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Assignment MasteringPhysics: Print View Page 1 of 20 Assignment Display Mode: View Printable Answers IUPhysicsP201F2009 Assignment 5b Due at 11:00pm on Sunday, October 5, 2008 View Grading Details Problem 6.57 Description: Early test flights for the space shuttle used a "glider" (mass of 980 kg including pilot) that was launched horizontally at 500 (km)/h from a height of 3500 m. The glider eventually landed at a speed of 200 (km)/h. (a) What would its landing speed... Early test flights for the space shuttle used a "glider" (mass of 980 at 500 Part A What would its landing speed have been in the absence of air resistance? Express your answer using two significant figures. ANSWER: = from a height of 3500 including pilot) that was launched horizontally . . The glider eventually landed at a speed of 200 Part B What was the average force of air resistance exerted on it if it came in at a constant glide of 10 ANSWER: = to the Earth? Problem 6.88 Description: Some electric-power companies use water to store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. (a) To store the energy produced in t hour by a P P * 10^6 (W) electric-power plant, how many cubic meters of... Some electric-power companies use water to store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. Part A To store the energy produced in 3.0 hour by a 150 electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 2 of 20 490 above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 . for every Express your answer using two significant figures. ANSWER: = Problem 6.76 Description: An airplane pilot fell h after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater d deep, but survived with only minor injuries. Assuming the pilot's mass was m and his terminal velocity was v_terminal. ... An airplane pilot fell 390 after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.5 deep, but survived with only minor injuries. Assuming the pilot's mass was 79 and his terminal velocity was 39 Part A Estimate the work done by the snow in bringing him to rest. Express your answer using two significant figures. ANSWER: = . Part B Estimate the magnitude of the average force exerted on him by the snow to stop him. Express your answer using two significant figures. ANSWER: = Part C Estimate the work done on him by air resistance as he fell. Express your answer using two significant figures. ANSWER: = Problem 6.58 Description: (a) How long will it take a P motor to lift a m piano to a sixth-story window y above? http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 3 of 20 Part A How long will it take a 630 ANSWER: motor to lift a 335 piano to a sixth-story window 17.0 above? = PSS 7.3: The Careless Roofer Description: Young/Geller Problem-Solving Strategy 7.3 Conservation of energy with nonconservative forces is illustrated. Learning Goal: To practice Problem-Solving Strategy 7.3 Conservation of energy with nonconservative forces. While a roofer is working on a roof that slants at = 8.50 = 22.0 = 36.0 above the horizontal, he accidentally nudges his toolbox, causing it to start sliding downward, starting from rest. A frictional force of magnitude acts on the toolbox as it slides. If the box starts = 4.25 from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof? Assume that the acceleration due to gravity is = 9.80 . Problem Solving Strategy 7.3 Conservation of energy with nonconservative forces SET UP 1. Identify the system you will analyze, and decide on the initial and final states (positions and velocities) you will use in solving the problem. Draw one or more sketches showing the initial and final states. 2. Define your coordinate system, particularly the zero points for gravitational and elastic potential energies (the point at which ). 3. List the initial and final kinetic and potential energies ( nonconservative forces. Write an expression for the work, SOLVE , , , and ) and identify any , done by the nonconservative forces. 4. Use the general expression for conservation of energy and solve to find the unknown quantity. REFLECT 5. Does your answer make sense? Did friction slow the object down? Did any pushing forces speed the object up? Can you explain any negative signs? SET UP Before writing any equations, organize your information and draw appropriate diagrams. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 4 of 20 Part A The initial and final states of the toolbox are illustrated in the figure. Identify the initial speed the vertical distance through which the toolbox moves. of the toolbox and Hint A.1 Right-triangle trigonometry Recall that the sides of a right angle triangle are related by the following: , , and . Enter the initial speed and the height symbolically in terms of the variables given in the problem introduction, separated by a comma. ANSWER: , = After identifying the initial and final positions and velocities of the toolbox, you must define your coordinate system. You can choose any coordinate system you wish. However, for this problem use the coordinate system shown in the figure. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 5 of 20 Part B Determine the initial and final kinetic energies, and . Enter the initial and final kinetic energies of the toolbox symbolically in terms of the variables given in the problem introduction separated by a comma. ANSWER: , = Part C Determine the initial and final potential energies, and . Enter the initial and final potential energies of the toolbox symbolically in terms of the variables given in the problem introduction separated by a comma. Do not use the variable introduced in Part A. ANSWER: , = Part D Determine the work done by any nonconservative forces acting on the toolbox. Hint D.1 How to find the work done by a force When an object undergoes a displacement with magnitude , making an angle with with magnitude along a straight line, while a constant force (as illustrated), acts on the object, the work done by the force on the object is given by . http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 6 of 20 Enter the work done by nonconservative forces symbolically in terms of the variables given in the problem introduction. ANSWER: = SOLVE Now that you have set up the problem, choose appropriate equations and solve for your unknowns. Part E Use the general expression for conservation of energy to write an equation relating the initial and final kinetic and potential energies and the work done by friction. Enter your equation symbolically using the variables given in the problem introduction. Do not use the variable . Enter the left side of the equation and the right side of the equation separated by a comma. Do not use an equal sign. ANSWER: , = The only unknown variable in this equation is . Use the values for the variables provided in the problem introduction to solve for numerically. Part F What is the speed of the toolbox as it falls off the roof? Enter your answer numerically in meters per second. ANSWER: http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 7 of 20 = REFLECT Think about whether your results make sense. Part G If the force if friction is removed, how would your answer change? ANSWER: The speed would be slower. The speed would be the same. The speed would be faster. Baby Bounce with a Hooke Description: Application of Hooke's Law One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer,which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 8 of 20 Part A The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer. Displacement from equilibrium, ( ) 0 0.005 0.010 0.015 0.020 What is the spring constant tested for the baby bouncer? Hint A.1 How to approach the problem Look at the pattern in the data to determine what number must multiply the distance to achieve the force exerted on the spring. Look at both the table and the graph. Part A.2 Find the spring constant from the graph , Force exerted on the spring, ( ) 0 2.5 5.0 7.5 10 of the spring being The relationship between the displacement and force is linear. This set of data follows the form of where so is the slope of the line and is the y intercept. For all springs, the force is 0 when the displacement is 0 . This leaves the slope of the line to determine the relationship between displacement and force. What is the slope that you get from the graph? Hint A.2.a Slope equation Slope is given by the change in divided by the change in . In this case, . Express your answer as a fraction in unsimplified form. ANSWER: = All you need to do now is to convert the fraction to its decimal value. Express your answer to two significant figures in newtons per meter. ANSWER: = Part B One of the greatest difficulties with setting up the baby bouncer is determining the right height above the floor so that the child can push off and bounce. Knowledge of physics can be really helpful here. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 9 of 20 If the spring constant , the baby has a mass , and the baby's legs reach a distance from the bouncer, what should be the height of the "empty" bouncer above the floor? Hint B.1 How to approach the problem Use Hooke's law to determine the displacement of the spring from equilibrium given the force the spring must exert to hold up the baby. The displacement must lower the baby toward the floor until the baby's feet can touch. Hint B.2 Which force to use The force the spring exerts is equal in magnitude but opposite in direction to the force exerted on it by the weight of the baby. Part B.3 Find the force exerted by the baby The weight of the baby is equal to the force exerted on the spring. What is the weight of the baby? Hint B.3.a Formula for weight Recall that the weight of an object is given by , where is the mass of the object and is the acceleration due to gravity. Express your answer in newtons to three significant figures. ANSWER: = Part B.4 Find the displacement of the spring Use Hooke's law to determine how far the spring would stretch downward once the baby is placed in the seat. How far does the bottom end of the spring move? Express your answer in meters to two significant figures. