1.5 Acceleration Near Earth s Surface

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1 Figure 14 shows three accelerometers attached to carts that are in motion. In each case, describe two possible motions that would create the condition shown. (a) (b) (c) stopper coloured liquid beads Figure 14 Making Connections 9. During part of the blastoff of a space shuttle, the velocity of the shuttle changes from 125 m/s [up] to 344 m/s [up] in 2.30 s. (a) Determine the average acceleration experienced by the astronauts on board during this time interval. (b) This rate of acceleration would be dangerous if the astronauts were standing or even sitting vertically in the shuttle. What is the danger? Research the type of training that astronauts are given to avoid the danger. Reflecting 10. Describe the most common difficulties you have in applying the tangent technique on position-time graphs. What do you do to reduce these difficulties? 11. Think about the greatest accelerations you have experienced. Where did they occur? Did they involve speeding up or slowing down? What effects did they have on you? 1.5 Acceleration Near Earth s Surface Amusement park rides that allow passengers to drop freely toward the ground attract long lineups (Figure 1). Riders are accelerated toward the ground until a braking system causes the cars to slow down over a small distance. If two solid metal objects of different masses, 20 g and 1000 g, for example, are dropped from the same height above the floor, they land at the same time. This fact proves that the acceleration of falling objects near the surface of Earth does not depend on mass. It was Galileo Galilei who first proved that, if we ignore the effect of air resistance, the acceleration of falling objects is constant. He proved this experimentally by measuring the acceleration of metal balls rolling down a ramp. Galileo found that, for a constant slope of the ramp, the acceleration was constant it did not depend on the mass of the metal ball. The reason he could not measure vertical acceleration was that he had no way of measuring short periods of time accurately. You will appreciate the difficulty of measuring time when you perform the next experiment. Figure 1 The Drop Zone at Paramount Canada s Wonderland, north of Toronto, allows the riders to accelerate toward the ground freely for approximately 3 s before the braking system causes an extreme slowing down. Motion 37

2 acceleration due to gravity: the vector quantity 9.8 m/s 2 [down], represented by the symbol g Had Galileo been able to evaluate the acceleration of freely falling objects near Earth s surface, he would have measured it to be approximately 9.8 m/s 2 [down]. This value does not apply to objects influenced by air resistance. It is an average value that changes slightly from one location on Earth s surface to another. It is the acceleration caused by the force of gravity. The vector quantity 9.8 m/s 2 [down], or 9.8 m/s 2 [ ], occurs so frequently in the study of motion that from now on, we will give it the symbol g, which represents the acceleration due to gravity. (Do not confuse this g with the g used as the symbol for gram. ) More precise magnitudes of g are determined by scientists throughout the world. For example, at the International Bureau of Weights and Measures in France, experiments are performed in a vacuum chamber in which an object is launched upwards by using an elastic. The object has a system of mirrors at its top and bottom that reflect laser beams used to measure time of flight. The magnitude of g obtained using this technique is m/s 2. Galileo would have been pleased with the precision! In solving problems involving the acceleration due to gravity, a av 9.8 m/s 2 [down] can be used if the effect of air resistance is assumed to be negligible. When air resistance on an object is negligible, we say the object is falling freely. Try This Activity Vertical accelerometers, available commercially in kit form, can be used to measure acceleration in the vertical direction (Figure 2). (a) Predict the reading on the accelerometer if you held it and kept it still moved it vertically upward at a constant speed moved it vertically downward at a constant speed (b) Predict what happens to the accelerometer bob if you thrust the accelerometer upward (c) A Vertical Accelerometer dropped the accelerometer downward Use an accelerometer to test your predictions in (a) and (b). Describe what you discover. (d) How do you think this device could be used on amusement park rides? Figure 2 A typical vertical accelerometer for student use Answers 1. (a) 29 m/s [ ] (b) 59 m/s [ ] 2. (a) 18 m/s [ ] (b) 26 m/s [ ] Practice Understanding Concepts 1. In a 1979 movie, a stuntman leaped from a ledge on Toronto s CN Tower and experienced free fall for 6.0 s before opening the safety parachute. Assuming negligible air resistance, determine the stuntman s velocity after falling for (a) 3.0 s and (b) 6.0 s. 2. A stone is thrown from a bridge with an initial vertical velocity of magnitude 4.0 m/s. Determine the stone s velocity after 2.2 s if the direction of the initial velocity is (a) upward and (b) downward. Neglect air resistance. 38 Chapter 1

