Forces, Newton's Laws and Circular Motion

OA4 Forces, Newton's Laws and Circular Motion Due: 11:59pm on Sunday, September 13, 2020 You will receive no credit for items you complete after the assignment is due. Grading Policy Motion from Force Graphing Question For each of the net force versus time graphs in Parts A, B, and C, construct a possible corresponding graph of velocity Assume one-dimensional motion. , or position , versus time. Part A Plot velocity versus time. Hint 1. Relating force and kinematics graphs Newton’s 2nd law states that the net force acting on an object is proportional to its acceleration. Therefore, graphs of net force versus time and acceleration versus time must have the same general shape. From the graph of acceleration versus time, you can then construct a velocity versus time graph. The velocity at a time is the initial velocity plus the area under the acceleration curve between and . By the same process, you can construct a position versus time graph from the graph of velocity versus time. The position at a time position plus the area under the velocity curve between and . is the initial Hint 2. Initial values Knowing the net force that acts on an object does not allow you to determine the initial velocity or position of the object. Therefore, the velocity or position graph can begin at any initial value. ANSWER: No elements selected 0 Select the elements from the list an main menu. Correct Part B Plot velocity versus time. Hint 1. Relating force and kinematics graphs Newton’s 2nd law states that the net force acting on an object is proportional to its acceleration. Therefore, graphs of net force versus time and acceleration versus time must have the same general shape. From the graph of acceleration versus time, you can then construct a velocity versus time graph. The velocity at a time is the initial velocity plus the area under the acceleration curve between and . By the same process, you can construct a position versus time graph from the graph of velocity versus time. The position at a time position plus the area under the velocity curve between and . is the initial Hint 2. Initial values Knowing the net force that acts on an object does not allow you to determine the initial velocity or position of the object. Therefore, the velocity or position graph can begin at any initial value. ANSWER: No elements selected 0 Select the elements from the list an main menu. Correct Part C Plot position versus time. Hint 1. Relating force and kinematics graphs Newton’s 2nd law states that the net force acting on an object is proportional to its acceleration. Therefore, graphs of net force versus time and acceleration versus time must have the same general shape. From the graph of acceleration versus time, you can then construct a velocity versus time graph. The velocity at a time is the initial velocity plus the area under the acceleration curve between and . By the same process, you can construct a position versus time graph from the graph of velocity versus time. The position at a time position plus the area under the velocity curve between and . is the initial Hint 2. Initial values Knowing the net force that acts on an object does not allow you to determine the initial velocity or position of the object. Therefore, the velocity or position graph can begin at any initial value. ANSWER: No elements selected 0 Select the elements from the list an main menu. Correct Prelecture Video: Newton’s Second Law Click Play to watch the video. Answer the ungraded questions in the video and the graded follow-up questions at right. Part A In the video, forces acting on the car that are parallel to the direction of motion are analyzed. How are these forces related? ANSWER: The forces are equal in size, act in the same direction, and produce a net force in the direction of motion. The forces are equal in size, act in opposite directions, and produce a net force in the direction of motion. The forces are unequal in size, act in opposite directions, and produce a net force in the direction of motion. The forces are equal in size, act in opposite directions, and produce a zero net force. The forces are unequal in size, act in the same direction, and produce a net force in the direction of motion. Correct The car is subject to two forces acting along the direction of motion. The propelling force acts in the direction of motion, while the force of drag acts opposite the direction of motion. Because the two forces are equal in size, they cancel, producing a zero net force. As a result, the car travels at constant speed. Part B The mass of a rocket decreases as it burns through its fuel. If the rocket engine produces constant force (thrust), how does the acceleration of the rocket change over time? ANSWER: It does not change. It decreases. It increases. Correct The constant-force rocket’s acceleration is inversely related to its mass. Because its mass decreases over time, its acceleration increases. Part C Newton’s second law relates an object’s acceleration to its mass and the net force acting on it. Does Newton’s second law apply to a situation in which there is no net force? Select the best explanation. ANSWER: No. The law applies only to situations in which a net force acts. Yes. The law applies and it tells us that the object has constant velocity. No. The law does not apply because a zero net force would produce an infinite acceleration. Yes. The law applies and it tells us that the object has a nonzero acceleration. Correct Newton’s second law applies to all situations, whether there is a net force or not. In the case of zero net force, any finite mass object must have zero acceleration, which means that its velocity is constant. Part D An experiment measures the acceleration of an object of known mass subject to a known net force. The experiment is then repeated while varying the mass and the net force. The table below summarizes the conditions used in each trial. Trial Mass 1 doubled Net force doubled 2 halved unchanged 3 doubled unchanged 4 halved doubled Rank the accelerations measured in each trial from largest to smallest. ANSWER: Reset 4 2 1 Help 3 The correct ranking cannot be determined. Correct The accelerations from largest to smallest are as follows: Trial 4 (quadrupled), Trial 2 (doubled), Trial 1 (unchanged) and Trial 3, (halved). Forces on Blocks in an Elevator Conceptual Question Two blocks are stacked on top of each other on the floor of an elevator. For each of the following situations, select the correct relationship between the magnitudes of the two forces given. You will be asked two questions about each of three situations. Each situation is described above the first in the pair of questions. Do not assume anything about a given situation except for what is given in the description for that particular situation. First situation The elevator is moving downward at a constant speed. Part A Hint 1. Comparing forces that act on the same object When comparing forces that act on the same object, draw a free-body diagram of the object being acted on. Then, determine the acceleration of the object. By Newton's 2nd law, the net force must be proportional to the object's acceleration. Hint 2. Draw a free-body diagram for the top block Complete the free-body diagram for the top block by drawing the force on the top block due to the earth. This force should act at the center of the block. ANSWER: No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is less than the magnitude of the force of the earth on the top unknown compared to block. Correct Part B Hint 1. Comparing forces that do not act on the same object If two forces do not act on the same object, they will not appear on the same free-body diagram. Therefore, Newton's 2nd law cannot be used to determine the relative sizes of these forces. Certain forces can, however, be compared using Newton's 3rd law. Hint 2. Newton's 3rd law Newton's 3rd law states that when two objects exert forces on each other, these forces are always equal in magnitude and opposite in direction. Thus, if you are sitting in a chair, the force the chair exerts upward on you is exactly the same as the force you exert downward on the chair, regardless of whether you are at rest in the chair, or have you feet up on your desk, or are in the process of getting up out of the chair, or in the process of landing in the chair after jumping from a great height, ... it does not matter! ANSWER: greater than equal to The magnitude of the force of the bottom block on top block is less than the magnitude of the force of the top block on bottom unknown compared to block. Correct Second situation The elevator is moving downward at an increasing speed. Part C Hint 1. Determining acceleration If the elevator is moving downward at an increasing speed, what is the direction of the elevator's acceleration? ANSWER: upward zero downward unknown ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is less than the magnitude of the force of the earth on the top unknown compared to block. Correct Part D Hint 1. Newton's 3rd law in accelerating elevator Newton's 3rd law holds that forces come in pairs of equal magnitude and opposite direction in all cases. Thus, the acceleration of the elevator should not affect the relative magnitude of two forces that form a 3rd law pair. ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is less than the magnitude of the force of the top block on the unknown compared to bottom block. Correct Third situation The elevator is moving upward. Part E Hint 1. Determining acceleration If the elevator is moving upward, what is the direction of the elevator's acceleration? ANSWER: upward zero downward unknown ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is less than the magnitude of the force of the earth on the top unknown compared to block. Correct Even though the elevator is moving upwards, you do not know in which direction it is accelerating, or indeed whether the elevator is accelerating at all! Part F ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is less than unknown compared to bottom block. the magnitude of the force of the top block on the Correct Question 4.23 Mary exerts an upward force of 30 to hold a bag of groceries. Part A Describe the "reaction" force (Newton's third law) by stating its magnitude. Express your answer to two significant figures and include the appropriate units. ANSWER: = 30 Correct Part B Describe the "reaction" force (Newton's third law) by stating its direction. ANSWER: upward downward Correct Part C Describe the "reaction" force (Newton's third law) by stating on what object it is exerted. ANSWER: on the bag of groceries on Mary's hands and arms on the Earth on the ground Correct Part D Describe the "reaction" force (Newton's third law) by stating by what object it is exerted. ANSWER: by Mary's hands and arms by the ground by the bag of groceries by the Earth Correct Video Tutor: Cart with Fan and Sail First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the question on the right. You can watch the video again at any point. Part A Which of the force diagrams in the figure correctly displays all of the horizontal forces exerted on the cart by the surrounding air? Hint 1. How to approach the problem First, what does the acceleration of the cart imply about the net force acting on the cart? (Only two of the choices are compatible with the cart’s behavior.) Next, decide which direction is correct for the force vectors. • When the fan pushes air to the right, in which direction does the air push the fan? (Remember how the cart moved in the video when only the fan was attached to it.) • When air moving to the right strikes the sail, in which direction does the air push the sail? ANSWER: A B C D Correct The net force on the cart is zero, since the air is the only thing acting on the cart in the horizontal direction. Problem 4.71 A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 , can accelerate on a level road from rest to 18 (65 ) in 13.4 . Part A Using these data, calculate the maximum steepness of a hill. Express your answer using two significant figures. ANSWER: = 7.9 Correct Problem 4.48 The block shown in the figure has mass at an angle =21.0 to the horizontal. =5.0 and lies on a fixed smooth frictionless plane tilted Part A Determine the acceleration of the block as it slides down the plane. ANSWER: = 3.51 Correct Part B If the block starts from rest 15.0 inclined plane. up the plane from its base, what will be the block's speed when it reaches the bottom of the incline? Caption: Block on ANSWER: = 10.3 Correct Problem 5.79 An 20.0 