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 10 of 20 ANSWER: = To finish the problem, you must consider the length of the baby's legs. Express your answer in meters to two significant figures. ANSWER: = for the spring holding up a baby may not seem very large but you must consider A displacement of how small babies are. Also, once the baby begins jumping up and down, the extra energy allows the spring to stretch further than 0.22 and a resonant frequency may be achieved. At resonance the bouncing may become too violent, leading to a potentially dangerous situation for the little bouncer. Circling Ball Description: Find difference between tension in string for bottom and top of vertical circle. Tagged hints. A ball of mass is attached to a string of length . It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, the ball's speeds are and , and the corresponding tensions in the string are and . and have magnitudes and . Part A Find , the difference between the magnitude of the tension in the string at the bottom relative to that at the top of the circle. Hint A.1 How to approach this problem Identify the forces that act on the ball as it moves along the circular path. Then, write equations for the sum of the forces on the ball at the top and the bottom of the path. Next, use Newton's second law to relate these net forces to the acceleration of the ball. Notice that the ball does not move with uniform speed so the acceleration of the ball at the top of the circle is different from the acceleration at the bottom of the circle. To finish the problem, you may want to use energy conservation to relate the speed of the ball at the bottom of the http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 11 of 20 circle to the speed at the top. Part A.2 Find the sum of forces at the bottom of the circle What is the magnitude of the net force in the y direction acting on the ball at the bottom of the circle? Express your answer in terms of the variables given in the problem. You may use acceleration of gravity, 9.8 ANSWER: = . to represent the Part A.3 Find Find the acceleration at the bottom of the circle , the magnitude of the vertical acceleration of the ball at the bottom of its circle. and possibly other given quantities. Express your answer in terms of ANSWER: = Part A.4 Find the tension at the bottom of the circle in the string when the ball is at the bottom of the circle. Find the magnitude of the tension Hint A.4.a What physical principle to use Apply Newton's 2nd law in the y direction to obtain Express your answer in terms of ANSWER: = , , . of the ball at the bottom of the circle. , and the speed Part A.5 Find the sum of forces at the top of the circle What is the magnitude of the net force in the y direction acting on the ball at the top of its circle? Express your answer in terms of the variables given in the problem. You may use acceleration of gravity, 9.8 ANSWER: = . to represent the Part A.6 Find Find the acceleration at the top of the circle , the magnitude of the vertical acceleration of the ball at the top of its circle. and possibly other given quantities. Express your answer in terms of http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 12 of 20 ANSWER: = Part A.7 Find the tension at the top of the circle in the string when the ball is at the top of the circle. Find the magnitude of the tension Hint A.7.a Relationship to solution for Follow the same steps you used to find reversed. Express your answer in terms of ANSWER: = , , , and the speed of the ball at the top of the circle. (see Hint 3), noting carefully where various directions (signs) are Part A.8 Find the relationship between and The total mechanical energy of the system is the same when the ball is at the top and bottom of the vertical circle. Use conservation of energy to write an expression for in terms of . Your answer may also include ANSWER: = , , and . Express the difference in tension in terms of final answer. ANSWER: = and . The quantities and should not appear in your The method outlined in the hints is really the only practical way to do this problem. If done properly, finding the difference between the tensions, , can be accomplished fairly simply and elegantly. Workhorses on Erie Canal Description: Compute the work done by one of two horses pulling a barge. Then compute the power provided by the horse. Two workhorses tow a barge along a straight canal. Each horse exerts a constant force of magnitude ropes make an angle speed . , and the tow with the direction of motion of the horses and the barge. Each horse is traveling at a constant http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 13 of 20 Part A How much work is done by each horse in a time ? Hint A.1 Formula for work For a constant force, the work done is the dot product of the force vector with the displacement vector (pointing from the initial to the final position of the object), . Part A.2 Find the x component of the force exerted by either horse (it's the same for both horses) along its What is the (x) component of the force direction of travel? Express your answer in terms of the quantities given in the problem introduction. ANSWER: = Part A.3 Find the distance traveled traveled by a horse during a time interval . Find the distance Express your answer in terms of the quantities given in the problem introduction. ANSWER: = Express the work in terms of the quantities given in the problem introduction. ANSWER: = Part B How much power Hint B.1 does each horse provide? Formula for power . Power is the time derivative of the work, Express your