3 1.5 Investigation Acceleration Due to Gravity As with Investigation 1.4.1, there are several possible methods for obtaining position-time data of a falling object in the laboratory. The ticker-tape timer, the motion sensor, and the videotape were suggested before. In this investigation, a picket fence and photogate can also be used to get very reliable results. If possible, try to use a different method from that used in the previous investigation. Here, the analysis will be shown for the picket fence and photogate method. If other methods of data collection are used, refer back to Investigation for analysis. Questioning Hypothesizing Predicting Planning Conducting INQUIRY SKILLS Recording Analyzing Evaluating Communicating Question What type of motion is experienced by a free-falling object? Hypothesis/Prediction (a) How will this motion compare with that on the inclined plane studied in Investigation 1.4.1? Make a prediction with respect to the general type of motion and the quantitative results. Also, think about how the motion will differ if the mass of the object is altered. Materials picket fence with photogate computer interfacing software light masses to add to the picket fence masking tape Procedure 1. Open the interface software template designed for use with a picket fence. 2. Obtain a picket fence and measure the distance between the leading edges of two bands as shown in Figure 3. Enter this information into the appropriate place in the experimental set-up window. 3. Before performing the experiment, become familiar with the picket fence and the software to find out how the computer obtains the values shown. 4. Enable the interface and get a pad ready for the picket fence to land on. 5. Hold the picket fence vertically just above the photogate. Drop the picket fence straight through the photogate and have your partner catch it. 6. After analyzing this trial, tape some added mass to the bottom of the picket fence and repeat the experiment. Figure 3 A picket fence is a clear strip of plastic with several black wide bands marked at regular intervals along the length. The black bands interrupt the beam of the photogate. As each band interrupts the beam, it triggers a clock to measure the time required for the picket fence to travel a distance equal to the spacing between the leading edges of two successive bands. Picket fences can be used with computer software applications or with stand-alone timing devices. Analysis (b) The position-time data should appear automatically on the computer screen. Look at the position-time graph of the data collected. What type of motion is represented by the graph? (c) Look at the velocity-time graph. What type of motion does it describe? (d) Determine the average acceleration from the velocity-time graph. (e) What type of motion is experienced by a free-falling object? State the average acceleration of the picket fence. How did the acceleration of the heavier object compare with that of the lighter one? Motion 39

4 DID YOU KNOW? Escape Systems One area of research into the effect of acceleration on the human body deals with the design of emergency escape systems from high-performance aircraft. In an emergency, the pilot would be shot upward away from the damaged plane from a sitting position through an escape hatch. The escape system would have to be designed to produce a high enough acceleration to quickly remove a pilot from danger, but not too high that the acceleration would cause injury to the pilot. Evaluation (f) Explain how the computer calculates the velocity values. Are these average or instantaneous velocities? (g) What evidence is there to support your answer to the Question? Refer to shapes of three graphs. (h) Look back in this text for the type of motion that a free-falling object should experience and the accepted value for the acceleration due to gravity on Earth s surface. How do your results compare with the accepted value? Determine the percentage error between the experimental value for the acceleration due to gravity and the accepted value. (i) Are your results the same as what you predicted? If not, what incorrect assumption did you make? (j) Identify any sources of error in this investigation. Do they reasonably account for the percentage error for your results? (k) How does the mass of an object affect its acceleration in a free-fall situation? (l) If you were to repeat the investigation, what improvements could you make in order to increase the accuracy of the results? Figure 4 This 1941 photograph shows W.R. Franks in the anti-gravity suit he designed. Figure 5 An astronaut participates in a launch simulation exercise as two crew members assist. Applications of Acceleration Galileo Galilei began the mathematical analysis of acceleration, and the topic has been studied by physicists ever since. However, only during the past century has acceleration become a topic that relates closely to our everyday lives. The study of acceleration is important in the field of transportation. Humans undergo acceleration in automobiles, airplanes, rockets, amusement park rides, and other vehicles. The acceleration in cars and passenger airplanes is usually small, but in a military airplane or a rocket, it can be great enough to cause damage to the human body. A person can faint when blood drains from the head and goes to the lower part of the body. In 1941, a Canadian pilot and inventor named W.R. Franks designed an anti-gravity suit to prevent pilot blackouts in military planes undergoing high-speed turns and dives. The suit had water encased in the inner lining to prevent the blood vessels from expanding outwards (Figure 4). Modern experiments have shown that the maximum acceleration a human being can withstand for more than about 0.5 s is approximately 30g (the vertical bars represent the magnitude of the vector, in this case, 294 m/s 2 ). Astronauts experience up to 10g (98 m/s 2 ) for several seconds during a rocket launch. At this acceleration, if the astronauts were standing, they would faint from loss of blood to the head. To prevent this problem, astronauts must sit horizontally during blastoff (Figure 5). In our day-to-day lives, we are more concerned with braking in cars and other vehicles than with blasting off in rockets. Studies are continually being done to determine the effect on the human body when a car has a collision or must stop quickly. Seatbelts, headrests, and airbags help prevent many injuries caused by rapid braking (Figure 6). In the exciting sport of skydiving, the diver jumps from an airplane and accelerates toward the ground, experiencing free fall for the first while (Figure 7). While falling, the skydiver s speed will increase to a maximum amount called 40 Chapter 1

