## Assignment 4 Due: 11:59pm on Wednesday, February 26, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy ± Two Forces Acting at a Point Two forces, and , act at a point. has a magnitude of 9.80 and is directed at an angle of 56.0 above the negative x axis in the second quadrant. has a magnitude of 5.20 and is directed at an angle of 54.1 below the negative x axis in the third quadrant. Part A What is the x component of the resultant force? Express your answer in newtons. Hint 1. How to approach the problem The resultant force is defined as the vector sum of all forces. Thus, its x component is the sum of the x components of the forces, and its y component is the sum of the y components of the forces. Hint 2. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . F 1 F 2 F 1 N F 2 N F 1 F 1 A A Ax = Acos Ay = Asin A Ax < 0 Ay > 0 < < 2 Ax < 0 Ay < 0 < < 3 2 Hint 2. Find the direction of is directed at an angle of 56.0 above the x axis in the second quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 56.0 . ANSWER: ANSWER: Hint 3. Find the x component of Find the x component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , F 1 F 1 F 1 F 1 = 180 − 180 + 90 + -5.48 N F 2 F 2 A A Ax = Acos Ay = Asin A Ax < 0 Ay > 0 < < 2 Typesetting math: 100% and if . Hint 2. Find the direction of is directed at an angle of 54.1 below the x axis in the third quadrant. When you calculate the components of , however, the direction of the force is commonly expressed in terms of the angle that the vector representing the force forms with the positive x axis. What is the angle that forms with the positive x axis? Select an answer from the following list, where 54.1 . ANSWER: ANSWER: ANSWER: Correct Part B What is the y component of the resultant force? Express your answer in newtons. Ax < 0 Ay < < < 3 2 F 2 F 2 F 2 F 2 = 180 − − 180 −90 − -3.05 N -8.53 N Typesetting math: 100% Hint 1. How to approach the problem Follow the same procedure that you used in Part A to find the x component of the resultant force, though now calculate the y components of the two forces. Hint 2. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: Hint 3. Find the y component of Find the y component of . Express your answer in newtons. Hint 1. Components of a vector F 1 F 1 A A Ax = Acos Ay = Asin A Ax < 0 Ay > 0 < < 2 Ax < 0 Ay < 0 < < 3 2 8.12 N F 2 F 2 Typesetting math: 100% Consider a vector that forms an angle with the positive x axis. The x and y components of are, respectively, and , where is the magnitude of the vector. Note that and if , and if . ANSWER: ANSWER: Correct Part C What is the magnitude of the resultant force? Express your answer in newtons. Hint 1. Magnitude of a vector Consider a vector , whose components are and . The magnitude of is . A A Ax = Acos Ay = Asin A Ax < 0 Ay > 0 < < 2 Ax < 0 Ay < 0 < < 3 2 -4.21 N 3.91 N A Ax Ay A A = A + 2 x A2 y −−−−−−− Typesetting math: 100% ANSWER: Correct Enhanced EOC: Problem 5.9 The figure shows acceleration-versus-force graphs for two objects pulled by rubber bands. You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Finding the Slope of a Line from a Graph Part A What is the mass ratio ? Express your answer using two significant figures. 9.38 N m1 m2 Typesetting math: 100% Hint 1. How to approach the problem How are the acceleration and the force on an object related to its mass? How is the slope of each line in the figure related to each object's mass? For each line, what two points are easy to measure accurately to determine the slope of line? How is the slope determined from the x and y coordinates of the two points you chose for each line? ANSWER: Correct A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude . Part A How much horizontal force must a sprinter of mass 54 exert on the starting blocks to produce this acceleration? Express your answer in newtons using two significant figures. Hint 1. Newton's 2nd law of motion According to Newton's 2nd law of motion, if a net external force acts on a body, the body accelerates, and the net force is equal to the mass of the body times the acceleration of the body: . ANSWER: = 0.36 m1 m2 15 m/s2 F kg Fnet m a Fnet = ma F = 810 N Typesetting math: 100% Correct Part B Which body exerts the force that propels the sprinter, the blocks or the sprinter? Hint 1. How to approach the question To start moving forward, sprinters push backward on the starting blocks with their feet. Newton's 3rd law tells you that the blocks exert a force on the sprinter of the same magnitude, but opposite in direction. ANSWER: Correct To start moving forward, sprinters push backward on the starting blocks with their feet. As a reaction, the blocks push forward on their feet with a force of the same magnitude. This external force accelerates the sprinter forward. Problem 5.12 The figure shows an acceleration-versus-force graph for a 600 object. the blocks the sprinter g Typesetting math: 100% Part A What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Part B What must equal in order for the graph to be correct? Express your answer with the appropriate units. ANSWER: Correct Free-Body Diagrams Learning Goal: To gain practice drawing free-body diagrams Whenever you face a problem involving forces, always start with a free-body diagram. a1 a1 = 1.67 m s2 a2 a2 = 3.33 m s2 Typesetting math: 100% To draw a free-body diagram use the following steps: Isolate the object of interest. It is customary to represent the object of interest as a point 1. in your diagram. Identify all the forces acting on the object and their directions. Do not include forces acting on other objects in the problem. Also, do not include quantities, such as velocities and accelerations, that are not forces. 2. Draw the vectors for each force acting on your object of interest. When possible, the length of the force vectors you draw should represent the relative magnitudes of the forces acting on the object. 