Acceleration Near Earth’s Surface

1.58. Figure 14 shows three accelerometers attached to carts that arein motion. In each case, describe two possible motions thatwould create the condition shown.(b)(a)stopperFigure 14(c)coloured liquidbeadsMaking Connections9. During part of the blastoff of a space shuttle, the velocity of theshuttle changes from 125 m/s [up] to 344 m/s [up] in 2.30 s.(a) Determine the average acceleration experienced by theastronauts on board during this time interval.(b) This rate of acceleration would be dangerous if theastronauts were standing or even sitting vertically in theshuttle. What is the danger? Research the type of trainingthat astronauts are given to avoid the danger.Reflecting10. Describe the most common difficulties you have in applying thetangent technique on position-time graphs. What do you do toreduce these difficulties?11. Think about the greatest accelerations you have experienced.Where did they occur? Did they involve speeding up or slowingdown? What effects did they have on you?1.5Acceleration Near Earth’s SurfaceAmusement park rides that allow passengers to drop freely toward the groundattract long lineups (Figure 1). Riders are accelerated toward the ground until abraking 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 Earthdoes not depend on mass.It was Galileo Galilei who first proved that, if we ignore the effect of airresistance, the acceleration of falling objects is constant. He proved thisexperimentally 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 notmeasure vertical acceleration was that he had no way of measuring short periodsof time accurately. You will appreciate the difficulty of measuring time when youperform the next experiment.Figure 1The Drop Zone at Paramount Canada’sWonderland, north of Toronto, allows theriders to accelerate toward the ground freelyfor approximately 3 s before the brakingsystem causes an extreme slowing down.Motion 37

acceleration due to gravity: thevector quantity 9.8 m/s2 [down], representedby the symbol g Had Galileo been able to evaluate the acceleration of freely falling objectsnear Earth’s surface, he would have measured it to be approximately 9.8 m/s2[down]. This value does not apply to objects influenced by air resistance. It is anaverage value that changes slightly from one location on Earth’s surface toanother. It is the acceleration caused by the force of gravity.The vector quantity 9.8 m/s2 [down], or 9.8 m/s2 [ ], occurs so frequently inthe 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 asthe symbol for “gram.”) More precise magnitudes of g are determined by scientists throughout the world. For example, at the International Bureau of Weightsand Measures in France, experiments are performed in a vacuum chamber inwhich an object is launched upwards by using an elastic. The object has a systemof mirrors at its top and bottom that reflect laser beams used to measure timeof flight. The magnitude of g obtained using this technique is 9.809 260 m/s2.Galileo would have been pleased with the precision!In solving problems involving the acceleration due to gravity, aav 9.8 m/s2[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 ThisActivityA Vertical AccelerometerVertical accelerometers, available commercially in kit form, can be usedto 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 dropped the accelerometer downward(c) 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 parkrides?Figure 2A typical vertical accelerometer forstudent usePracticeUnderstanding ConceptsAnswers1. (a) 29 m/s [ ](b) 59 m/s [ ]2. (a) 18 m/s [ ](b) 26 m/s [ ]38Chapter 11. In a 1979 movie, a stuntman leaped from a ledge on Toronto’s CNTower and experienced free fall for 6.0 s before opening the safetyparachute. Assuming negligible air resistance, determine thestuntman’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 ofmagnitude 4.0 m/s. Determine the stone’s velocity after 2.2 s if thedirection of the initial velocity is (a) upward and (b) downward.Neglect air resistance.

1.5Investigation 1.5.1Acceleration Due to GravityAs with Investigation 1.4.1, there are several possible methods for obtainingposition-time data of a falling object in the laboratory. The ticker-tape timer, themotion sensor, and the videotape were suggested before. In this investigation, apicket 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 othermethods of data collection are used, refer back to Investigation 1.4.1 for analysis.INQUIRY uestionWhat 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 inInvestigation 1.4.1? Make a prediction with respect to the general type ofmotion and the quantitative results.Also, think about how the motion will differ if the mass of the object is altered.Materialspicket fence with photogatecomputer interfacing softwarelight masses to add to the picket fencemasking tapeProcedure1. Open the interface software template designed for use with a picket fence.2. Obtain a picket fence and measure the distance between the leading edgesof 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 fenceand 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 picketfence straight through the photogate and have your partner catch it.6. After analyzing this trial, tape some added mass to the bottom of the picketfence and repeat the experiment.Figure 3A picket fence is a clear strip of plastic withseveral black wide bands marked at regularintervals along the length. The black bandsinterrupt the beam of the photogate. As eachband interrupts the beam, it triggers a clockto measure the time required for the picketfence to travel a distance equal to thespacing between the leading edges of twosuccessive bands. Picket fences can be usedwith computer software applications or withstand-alone timing devices.Analysis(b) The position-time data should appear automatically on the computerscreen. Look at the position-time graph of the data collected. What type ofmotion 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 theaverage acceleration of the picket fence. How did the acceleration of theheavier object compare with that of the lighter one?Motion 39

DID YOU KNOW ?Escape SystemsOne area of research into the effect of acceleration on the human body deals with thedesign of emergency escape systems fromhigh-performance aircraft. In an emergency,the pilot would be shot upward away fromthe damaged plane from a sitting positionthrough an escape hatch. The escape systemwould have to be designed to produce a highenough acceleration to quickly remove a pilotfrom 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 averageor instantaneous velocities?(g) What evidence is there to support your answer to the Question? Refer toshapes of three graphs.(h) Look back in this text for the type of motion that a free-falling objectshould experience and the accepted value for the acceleration due togravity on Earth’s surface. How do your results compare with the acceptedvalue? Determine the percentage error between the experimental value forthe acceleration due to gravity and the accepted value.(i) Are your results the same as what you predicted? If not, what incorrectassumption did you make?(j) Identify any sources of error in this investigation. Do they reasonablyaccount for the percentage error for your results?(k) How does the mass of an object affect its acceleration in a free-fallsituation?(l) If you were to repeat the investigation, what improvements could you makein order to increase the accuracy of the results?Applications of AccelerationFigure 4This 1941 photograph shows W.R. Franks inthe “anti-gravity” suit he designed.Figure 5An astronaut participates in a launch simulation exercise as two crew members assist.40Chapter 1Galileo Galilei began the mathematical analysis of acceleration, and the topic hasbeen studied by physicists ever since. However, only during the past century hasacceleration 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, amusementpark rides, and other vehicles. The acceleration in cars and passenger airplanes isusually small, but in a military airplane or a rocket, it can be great enough tocause damage to the human body. A person can faint when blood drains from thehead and goes to the lower part of the body. In 1941, a Canadian pilot andinventor named W.R. Franks designed an “anti-gravity” suit to prevent pilotblackouts in military planes undergoing high-speed turns and dives. The suit hadwater encased in the inner lining to prevent the blood vessels from expandingoutwards (Figure 4).Modern experiments have shown that the maximum acceleration a humanbeing can withstand for more than about 0.5 s is approximately 30g (thevertical bars represent the magnitude of the vector, in this case, 294 m/s2).Astronauts experience up to 10g (98 m/s2) for several seconds during a rocketlaunch. At this acceleration, if the astronauts were standing, they would faintfrom 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 andother vehicles than with blasting off in rockets. Studies are continually beingdone to determine the effect on the human body when a car has a collision ormust stop quickly. Seatbelts, headrests, and airbags help prevent many injuriescaused by rapid braking (Figure 6).In the exciting sport of skydiving, the diver jumps from an airplane andaccelerates 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