Homework 4 Forces

HW4: Forces Due: 11:59pm on Sunday, February 21, 2021 You will receive no credit for items you complete after the assignment is due. Grading Policy Understanding Newton's Laws Part A An object at rest cannot remain at rest unless which of the following holds? Hint 1. How to approach the problem This problem describes a situation of static equilibrium (i.e., a body that remains at rest). Hence, it is appropriate to apply Newton's 1st law. Hint 2. Newton's 1st law: a body at rest According to Newton's 1st law, a body at rest remains at rest if the net force acting on it is zero. ANSWER: The net force acting on it is zero. The net force acting on it is constant and nonzero. There are no forces at all acting on it. There is only one force acting on it. Correct If there is a net force acting on a body, regardless of whether it is a constant force, the body accelerates. If the body is at rest and the net force acting on it is zero, then it will remain at rest. The net force could be zero either because there are no forces acting on the body at all or because several forces are acting on the body but they all cancel out. Part B If a block is moving to the left at a constant velocity, what can one conclude? Hint 1. How to approach the problem This problem describes a situation of dynamic equilibrium (i.e., a body that moves at a constant velocity). Hence, it is appropriate to apply Newton's 1st law. Hint 2. Newton's 1st law: a body in motion According to Newton's 1st law, a body initially in motion continues to move with constant velocity if the net force acting on it is zero. 1/41 ANSWER: There is exactly one force applied to the block. The net force applied to the block is directed to the left. The net force applied to the block is zero. There must be no forces at all applied to the block. Correct If there is a net force acting on a body, regardless of whether the body is already moving, the body accelerates. If a body is moving with constant velocity, then it is not accelerating and the net force acting on it is zero. The net force could be zero either because there are no forces acting on the body at all or because several forces are acting on the body but they all cancel out. Part C A block of mass is acted upon by two forces: you say about the block's motion? (directed to the left) and (directed to the right). What can Hint 1. How to approach the problem This problem describes a situation of dynamic motion (i.e., a body that is acted on by a net force). Hence, it is appropriate to apply Newton's 2nd law, which allows you to relate the net force acting on a body to the acceleration of the body. Hint 2. Newton's 2nd law Newton's 2nd law states that a body accelerates if a net force acts on it. The net force is proportional to the acceleration of the body and the constant of proportionality is equal to the mass of the body. In other words, , where is the net force acting on the body, and respectively. and are the mass and the acceleration of the body, Hint 3. Relating acceleration to velocity Acceleration is defined as the change in velocity per unit time. Keep in mind that both acceleration and velocity are vector quantities. ANSWER: 2/41 It must be moving to the left. It must be moving to the right. It must be at rest. It could be moving to the left, moving to the right, or be instantaneously at rest. Correct The acceleration of an object tells you nothing about its velocity, which is the direction and speed at which it is moving. In this case, the net force on (and therefore the acceleration of) the block is to the right, but the block could be moving left, right, or in any other direction. The block could also be instantaneously at rest, because a zero velocity again implies nothing about the acceleration. Part D A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________. Hint 1. How to approach the problem This problem describes a situation of dynamic motion (i.e., a body that is acted on by a net force). Hence, it is appropriate to apply Newton's 2nd law, which allows you to relate the net force acting on a body to the acceleration of the body. Hint 2. Newton's 2nd law Newton's 2nd law states that a body accelerates if a net force acts on it. The net force is proportional to the acceleration of the body and the constant of proportionality is equal to the mass of the body. In other words, , where is the net force acting on the body, and respectively. and are the mass and the acceleration of the body, ANSWER: continuously changing direction moving at constant velocity moving with a constant nonzero acceleration moving with continuously increasing acceleration Correct Since there is a net force acting, the body does not move at a constant velocity, but it accelerates instead. However, the force acting on the body is constant. Hence, according to Newton's 2nd law of motion, the acceleration of the body is also constant. 