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Assignment MasteringPhysics: Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... [ Print View ] [ Print ] Physics 2211-001, Fall 2008 Newton's third Law Due at 11:00pm on Wednesday, September 17, 2008 View Grading Details Position, Velocity, and Acceleration Learning Goal: To identify situations when position, velocity, and /or acceleration change, realizing that change can be in direction or magnitude. If an object's position is described by a function of time, (measured from a nonaccelerating reference frame), then , and the object's acceleration is the object's velocity is described by the time derivative of the position, described by the time derivative of the velocity, . It is often convenient to discuss the average of the latter two quantities between times and : and . Part A You throw a ball. Air resistance on the ball is negligible. Which of the following functions change with time as the ball flies through the air? Hint A.1 Newton's 2nd Law Hint not displayed ANSWER: only the position of the ball only the velocity of the ball only the acceleration of the ball the position and velocity of the ball the position and the velocity and acceleration of the ball Part B You are driving a car at 65 mph. You are traveling north along a straight highway. What could you do to give the car a nonzero acceleration? Hint B.1 What constitutes a nonzero acceleration? 1 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Hint not displayed ANSWER: Press the brake pedal. Turn the steering wheel. Either press the gas or the brake pedal. Either press the gas or the brake pedal or turn the steering wheel. Part C A ball is lodged in a hole in the floor near the outside edge of a merry-go-round that is turning at constant speed. Which kinematic variable or variables change with time, assuming that the position is measured from an origin at the center of the merry-go-round? Hint C.1 Change of a vector Hint not displayed ANSWER: the position of the ball only the velocity of the ball only the acceleration of the ball only both the position and velocity of the ball the position and velocity and acceleration of the ball Part D For the merry-go-round problem, do the magnitudes of the position, velocity, and acceleration vectors change with time? Hint D.1 Change of magnitude of a vector Hint not displayed ANSWER: yes no Problem 7.9 To withstand "g-forces" of up to 10 g's, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a "human centrifuge." 10 g's is an acceleration of . Part A If the length of the centrifuge arm is 10.0 ANSWER: 31.3 m/s , at what speed is the rider moving when she experiences 10 g's? Problem 7.32 2 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. Part A What is the size of the friction force on the car? ANSWER: 6750 A Mass on a Turntable: Conceptual A small metal cylinder rests on a circular turntable that is rotating at a constant rate, as illustrated in the diagram. Part A Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? Hint A.1 The direction of acceleration can be determined from Newton's second law Hint not displayed View Full Document

b c d e 3 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Part B Let be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to from the center of the turntable. Which of the following statements accurately describe the a new location motion of the cylinder at the new location? Part B.1 Find the speed of the cylinder Part not displayed Part B.2 Find the acceleration of the cylinder Part not displayed Check all that apply. ANSWER: The speed of the cylinder has decreased. The speed of the cylinder has increased. The magnitude of the acceleration of the cylinder has decreased. The magnitude of the acceleration of the cylinder has increased. The speed and the acceleration of the cylinder have not changed. Two Cars on a Curving Road Part A A small car of mass and a large car of mass drive along a highway. They approach a curve of radius . To not slip, both cars need to maintain a net force of compare to the speed of the large as they travel around the curve. How does the speed of the small car car as they round the curve? Hint A.1 How to approach the problem Hint not displayed Part A.2 Determine which equation to use Part not displayed Hint A.3 Relating the speeds of the cars Hint not displayed ANSWER: 4 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Now apply this method for using proportional reasoning to the next problem. Part B Now assume that two identical cars of mass first car, drive along a highway. One car approaches a curve of radius at a speed of ? at speed . The second car approaches a curve of radius . How does the the net force exerted on the , compare to the net force exerted on the second car, Part B.1 Determine the equation to use for the comparison Part not displayed ANSWER: Being able to use proportional reasoning is a useful skill to have. The more you practice, the better you will become at it. Centripetal Acceleration Explained Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle. Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius angular with velocity , . The main point of the problem is to compute the acceleration using geometric arguments. 