3. In most problems, after you have drawn the free-body diagrams, you will explicitly label your coordinate axes and directions. Always make the object of interest the origin of your coordinate system. Then you will need to divide the forces into x and y components, sum the x and y forces, and apply Newton's first or second law. In this problem you will only draw the free-body diagram. Suppose that you are asked to solve the following problem: Chadwick is pushing a piano across a level floor (see the figure). The piano can slide across the floor without friction. If Chadwick applies a horizontal force to the piano, what is the piano's acceleration? To solve this problem you should start by drawing a free-body diagram. Part A Determine the object of interest for the situation described in the problem introduction. Hint 1. How to approach the problem You should first think about the question you are trying to answer: What is the acceleration of the piano? The object of interest in this situation will be the object whose acceleration you are asked to find. ANSWER: Typesetting math: 100% Correct Part B Identify the forces acting on the object of interest. From the list below, select the forces that act on the piano. Check all that apply. ANSWER: Correct Now that you have identified the forces acting on the piano, you should draw the free-body diagram. Draw the length of your vectors to represent the relative magnitudes of the forces, but you don't need to worry about the exact scale. You won't have the exact value of all of the forces until you finish solving the problem. To maximize your learning, you should draw the diagram yourself before looking at the choices in the next part. You are on your honor to do so. Part C For this situation you should draw a free-body diagram for the floor. Chadwick. the piano. acceleration of the piano gravitational force acting on the piano (piano's weight) speed of the piano gravitational force acting on Chadwick (Chadwick's weight) force of the floor on the piano (normal force) force of the piano on the floor force of Chadwick on the piano force of the piano pushing on Chadwick Typesetting math: 100% Select the choice that best matches the free-body diagram you have drawn for the piano. Hint 1. Determine the directions and relative magnitudes of the forces Which of the following statements best describes the correct directions and relative magnitudes of the forces involved? ANSWER: ANSWER: The normal force and weight are both upward and the pushing force is horizontal. The normal force and weight are both downward and the pushing force is horizontal. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a greater magnitude than the weight. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force and weight have the same magnitude. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a smaller magnitude than the weight. Typesetting math: 100% Typesetting math: 100% Correct If you were actually going to solve this problem rather than just draw the free-body diagram, you would need to define the coordinate system. Choose the position of the piano as the origin. In this case it is simplest to let the y axis point vertically upward and the x axis point horizontally to the right, in the direction of the acceleration. Chadwick now needs to push the piano up a ramp and into a moving van. at left. The ramp is frictionless. Is Chadwick strong enough to push the piano up the ramp alone or must he get help? To solve this problem you should start by drawing a free-body diagram. Part D Determine the object of interest for this situation. ANSWER: Correct Now draw the free-body diagram of the piano in this new situation. Follow the same sequence of steps that you followed for the first situation. Again draw your diagram before you look at the choices For this situation, you should draw a free-body diagram for the ramp. Chadwick. the piano. Typesetting math: 100% below. Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER: Typesetting math: 100% Typesetting math: 100% Correct In working problems like this one that involve an incline, it is most often easiest to select a coordinate system that is not vertical and horizontal. Instead, choose the x axis so that it is parallel to the incline and choose the y axis so that it is perpendicular to the incline. Problem 5.18 The figure shows two of the three forces acting on an object in equilibrium. Part A Redraw the diagram, showing all three forces. Label the third force . Draw the force vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. ANSWER: F 3 Typesetting math: 100% Correct Problem 5.25 An ice hockey puck glides across frictionless ice. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the ice hockey puck. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Normal force ; Gravity Normal force ; Gravity ; Kinetic friction Tension ; Weight Thrust ; Gravity n F G n F G fk T w Fthrust F G Typesetting math: 100% Correct Problem 5.26 Your physics textbook is sliding to the right across the table. Part A Identify all forces acting on the object. ANSWER: Typesetting math: 100% Correct Part B Draw a free-body diagram of the object. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Weight ; Kinetic friction Thrust ; Kinetic friction Normal force ; Weight ; Kinetic friction Normal force ; Weight ; Static friction w fk Fthrust fk n w fk n w fs Typesetting math: 100% Correct Enhanced EOC: Problem 5.35 A constant force is applied to an object, causing the object to accelerate at 13 . You may want to review ( pages 127 - 130) . For help with math skills, you may want to review: Proportions I Proportions II Part A m/s2 Typesetting math: 100% What will the acceleration be if the force is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is halved but the mass remains the same? ANSWER: Correct Part B What will the acceleration be if the object's mass is halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the mass is halved but the force remains the same? ANSWER: Correct Part C a = 6.50 m s2 a = 26.0 m s2 Typesetting math: 100% What will the acceleration be if the force and the object's mass are both halved? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if both the force and mass are reduced by a factor of two? ANSWER: Correct Part D What will the acceleration be if the force is halved and the object's mass is doubled? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the acceleration of an object related to its mass and the force applied? Expressing the acceleration in terms of the force and mass, what happens to the acceleration if the force is decreased by a factor of two and the mass is increased by a factor of two? Check your answer by choosing numerical values of the force and mass, and then halve the force and double the mass. ANSWER: Correct a = 13.0 m s2 a = 3.25 m s2 Typesetting math: 100% Problem 5.44 A rocket is being launched straight up. Air resistance is not negligible. Part A Which of the following is the correct motion diagram for the situation described above? Enter the letter that corresponds with the best answer. ANSWER: Correct Part B Draw a free-body diagram. Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded but the relative length of one to the other will be graded. ANSWER: Typesetting math: 100% Correct Score Summary: Your score on this assignment is 99.7%. You received 63.82 out of a possible total of 64 points. Typesetting math: 100%

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