed number of photographs per second. Knowing this number, you can calculate the time of flight much more accurately than a stopwatch. 2.2.1. Traditional movie cameras record video at a rate of 24 frames per second (fps). This means that 24 photographs are recorded each second. Recently, some directors choose to use cameras with higher frame rates for a "heightened sense of reality."11 Suppose you plan to use a camera with a frame rate of 40 fps. How long (in seconds) does each photograph take? In other words, what is the time interval (in seconds) between two consecutive frames?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
Question
Transcribed Image Text:2. DETERMINING GRAVITATIONAL ACCELERATION: In this step, we will determine Earth's
gravitational acceleration using free-fall data. We also wish to gain some appreciation for
why measuring gravitational acceleration is difficult.
2.1. One way to measure gravitational acceleration is to simply drop an object and measure
its time of flight, i.e. the time it is in air before landing. Suppose you drop an object from
height h = 2 m. To minimize the effect of drag (air resistance), suppose the object is
aerodynamic in shape, and has a small cross-sectional area but a large mass. Under
these conditions, drag will be negligible. You will measure the time of flight using a
stopwatch.
2.1.1. Suppose you measure the time of flight to be 0.639 s.
Use the kinematic
equations to calculate g:
What is the percent difference
between this value and the expected value of 9.8 m/s²?
2.1.2. Suppose you repeat the measurement to verify your results. When you repeat
the measurement, you find the time of flight to be 0.739 s. Use the kinematic
equations to calculate g:
What is the percent difference
between this value and the expected value of 9.8 m/s²?
The
human reaction time is approximately 0.2 seconds.10 This is the minimum time
required to respond to a stimulus, such as an object hitting the ground. Notice
that a difference of only 0.1 seconds between the flight times – less than the
human reaction time – makes a large difference in your result. This is clearly
not a good method for measuring gravitational acceleration.
2.2. A better way to measure gravitational acceleration is to use a video camera. A video
camera takes a fixed number of photographs per second. Knowing this number, you can
calculate the time of flight much more accurately than a stopwatch.
2.2.1. Traditional movie cameras record video at a rate of 24 frames per second (fps).
This means that 24 photographs are recorded each second. Recently, some
directors choose to use cameras with higher frame rates for a “heightened sense
of reality."11 Suppose you plan to use a camera with a frame rate of 40 fps. How
long (in seconds) does each photograph take? In other words, what is the time
interval (in seconds) between two consecutive frames?
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