5 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Part A What is the velocity of the mass at a time ? You can work this out geometrically with the help of the hints, or by differentiating the expression for given in the introduction. Part A.1 Direction of the velocity Part not displayed Part A.2 Speed What is Express ANSWER: , the speed (magnitude of velocity) of the mass at time ? in terms of = and . Express this velocity in terms of ANSWER: = , , , and the unit vectors and . Assume that the mass has been moving along its circular path for some time. You start timing its motion with a stopwatch when it crosses the positive x axis, an instant that corresponds to . [Notice that when , .] For the remainder of this problem, assume that the time timing the motion. Then the time Part B What is the velocity of the mass at a time Express this velocity in terms of ANSWER: = , ? , , and the unit vectors and . refers to the moment a time is measured from the moment you start before you start your stopwatch. Part C 6 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... What is the average acceleration of the mass during the time interval from to ? Hint C.1 Average acceleration Hint not displayed Express this acceleration in terms of ANSWER: = , , , and the unit vectors and . Part D What is the magnitude of this acceleration in the limit of small ? In this limit, the average acceleration becomes the instantaneous acceleration. Part D.1 Expansion of For small times (or more precisely when ? Hint D.1.a Taylor series expansion The Taylor series expansion of is . Express your answer in terms of ANSWER: = and . ), what is the first term in the Taylor series expansion for Express your answer in terms of ANSWER: = and . Part E 7 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Consider the following statements: a. The centripetal acceleration might better be expressed as b. The magnitude of the centripetal acceleration is c. The magnitude of the centripetal acceleration is acceleration . . . at speed experiences a centripetal because it is a vector. d. A particle that is going along a path with local radius of curvature e. If you are in a car turning left, the force you feel pushing you to the right is the force that causes the centripetal acceleration. In these statements refers to the component of the velocity of an object in the direction toward or away from the origin of the coordinate system or the rotation axis. Conversely, refers to the component of the velocity perpendicular to . Identify the statement or statements that are false. only b only c only d only e only b and e c and e d and e That's right; the true statements are therefore: a. The centripetal acceleration might better be expressed as c. The magnitude of the centripetal acceleration is acceleration . . at speed experiences an because it is a vector. d. A particle that is going along a path with local radius of curvature There is so much confusion about centripetal force that you should probably ban this term from your vocabulary and thought processes. If you are in a car turning left, your centripetal acceleration is to the left (i.e., inward) and some real force must be applied to you to give you this acceleration--typically this would be provided by friction with the seat. The force you "feel" pushing you to the right is not a real force but rather a "fictitious force" that is present if you are in an accelerating coordinate system (in this case the car). It is best to stick to inertial (i.e., nonaccelerating) coordinate systems when doing kinematics and dynamics (i.e., calculations). Banked Frictionless Curve, and Flat Curve with Friction A car of mass = 1500 traveling at 40.0 enters a banked turn covered with ice. The road is banked at an angle , and there is no friction between the road and the car's tires. 8 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Part A What is the radius turn)? Hint A.1 How to approach the problem Hint not displayed Part A.2 Identify the free-body diagram and coordinate system Part not displayed Part A.3 Calculate the normal force Part not displayed Part A.4 Determine the acceleration in the horizontal plane Part not displayed Express your answer in meters. ANSWER: = 34.6 of the turn if = 20.0 (assuming the car continues in uniform circular motion around the Part B Now, suppose that the curve is level ( ) and that the ice has melted, so that there is a coefficient of static friction between the road and the car's tires. What is , the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from slipping? Assume that the car's speed is still 40.0 and that the radius of the curve is given by the value you found for in Part A. Hint B.1 How to approach the problem 9 of 10 10/11/08 11:32 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignm... Hint not displayed Part B.2 Identify the correct free-body diagram Part not displayed Part B.3 Calculate the net force Part not displayed Part B.4 Calculate the friction force Part not displayed Express your answer numerically. ANSWER: = 0.364 Problem 7.61 Two wires are tied to the 200 of 8.30 . sphere shown in figure. The sphere revolves in a horiIzontal circle at a constant speed Part A What is the tension in the upper wire? ANSWER: 11.1 Part B What is the tension in the lower wire? ANSWER: 7.22 Summary 8 of 8 items complete (80.26% avg. score) 13.8 of 17 points 10 of 10 10/11/08 11:32 PM ...