3/41 Part E Two forces, of magnitude and , are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________. Check all that apply. Hint 1. How to approach the problem By definition, the net force is the vector sum of all forces acting on the object. To find the magnitude of the net force you need to add the components of the two forces acting. Try adding the two forces graphically (by connecting the head of one force to the tail of the other). The directions of the two forces are arbitrary, but by trying different possibilities you should be able to determine the maximum and minimum net forces that could act on the object. Hint 2. Find the net force when the two forces act on the object in opposite directions Find the magnitude of the net force if both the forces acting on the object are horizontal and the 10-N force is directed to the right, while the 4-N force is directed to the left. Express your answer in newtons. Hint 1. Vector addition The magnitude of the vector sum of two parallel forces is the sum of the magnitudes of the forces. The magnitude of the vector sum of two antiparallel forces is the absolute value of the difference in magnitudes of the forces. ANSWER: 6.0 Hint 3. Find the direction of the net force when the two forces act in opposite directions If both the forces acting on the object are horizontal and the 10-N force is directed to the right, while the 4-N force is directed to the left, the net force is horizontal and directed __________. ANSWER: in the same direction as the 10-N force in the opposite direction to the 10-N force ANSWER: 4/41 cannot have a magnitude equal to cannot have a magnitude equal to cannot have the same direction as the force with magnitude must have a magnitude greater than Correct Conceptual Questions on Newton's 1st and 2nd Laws Learning Goal: To understand the meaning and the basic applications of Newton's 1st and 2nd laws. In this problem, you are given a diagram representing the motion of an object: a motion diagram. The dots represent the object's position at moments separated by equal intervals of time. The dots are connected by arrows representing the object's average velocity during the corresponding time interval. Your goal is to use this motion diagram to determine the direction of the net force acting on the object. You will then determine which force diagrams and which situations may correspond to such a motion. Part A What is the direction of the net force acting on the object at position A? Hint 1. Using Newton's 2nd law According to Newton's 2nd law, vectors and have the same direction. All you need to do then is to determine the direction of acceleration at position A by analyzing the diagram. Hint 2. Find the direction of acceleration Determine the direction of acceleration at position A by analyzing the diagram. Hint 1. How to analyze the motion diagram The velocity vectors connecting position A to the adjacent positions appear to have the same magnitude and direction. Does then the object accelerate as it travels through position A? 5/41 ANSWER: The acceleration is directed upward. The acceleration is directed downward. The acceleration is directed to the left. The acceleration is directed to the right. The acceleration is zero. ANSWER: upward downward to the left to the right The net force is zero. Correct The velocity vectors connecting position A to the adjacent positions appear to have the same magnitude and direction. Therefore, the acceleration is zero—and so is the net force. Part B What is the direction of the net force acting on the object at position B? Hint 1. Find the direction of acceleration Determine the direction of acceleration at position B by analyzing the diagram. Hint 1. How to analyze the motion diagram The velocity vectors connecting position B to the adjacent positions appear to have the same direction but decreasing magnitude. What is the direction of the acceleration of the object at point B? ANSWER: 6/41 The acceleration is directed upward. The acceleration is directed downward. The acceleration is directed to the left. The acceleration is directed to the right. The acceleration is zero. ANSWER: upward downward to the left to the right The net force is zero. Correct The velocity is directed to the right; however, it is decreasing. Therefore, the acceleration is directed to the left —and so is the net force. Part C What is the direction of the net force acting on the object at position C? Hint 1. Consider the components of the velocity Instead of representing the velocity of an object with just one vector, one can break the velocity vector into two components. For example, in the figure below the average velocity at position C is shown together with its horizontal component and its vertical component . As the object travels through position C, the horizontal component of the velocity appears to remain constant. What about the vertical one? 7/41 ANSWER: It increases. It decreases. It remains constant. ANSWER: upward downward to the left to the right The net force is zero. Correct The horizontal component of the velocity does not change. The vertical component of the velocity increases. Therefore, the acceleration—and hence the net force—is directed straight downward. Consider the following situations: a. A car is moving along a straight road at a constant speed. b. A car is moving along a straight road while slowing down. c. A car is moving along a straight road while speeding up. d. A hockey puck slides along a smooth (i.e., frictionless) icy surface. e. A hockey puck slides along a rough concrete surface. f. A cockroach is speeding up from rest. g. A rock is thrown horizontally; air resistance is negligible. h. A rock is thrown horizontally; air resistance is substantial. 