box is released on a 32.0 incline and accelerates down the incline at 0.200 . Part A Find the friction force impeding its motion. ANSWER: = 99.9 Correct Part B How large is the coefficient of friction? ANSWER: = 0.601 Correct Kinetic Friction in a Block-and-Pulley System Consider the system shown in the figure . Block A has weight and block B has weight . Once block B is set into downward motion, it descends at a constant speed. Assume that the mass and friction of the pulley are negligible. Part A Calculate the coefficient of kinetic friction between block A and the table top. Express your answer in terms of some or all of the variables (double-u subscript A), , and (the acceleration due to gravity). Hint 1. How to approach the problem In this problem, blocks A and B are in dynamic equilibrium; their velocities are constant. This means that the net force on each, zero. , is equal to The tension is constant throughout the rope. By setting the sum of the forces acting on both blocks A and B equal to zero, you should be able to obtain two different expressions for the tension in the rope. Set these equal to each other and solve for . Hint 2. Find the net force on block A Write an expression for , the net force acting horizontally on block A. Express your answer in terms of some or all of the variables , right. (the tension in the rope), and other given variables. Take positive to be to the ANSWER: = Hint 3. Find the net force on block B Write an expression for , the net force acting vertically on block B. Express your answer in terms of some or all of the variables , downward. ANSWER: (the tension in the rope), and other given variables. Take positive to be = ANSWER: = Correct Part B A cat, also of weight , falls asleep on top of block A. If block B is now set into downward motion, what is the magnitude of its acceleration? Express your answer in terms of some or all of the variables , , and (the acceleration due to gravity). Hint 1. How to approach the problem This problem involves solving two equations with two unknowns. Your two equations are for each of the blocks, and your unknowns are , the tension in the rope, and , the magnitude of the acceleration of blocks A and B. (These accelerations are equal because the rope connecting blocks A and B constrains their motion.) Once you have two expressions for , set them equal to each other. Also, remember that the accelerations of blocks A and B are equal in magnitude because the connecting rope constrains their motion. Set both of these accelerations to , solve for the acceleration, and you will have the answer. Hint 2. How to find the mass Recall that , where is mass, is weight, and is the magnitude of the acceleration due to gravity. Hint 3. Find the net force on block A and the cat Find an expression for , the net force acting on both block A and the cat in the horizontal direction. Take positive to be to the right. Express your answer in terms of some or all of the given variables and answer from Part A for . (the tension in the rope). Use your ANSWER: = Correct Now solve this equation for . Hint 4. Find the net force on block B Find an expression for , the forces acting on block B in the vertical direction. Take positive to be downward. Express your answer in terms of some or all of the given variables and ANSWER: = ANSWER: = Correct (the tension in the rope). Part C Is block B speeding up or slowing down once it is set into downward motion and the cat is on block A? ANSWER: Speeding up Slowing down Correct Circular Motion Ranking Task Six artificial satellites circle a space station at constant speed. The mass of each satellite, distance from the space station, and the speed of each satellite are listed below. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible. Part A Rank each satellite based on its period. Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. Definition of a period The period of any object undergoing circular motion is the time needed to complete one cycle of its motion. One cycle involves traveling around the entire circumference of its circular path, a distance of , where is the radius of the circle. Hint 2. Relating period, speed, and circumference Since the satellites move at constant speed , the distance they travel during some time interval is given by . For a complete orbit around the space station, the distance traveled is the circumference of the orbit and the time required is one period ( ). Thus, , or . ANSWER: Reset The correct ranking cannot be determined. Correct Part B Rank each satellite based on its acceleration. Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. Relating acceleration, speed, and radius Although the satellites are traveling at constant speed, their direction of travel is constantly changing. Since acceleration is proportional to the change in velocity, and velocity involves both speed and direction of travel, the acceleration of the satellites is not zero. Any object traveling along a circular path experiences a centripetal acceleration given by , where is the radius of the circle. This component of the object's acceleration, directed inward toward the center of the circle, reflects a constant change in direction and keeps the object traveling in a circle. In addition to this acceleration component, an object may experience a tangential acceleration, directed along the circular path. However, in such a case, the object no longer moves with constant speed. ANSWER: Help Reset The correct ranking cannot be determined. Correct Part C Rank each satellite based on the net force acting on it. Rank from largest to smallest. To rank items as equivalent, overlap them. Hint 1. 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 satellite must be equal to the product of its mass and acceleration: . ANSWER: Help Reset The correct ranking cannot be determined. Correct Problem 5.28 Two masses = 2.1 and = 5.0 are on inclines and are connected together by a string as shown in the figure . The coefficient of kinetic friction between each mass and its incline is = 0.30. Part A If moves up, and moves down, determine their acceleration. Express your answer using two significant figures. ANSWER: = -2.3 Correct Score Summary: Your score on this assignment is 97.6%. You received 136.66 out of a possible total of 140 points. Help