5 1.5 Figure 6 As the test vehicle shown crashes into a barrier, the airbag being researched expands rapidly and prevents the dummy s head from striking the windshield or steering wheel. After the crash, the airbag deflates quickly so that, in a real situation, the driver can breathe. terminal speed. Air resistance prevents a higher speed. At terminal speed, the diver s acceleration is zero; in other words, the speed remains constant. For humans, terminal speed in air is about 53 m/s or 190 km/h. After the parachute opens, the terminal speed is reduced to between 5 m/s and 10 m/s. Terminal speed is also important in other situations. Certain plant seeds, such as dandelions, act like parachutes and have a terminal speed of about 0.5 m/s. Some industries take advantage of the different terminal speeds of various particles in water when they use sedimentation to separate particles of rock, clay, or sand from one another. Volcanic eruptions produce dust particles of different sizes. The larger dust particles settle more rapidly than the smaller ones. Thus, very tiny particles with low terminal speeds travel great horizontal distances around the world before they settle. This phenomenon can have a serious effect on Earth s climate. terminal speed: maximum speed of a falling object at which point the speed remains constant and there is no further acceleration Practice Understanding Concepts 3. Sketch the general shape of a velocity-time graph for a skydiver who accelerates, then reaches terminal velocity, then opens the parachute and reaches a different terminal velocity. Assume that downward is positive. SUMMARY Acceleration Near Earth s Surface On average, the acceleration due to gravity on Earth s surface is g 9.8 m/s 2 [ ]. This means that in the absence of air resistance, an object falling freely toward Earth accelerates at 9.8 m/s 2 [ ]. Various experimental ways can be used to determine the local value of g. The topic of accelerated motion is applied in various fields, including transportation and the sport of skydiving. Figure 7 This skydiver experiences free fall immediately upon leaving the aircraft, but reaches terminal speed later. Motion 41

6 Section 1.5 Questions Understanding Concepts 1. An apple drops from a tree and falls freely toward the ground. Sketch the position-time, velocity-time, and acceleration-time graphs of the apple s motion, assuming that (a) downward is positive, and (b) upward is positive. 2. An astronaut standing on the Moon drops a feather, initially at rest, from a height of over 2.0 m above the Moon s surface. The feather accelerates downward, just as a ball or any other object would on Earth. In using frame-by-frame analysis of a videotape of the falling feather, the data in Table 1 are recorded. Table 1 Time (s) Position (m [down]) (a) Use the data to determine the acceleration due to gravity on the Moon. (b) Why can a feather accelerate at the same rate as all other objects on the Moon? 3. Give examples to verify the following statement: In general, humans tend to experience greater magnitudes of acceleration when slowing down than when speeding up. 4. Sketch an acceleration-time graph of the motion toward the ground experienced by a skydiver from the time the diver leaves the plane and reaches terminal speed. Assume downward is positive. 5. During a head-on collision, the airbag in a car increases the time for a body to stop from 0.10 s to 0.30 s. How will the airbag change the magnitude of acceleration of a person travelling initially at 28 m/s? Applying Inquiry Skills 6. Two student groups choose different ways of performing an experiment to measure the acceleration due to gravity. Group A chooses to use a ticker-tape timer with a mass falling toward the ground. Group B chooses to use a motion sensor that records the motion of a falling steel ball. If both experiments are done well, how will the results compare? Why? 7. Describe how you would design and build an accelerometer that measures vertical acceleration directly using everyday materials. Making Connections 8. Today s astronauts wear an updated version of the anti-gravity suit invented by W.R. Franks. Research and describe why these suits are required and how they were developed. Follow the links for Nelson Physics 11, 1.5. GO TO 42 Chapter 1