8/41 i. A rock is dropped vertically; air resistance is negligible. j. A rock is dropped vertically; air resistance is substantial. Part D Which of these situations describe the motion shown in the motion diagram at point A? Type the letters corresponding to all the right answers. Do not use commas. For instance, if you think that only situations c and d are correct, type cd. ANSWER: ad Correct Part E Which of these situations describe the motion shown in the motion diagram at point B? Type the letters corresponding to all the right answers. Do not use commas. For instance, if you think that only situations c and d are correct, type cd. ANSWER: be Correct Part F Which of these situations describe the motion shown in the motion diagram at point C? Type the letters corresponding to all the right answers. Do not use commas. For instance, if you think that only situations c and d are correct, type cd. ANSWER: g Correct A Book on a Table A book weighing 5 N rests on top of a table. 9/41 Part A A downward force of magnitude 5 N is exerted on the book by the force of ANSWER: the table. gravity. inertia. Correct Part B An upward force of magnitude _____ is exerted on the _____ by the table. ANSWER: 6 N / table 5 N / table 5 N / book 6 N / book Correct Part C Do the downward force in Part A and the upward force in Part B constitute a 3rd law pair? 10/41 Hint 1. The force of gravity The force of gravity is another name for the force exerted by the earth (or any astronomical object) on objects near its surface. Hint 2. Exploring Newton's 3rd law Indicate whether the following statements about Newton's 3rd law are true, false, or indeterminate. 1. According to Newton's 3rd law, every real force has a unique pair force. 2. The pair force is called a "fictitious force." 3. The force and pair force must act on different point masses. 4. The force and the pair force must always have the same magnitude and must also act in exactly opposite directions. Enter t for true, f for false, or i for indeterminate for each statement, separating the answers with commas (e.g., if all but the first statement were true, you would enter f,t,t,t). ANSWER: , , , ANSWER: yes no Correct Part D The reaction to the force in Part A is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____ . Hint 1. The force of gravity The force of gravity is another name for the force exerted by the earth (or any astronomical object) on objects near its surface. ANSWER: 11/41 5 N / earth / book / upward 5 N / book / table / upward 5 N / book / earth / upward 5 N / earth / book / downward Correct Part E The reaction to the force in Part B is a force of magnitude _____, exerted on the _____ by the _____. Its direction is _____. ANSWER: 5 N / table / book / upward 5 N / table / earth / upward 5 N / book / table / upward 5 N / table / book / downward 5 N / earth / book / downward Correct Part F Which of Newton's laws could we have used to predict that the forces in Parts A and B are equal and opposite? Check all that apply. ANSWER: Newton's 1st law Newton's 2nd law Newton's 3rd law Correct Since the book is at rest, either Newton's 1st or 2nd law can tell us that the net force on it must be zero. This means that the force exerted on it by the earth must be equal and opposite to the force exerted on it by the table. 12/41 Part G Which of Newton's laws could we have used to predict that the forces in Parts B and E are equal and opposite? Check all that apply. ANSWER: Newton's 1st law Newton's 2nd law Newton's 3rd law 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. To draw a free-body diagram use the following steps: 1. Isolate the object of interest. It is customary to represent the object of interest as a point in your diagram. 2. 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. 3. 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. 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. 13/41 Part A Determine the object of interest for the situation described in the problem introduction. For this situation you should draw a free-body diagram for 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: the floor. Chadwick. the piano. 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: 14/41 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 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 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: 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. ANSWER: 15/41 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. 16/41 Chadwick now needs to push the piano up a ramp and into a moving van. The piano slides up the ramp without friction. 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. For this situation, you should draw a free-body diagram for ANSWER: the ramp. Chadwick. the piano. 