1 of 5 10/4/2009 8:45 PM

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1 1 of 5 10/4/2009 8:45 PM Chapter 8 Homework Due: 9:00am on Wednesday October Note: To understand how points are awarded read your instructor's Grading Policy [Return to Standard Assignment View] Normal Force and Centripetal Force Ranking Task A roller-coaster track has six semicircular "dips" with different radii of curvature The same roller-coaster cart rides through each dip at a different speed For the different values given for the radius of curvature and speed rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip Hint A1 Newton s 2nd law Newton s 2nd law is valid for any motion whether the motion is along a straight line or a circular path The net force acting on the cart must be equal to the product of its mass and acceleration and since the cart is moving along a circular path its acceleration (toward the center of the circular path) is given by Hint A2 Determine the net force on the cart Defining up as the positive direction which of the following expressions describes the net force acting on the cart in the vertical direction while it's at the bottom of the dip? The variables and are the magnitudes of the forces Substituting the expression for the net force on the cart and the centripetal acceleration of the cart into Newton's 2nd law Keep in mind that the same cart passes through the six different dips along the track so the mass in the expression doesn't vary Rank from largest to smallest To rank items as equivalent overlap them View Velocity of a Roller Coaster Ranking Task Six roller-coaster carts pass over the same semicircular "bump" The mass of each cart (including passenger) and the normal force of the track on the cart at the top of each bump are given in the figures

2 2 of 5 10/4/2009 8:45 PM Rank the speeds of the different carts as each passes over the top of the bump Hint A1 Newton's 2nd law Newton's 2nd law is valid for any motion whether the motion is along a straight line or a circular path The net force acting on the cart must be equal to the product of its mass and acceleration and since the cart is moving along a circular path its acceleration (toward the center of the circular path) has magnitude Hint A2 Determine the net force on the cart Defining the down direction (toward the center of the circular path) as positive which of the following expressions describes the component of the net force acting on the cart in the vertical direction? Taking the expressions for the net force on the cart and the centripetal acceleration of the cart and substituting into Newton's 2nd law Since the radius is the same for every cart we can ignore and write But is simply so or Rank from largest to smallest To rank items as equivalent overlap them View Taking the expressions for the net force on the cart and the centripetal acceleration of the cart and substituting into Newton's 2nd law Since the radius is the same for every cart we can ignore and write But is simply so or

3 Therefore larger implies smaller A Ride on the Ferris Wheel A woman rides on a Ferris wheel of radius 16 that maintains the same speed throughout its motion To better understand physics she takes along a digital bathroom scale (with memory) and sits on it When she gets off the ride she uploads the scale readings to a computer and creates a graph of scale reading versus time Note that the graph has a minimum value of 510 and a maximum value of 666 What is the woman's mass? Hint A1 The woman is moving in a circle with constant speed To maintain this motion she must experience a net acceleration (called centripetal acceleration) directed toward the center of the Ferris wheel Draw and analyze the woman's free-body diagram at a wisely chosen point on the circular path and use Newton's 2nd law to determine her mass Hint A2 Find the extreme points on the circular path The bathroom scale does not record the woman s weight If it did the reading would not vary as she rides the Ferris wheel Instead the scale records the normal force acting on the woman which can vary as she moves along the circular path and experiences different accelerations This normal force is sometimes referred to as an apparent weight because it mimics the feelings of being heavier or lighter As the woman travels along the circular path her apparent weight fluctuates between a maximum value and a minimum value At what location (A - D) will the apparent weight be a maximum? Where will it be a minimum? Hint A21 Analyze the free-body diagram Draw a free-body diagram for the woman Assume that the y direction points vertically upward Which of the following statements are true for every point on the circle traveled by the woman? Check all that apply The woman's weight points in the y direction The woman's weight points in the y direction The magnitude of the woman's weight is constant The normal force points in the y direction The normal force points in the y direction The magnitude of the normal force is constant Hint A22 Analyze the acceleration At all times during the woman's motion she experiences a net acceleration (called centripetal acceleration) directed toward the center of the Ferris wheel At what location (A - D) will the acceleration be in only the vertical direction? Check all that apply 3 of 5 10/4/2009 8:45 PM

4 4 of 5 10/4/2009 8:45 PM A B C D Hint A23 Applying Newton's 2nd law Since the normal force and weight are the only forces acting on the woman in the vertical (y) direction where and are the magnitudes of the normal force and the weight respectively Apply what you know about the acceleration of the woman in the y direction at certain points along the circular path to determine when will be a maximum or minimum Enter the letters that correspond to the correct positions separated by a comma CA Answer Requested You can read the value of the woman's apparent weight from the graph at either of these locations Pick one of these locations and apply Newton's 2nd law to the woman at that point to solve for her mass Hint A3 Find the acceleration of the woman What is the acceleration of the woman? Hint A31 You can use the information from the problem statement and the graph to determine the woman's speed This can be used to find her centripetal acceleration: Hint A32 What is the speed Find the woman's speed of the woman? Hint A321 Determining the speed Since the Ferris wheel turns at constant speed the distance the woman travels during some time interval is given by where is the speed and is the time For a complete cycle the distance traveled is the circumference of the Ferris wheel and the time required is one period Thus for a Ferris wheel of radius Hint A322 Find the period The easiest way to determine the speed of the woman is to calculate the distance she travels during one complete cycle of motion and divide this by the time that it takes to complete this cycle The time for a complete cycle is called the period What is the period of the Ferris wheel? Express your answer in seconds = 22 Answer Requested Express your answer in meters per second = 457 Express your answer in meters per second squared = 131 Hint A4 The weight Mass and weight of the woman is the force of gravity that acts on her Her mass is related to the number and type of atoms that comprise her The two quantities are related by Express your answer in kilograms = 60 Problem 830 A 500 g ball swings in a vertical circle at the end of a 15-m-long string When the ball is at the bottom of the circle the tension in the string is 15 N What is the speed of the ball at that point?

5 5 of 5 10/4/2009 8:45 PM 550 Mass on Turntable A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram The small metal cylinder has a mass of from the center of the turntable the coefficient of static friction between the cylinder and the turntable is 0080 and the cylinder is located Take the magnitude of the acceleration due to gravity to be 981 What is the maximum speed that the cylinder can move along its circular path without slipping off the turntable? Hint A1 Hint A2 Hint A3 Hint A4 Centripetal acceleration Determine the force causing acceleration Find the maximum possible friction force Newton's 2nd law Express your answer numerically in meters per second to two significant figures = 034 At the Test Track You want to test the grip of the tires on your new race car You decide to take the race car to a small test track to experimentally determine the coefficient of friction The racetrack consists of a flat circular road with a radius of 45 The applet shows the result of driving the car around the track at various speeds What is Hint A1 Hint A2 Hint A3 the coefficient of static friction between the tires and the track? Use the applet to find the speed Find an expression for Express your answer to two significant figures = 091 Score Summary: Your score on this assignment is 1274% You received 343 out of a possible total of 35 points plus 103 points of extra credit