answer in terms of the quantities given in the problem introduction. ANSWER: = One way to compute the power provided by each horse is to first compute the work done by each horse during a time interval (as in Part A), then take the time derivative. However, an easier way to compute the power provided when a force acts on an object moving with velocity is to use the formula . http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 14 of 20 Fat: The Fuel of Migrating Birds Description: Find the maximum distance a bird can fly without feeding, given the amount of fat consumed in the flight and the bird's average speed and power consumption. Also, find how many grams of fat a hummingbird needs to fly across the Gulf of Mexico without feeding. Small birds can migrate over long distances without feeding, storing energy mostly as fat rather than carbohydrate. Fat is a good form of energy storage because it provides the most energy per unit mass: 1 gram of fat provides about 9.4 (food) Calories, compared to 4.2 (food) Calories per 1 gram of carbohydrate. Remember that Calories associated with food, which are always capitalized, are not exactly the same as calories used in physics or chemistry, even though they have the same name. More specifically, one food Calorie is equal to 1000 calories of mechanical work or 4186 joules. Therefore, in this problem use the conversion factor . Part A Consider a bird that flies at an average speed of 10.7 average rate of 3.70 and releases energy from its body fat reserves at an (this rate represents the power consumption of the bird). Assume that the bird consumes without stopping for feeding. How far will the bird fly before feeding again? of fat to fly over a distance Hint A.1 How to approach the problem From the average speed of the bird, you can calculate how far the bird can fly without stopping if you know the duration of the flight. To determine the duration of the flight, first find the amount of energy available from converting 4 grams of fat, and then use the definition of power. Part A.2 Find the energy used during the flight does the bird have available when it converts 4 grams of fat? How much energy Hint A.2.a Converting fat into energy As stated in the introduction of this problem,1 gram of fat provides about 9.4 (food) Calories. Also keep in mind http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 15 of 20 that Express your answer in kilojoules. ANSWER: = . Part A.3 Find the duration of the flight , how many hours can it fly using the energy supply provided If the bird consumes energy at a rate of 3.70 by 4 grams of fat? Hint A.3.a Definition of power The average power (measured in watts) is the ratio of the energy transformed in the time interval : Note that power measures either the rate at which energy is transferred (or transformed) or the rate at which work is performed. Hint A.3.b Power: units Power is measured in watts. One watt is equal to 1 joule per second (i.e., Express your answer in hours. ANSWER: = ). Part A.4 Find the distance in terms of average velocity traveled in the time interval at an average speed ? Which of the following expressions gives the distance ANSWER: Now use this expression to find the distance traveled by the bird. Make sure that the units are consistent! Express your answer in kilometers. ANSWER: = Part B http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 16 of 20 How many grams of carbohydrate Hint B.1 would the bird have to consume to travel the same distance ? How to approach the problem As stated in the introduction of this problem,1 gram of fat provides about 9.4 Calories, while 1 gram of carbohydrate provides 4.2 Calories. Express your answer in grams ANSWER: = This is more than twice the amount of fat that was needed! In addition, to store 1 gram of carbohydrate (in the form of glycogen, the most common form of animal carbohydrate) about 3 grams of water are needed. Therefore, if energy were stored as carbohydrates, the bird would need to carry more than eight times the fuel mass to perform the same migratory flight! Part C Field observations suggest that a migrating ruby-throated hummingbird can fly across the Gulf of Mexico on a nonstop flight traveling a distance of about 800 . Assuming that the bird has an average speed of 40.0 and an average power consumption of 1.70 , how many grams of fat does a ruby-throated hummingbird need to accomplish the nonstop flight across the Gulf of Mexico? Hint C.1 How to approach the problem In Part A you were given the amount of fat consumed over the entire flight and were asked to calculate the distance traveled by the migrating bird. Now you need to solve the reverse problem. That is, given the distance traveled, calculate the amount of energy required to perform the flight. Thus, apply the same method as the one used in part A, only in reverse. From the information on distance and average speed, calculate the duration of the nonstop flight. Then use your result and the given power consumption to determine the amount of energy required for the flight. Finally, calculate how many grams are needed to provide that amount of energy. Part C.2 Find the duration of the flight will the ruby-throated hummingbird fly to travel a distance of 800 at an average speed of How many hours 40.0 ? Express your answer in hours ANSWER: = Part C.3 Find the energy required for the nonstop flight Given that the hummingbird consumes energy at an average rate of 1.70 during the nonstop flight over the Gulf of Mexico? Hint C.3.a How to use power and time , how much energy will it require Remember that power is energy transferred (or transformed) per unit time. Make sure you are using the correct unit for time. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 17 of 20 Express your answer in joules. ANSWER: = Now calculate how many grams of fat are required to provide this amount of energy. Recall that 1 gram of fat provides 9.4 Calories of energy. Express your answer in grams. ANSWER: = Considering that in normal conditions the mass of a ruby-throated hummingbird is only 3 or 4 grams, the bird will need to almost double its body mass to store enough fat to perform the nonstop flight. Work on a Block Sliding Up a Frictionless Incline Description: A box is pulled up a frictionless incline. Find the work done by gravity, the pulling force, and the normal force. (version for algebra-based courses) A block of weight = 35.0 sits on a frictionless inclined plane, which makes an angle = 18.5 = 32.0 with respect to the horizontal, as shown in the figure. A force of magnitude sufficient to pull the block up the plane at constant speed. , applied parallel to the incline, is just Part A The block moves up an incline with constant speed. What is the total work the block moves a distance = 4.10 done on the block by all forces as up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest. Hint A.1 What physical principle to use To find the total work done on the block, use the work-energy theorem, which relates the total work done to the http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 18 of 20 initial and final kinetic energies: . Part A.2 Find the change in kinetic energy What is the change in the kinetic energy of the block during this process? Keep in mind that that the block moves at constant speed. Hint A.2.a A formula for kinetic energy The kinetic energy of an object is related to its mass and velocity by the formula . Express your answer numerically in joules. ANSWER: = Express your answer numerically in joules. ANSWER: = Part B What is the incline? Hint B.1 An equation for work done by a constant force , where is the angle , the work done on the block by the force of gravity as the block moves a distance = 4.10 up Recall that the equation for the work done by a constant force is given as between the force vector the equation and the displacement vector . Another way to express this relationship is through , where is the component of the force vector that lies in the same direction as the , displacement. When using this expression, you must be careful to determine the sign of the work done by the force. If points in the same direction as , then is positive. If points in the opposite direction from then is negative. The next two hints will help you find , the parallel component of the gravitational force. . Then you can find the work done by gravity using the general formula Hint B.2 Force diagram The figure shows a diagram of the forces acting on the block. http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 19 of 20 Part B.3 What is Find the component of the gravitational force parallel to the plane , the magnitude of the component of the force of gravity along the inclined plane? Hint B.3.a Vector components of the force of gravity The force due to gravity, often called the weight, has components both parallel and perpendicular to the inclined plane. Based on the force diagram in Hint B.2, the component of parallel to the inclined plane has magnitude given by . Express your answer numerically in newtons. ANSWER: = Hint B.4 Relative directions of force and motion Keep in mind that work done by a force is positive if a force acts in the direction of motion, and is negative if the force acts against the direction of motion. Express your answer numerically in joules. ANSWER: = Part C What is incline? Hint C.1 Equation for work done by a constant force Use the same procedure as that presented in Hint B.1. The displacement different. Express your answer numerically in joules. ANSWER: = . This is not a coincidence, of course. Can you see why? If yes, the is the same, but the force vector is , the work done on the block by the applied force as the block moves a distance = 4.10 up the You may have noticed that next part will be easy. Part D http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 MasteringPhysics: Assignment Print View Page 20 of 20 What is , the work done on the block by the normal force as the block moves a distance = 4.10 up the inclined plane? Hint D.1 The parallel component of the normal force The normal force and the block's displacement vector are perpendicular. Express your answer numerically in joules. ANSWER: = . Also, and . Therefore, , Now consider this: or . It may have been easier to solve Part C first. Perhaps that is what you did. Summary 0 of 10 items complete (0% avg. score) 0 of 10 points http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1144577 9/17/2008 ... View Full Document