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. Assume that Chadwick pushes in a direction parallel to the inclined plane. Again, draw your diagram before you look at the choices below. Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER: 17/41 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. 18/41 Pulling Two Blocks In the situation shown in the figure, a person is pulling with a constant, nonzero force block A. Block A is also attached to block B via string 2, as shown. on string 1, which is attached to For this problem, assume that neither string stretches and that friction is negligible. Both blocks have finite (nonzero) mass. Part A Which one of the following statements correctly descibes the relationship between the accelerations of blocks A and B? Hint 1. Relative movement of the blocks The two masses are connected (by string 2), which means, if they are being pulled, they must move together. ANSWER: Block A has a larger acceleration than block B. Block B has a larger acceleration than block A. Both blocks have the same acceleration. More information is needed to determine the relationship between the accelerations. Correct Since the two blocks are connected, they won't move independently when string 1 is pulled. As block A is accelerated, its motion will impart the same acceleration to block B. Part B How does the magnitude of the tension in string 1, , compare with the tension in string 2, ? 19/41 Hint 1. How to approach the problem Suppose that block A has a mass . Draw a free-body diagram for block A, then write down Newton's 2nd law for block A's horizontal motion. What is the tension ? Express the tension in terms of , , and the block's acceleration . Hint 1. Free-body diagram for block A Taking the positive direction to be to the right, what is the net horizontal force acting on block A? (Note that, in the figure, forces are not drawn to scale.) Express your answer in terms of , and . , , ANSWER: = ANSWER: = ANSWER: More information is needed to determine the relationship between and . 20/41 Correct The force transmitted through string 1 (proportional to ) must be enough to accelerate both blocks, but the force transmitted through string 2 only needs to accelerate block B. Consider the case where block A is very heavy and block B is very light: In this case, string 2 would only need to supply a tiny amount of tension to keep the blocks connected as block A is pulled around. The Normal Force When an object rests on a surface, there is always a force perpendicular to the surface; we call this the normal force, denoted by . The two questions to the right will explore the normal force. Part A A man attempts to pick up his suitcase of weight by pulling straight up on the handle. However, he is unable to lift the suitcase from the floor. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man pulls upward on the suitcase? Hint 1. How to approach this problem First, identify the forces that act on the suitcase and draw a free-body diagram. Then use the fact that the suitcase is in equilibrium, , to examine how the forces acting on the suitcase relate to each other. Hint 2. Identify the correct free-body diagram Which of the figures represents the free-body diagram of the suitcase while the man is pulling on the handle with a force of magnitude ? 21/41 ANSWER: A B C D ANSWER: The magnitude of the normal force is equal to the magnitude of the weight of the suitcase. The magnitude of the normal force is equal to the magnitude of the weight of the suitcase minus the magnitude of the force of the pull. The magnitude of the normal force is equal to the sum of the magnitude of the force of the pull and the magnitude of the suitcase's weight. The magnitude of the normal force is greater than the magnitude of the weight of the suitcase. Correct Part B Now assume that the man of weight is tired and decides to sit on his suitcase. Which statement about the magnitude of the normal force acting on the suitcase is true during the time that the man is sitting on the suitcase? 22/41 Hint 1. Identify the correct free-body diagram. Which of the figures represents the free-body diagram while the man is sitting atop the suitcase? Here the vector labeled is a force that has the same magnitude as the man's weight. ANSWER: A B C D ANSWER: 23/41 The magnitude of the normal force is equal to the magnitude of the suitcase's weight. The magnitude of the normal force is equal to the magnitude of the suitcase's weight minus the magnitude of the man's weight. The magnitude of the normal force is equal to the sum of the magnitude of the man's weight and the magnitude of the suitcase's weight. The magnitude of the normal force is less than the magnitude of the suitcase's weight. Correct Recognize that the normal force acting on an object is not always equal to the weight of that object. This is an important point to understand. Two Hanging Masses Two blocks with masses and hang one under the other. For this problem, take the positive direction to be upward, and use for the magnitude of the free-fall acceleration. Case 1: Blocks at rest For Parts A and B assume the blocks are at rest. Part A Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , and . Hint 1. Free-body diagram Isolate the lower block (mass ) by considering just the forces that act on it. Use Newton's 2nd law while noting that the acceleration of this block is zero. Hint 2. Sum of forces 24/41 Write down the sum of the y components of all the forces acting on the lower block. Express your answer in terms of some or all of the variables , , and . ANSWER: = ANSWER: = Correct Part B Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , and . Hint 1. Sum of forces Write down the sum of the y components of all the forces acting on the upper block. Express your answer in terms of some or all of the variables , , , , and . ANSWER: = ANSWER: = Correct Case 2: Accelerating blocks For Parts C and D the blocks are now accelerating upward (due to the tension in the strings) with acceleration of magnitude . Part C Find , the tension in the lower rope. Express your answer in terms of some or all of the variables , , , and . 25/41 Hint 1. Sum of forces Apply Newton's 2nd law, , to the lower block. Write the sum of the y components of the forces. Express your answer in terms of some or all of the variables , , and . ANSWER: = ANSWER: = Correct Good! Now notice that acceleration acts in the tension equation the same way that gravity does. If we look at a limiting case in which the block of mass is in free fall, accelerating downward with , then the tension goes to zero. Part D Find , the tension in the upper rope. Express your answer in terms of some or all of the variables , , , and . Hint 1. Sum of forces Consider the block of mass as an isolated system and apply Newton's 2nd law, value of found in the previous part. , with the ANSWER: = Correct The force exerted by a rope is a result of the rope's tension and points along the rope. Problem 4.10 A9 block sits at rest on a frictionless horizontal table. A 15 maintained as the block begins moving. horizontal force is suddenly applied to the block and Part A What is the acceleration of the block after the force is applied? 26/41 Express your answer in meters per second squared to two significant figures. ANSWER: 1.7 Correct Part B What is the speed of the block after it has moved a distance of 0.5 ? Express your answer in meters per second to one significant figure. ANSWER: 1 Correct Problem 4.46 You leave the doctor's office after your annual checkup and recall that you weighed 686 in her office. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator's acceleration if the scale reads Part A Find the magnitude of the elevator's acceleration if the scale reads 725 . ANSWER: = 0.557 Correct Part B Find the magnitude of the elevator's acceleration if the scale reads 725 . ANSWER: upward downward Correct 27/41 Part C Find the magnitude of the elevator's acceleration if the scale reads 597 . ANSWER: = 1.27 Correct Part D Find the magnitude of the elevator's acceleration if the scale reads 597 . ANSWER: upward downward Correct Problem 5.04 Two weights are hanging as shown in the figure. Part A Draw a free-body diagram for the top weight. Complete the free-body diagram by starting each vector at the top cable loop (the black dot). The starting point and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: 28/41 No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Correct Part B Draw a free-body diagram for the bottom weight. Complete the free-body diagram by starting each vector at the bottom cable loop (the black dot). The starting point and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: 29/41 No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Correct Part C Find the tension in cable if = 59.0 and = 200 . Express your answer as an integer. ANSWER: 200 Correct 30/41 Part D Find the tension in cables and if = 59.0 and = 200 . Express your answer to three significant figures. ANSWER: 150 Correct Problem 5.40 A person pushes on a stationary 125- box with a force of 65 coefficient of static friction between the box and the horizontal floor is 0.89. at 30 below the horizontal, as shown in the figure. The Part A Make a free-body diagram of the box. 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. ANSWER: 31/41 No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. All attempts used; correct answer displayed Part B What is the normal force on the box? Express your answer in newtons to three significant figures. ANSWER: = 158 Correct 32/41 Part C What is the friction force on the box? Express your answer in newtons to three significant figures. ANSWER: = 56.3 All attempts used; correct answer displayed Part D What is the largest the friction force could be? Express your answer in newtons to three significant figures. ANSWER: = 140 Correct Part E The person now replaces his push with a 65 case. pull at 30 above the horizontal. Find the normal force on the box in this Express your answer in newtons to three significant figures. ANSWER: = 92.5 Correct Problem 5.48 A3 mass and a 10 mass are attached to each other by a spring with spring constant and placed on a frictionless table, as shown in the figure below. The masses are then pressed toward each other in such a way as to compress the spring 0.07 . 33/41 Part A Calculate the magnitude of the acceleration of the smaller mass the moment after it is released. Express your answer in meters per second squared to two significant figures. ANSWER: 14 Correct Part B Is the acceleration to the left or to the right? ANSWER: to the left to the right Correct Part C Calculate the magnitude of the acceleration of the larger mass the moment after it is released. Express your answer in meters per second squared to two significant figures. ANSWER: 4.2 Correct Part D Is the acceleration to the left or to the right? ANSWER: to the left to the right Correct 34/41 Kinetic Friction in a Block-and-Pulley System Consider the system shown in the figure. Block A has weight 5.2 and block B has weight 3.4 . 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 numerically. 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, , is equal to zero. 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 expressions equal to each other and then solve for . Hint 2. Find the net force on block A Which of the following equations is the correct expression for , the net force acting horizontally on block A? is the tension in the rope, 5.2 is the weight of block A, is the coefficient of kinetic friction, and is the acceleration due to gravity. Also, take the positive direction to be to the right. ANSWER: Correct Hint 3. Find the net force on block B Which of the following equations is the correct expression for , the net force acting vertically on block B? the tension in the rope, 3.4 is the weight of block B, and is the acceleration due to gravity. Also, take the positive direction to be downward. is ANSWER: 35/41 Correct ANSWER: = 0.65 Correct Multiple Choice Problem 5.04 A horizontal force with a magnitude that and pulls two wagons over a horizontal frictionless floor, as shown in the figure . Assume . Part A The tension in the light horizontal rope connecting the wagons is ANSWER: equal to , by Newton’s third law. equal to 2800 greater than less than . . . Correct 36/41 Multiple Choice Problem 5.02 Part A You slide an = 750- table across the kitchen floor by pushing with a force of 130 constant speed, the friction force with the floor must be . If the table moves at a ANSWER: more than 750 130 more than 130 750 Correct Multiple Choice Problem 4.11 Far from any gravity, an astronaut accidentally releases a metal wrench inside a spaceship that is traveling at a constant velocity of 250 away from earth in outer space. Part A What will be the subsequent behavior of that wrench as observed by the astronaut? ANSWER: It will fall to the floor with constant velocity. It will fall to the floor with constant acceleration. It will fall to the back of the spaceship with constant velocity. It will fall to the back of the spaceship with constant acceleration. It will remain right where the astronaut released it. Correct Multiple Choice Problem 4.12 A worker pulls horizontally on a crate on a rough horizontal floor, causing it to move forward with constant velocity. In the figure , force is the pull of the worker and force is the force of friction due to the floor. 37/41 Part A Which one of the following statements about these forces is correct? ANSWER: Correct Multiple Choice Question 4.5 Part A Consider what happens when you jump up in the air. Which of the following is the most accurate statement? ANSWER: It is the upward force exerted by the ground that pushes you up, but this force can never exceed your weight. When you push down on the earth with a force greater than your weight, the earth will push back with the same magnitude force and thus propel you into the air. Since the ground is stationary, it cannot exert the upward force necessary to propel you into the air. Instead, it is the internal forces of your muscles acting on your body itself which propels the body into the air. You are able to spring up because the earth exerts a force upward on you which is stronger than the downward force you exert on the earth. Correct Problem 5.06 38/41 A 1100car is being pulled up a frictionless ramp at a constant speed, as shown in the figure. The cable makes an angle of 31.0 above the surface of the ramp, and the ramp itself rises at 25.0 above the horizontal. Part A Draw a free-body diagram for the car. Draw all the required force vectors with their tails starting at the black dot on the front bumper. The location and orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: 39/41 No elements selected Select the elements from the list and add them to the canvas setting the appropriate attributes. Correct Part B Find the tension in the cable. Express your answer in newtons to three significant figures. ANSWER: = 5320 Correct 40/41 Part C How hard does the surface of the ramp push on the car? Express your answer in newtons to three significant figures. ANSWER: = 7030 Correct Score Summary: Your score on this assignment is 105%. You received 334.05 out of a possible total of 360 points, plus 45 points of extra credit. 41/41