Physics 4A Chapter 5: Force and Motion - I

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1 Physics 4A Chapter 5: Force and Motion - I The answers you receive depend upon the questions you ask. Thomas Kuhn Life is a mirror and will reflect back to the thinker what he thinks into it. Ernest Holmes Reading: pages Outline: Newton s Laws (PowerPoint) Newton s 1 st Law Newton s 2 nd Law Newton s 3 rd Law some particular forces weight normal force tension applications of Newton s 2 nd Law free-body diagrams inclined planes example problems Problem Solving A definite procedure has been devised to solve Newton s laws problems. It ensures that you consider only one object at a time, reminds you to include all forces on the object you are considering, and guides you in writing Newton's second law in an appropriate form. Follow it closely. Use the list below as a check list until the procedure becomes automatic. 1. Identify the object to be considered. It is usually the object on which the given forces act or about which a question is posed. 2. Represent the object by a dot on a diagram or by a sketch of its outline. Do not include the environment of the object since this is replaced by the forces it exerts on the object. 3. On the diagram, draw arrows to represent the forces of the environment on the object. Try to draw them in roughly the correct directions. The tail of each arrow should be at the dot or outline. Label each arrow with an algebraic symbol to represent the magnitude of the force, regardless of whether a numerical value is given in the problem statement. The hard part is getting all the forces. If appropriate, don't forget to include the gravitational force on the object, the normal force of a surface on the object, and the forces of any strings or rods attached to the object. Carefully go over the sample problems in the text to see how to handle these forces.

2 Some students erroneously include forces that are not acting on the object. For each force you include you should be able to point to something in the environment that is exerting the force. This simple procedure should prevent you from erroneously including a normal force, for example, when the object you are considering is not in contact with a surface. 4. Draw a coordinate system on the diagram. In principle, the placement and orientation of the coordinate system do not matter as far as obtaining the correct answer is concerned but some choices reduce the work involved. If you can guess the direction of the acceleration, place one of the axes along that direction. The acceleration of an object sliding on a surface at rest, such as a table top or inclined plane, for example, is parallel to the surface. Once the coordinate system is drawn, label the angle each force makes with a coordinate axis. This will be helpful in writing down the components of the forces later. The diagram, with all forces shown but without the coordinate system, is called a free-body diagram. We add the coordinate system to help us carry out the next step in the solution of the problem. 5. Write Newton's second law in component form: F net x = ma x, F net y = ma y, and, if necessary, F net z = ma z. The left sides of these equations should contain the appropriate components of the forces you drew on your diagram. You should be able to write the equations by inspection of your diagram. Use algebraic symbols to write them, not numbers; most problems give or ask for force magnitudes so you should usually write each force component as the product of a magnitude and the sine or cosine of an appropriate angle. 6. If more than one object is important, as when two objects are connected by a string, you can sometimes treat them as a single object. To do this you must know that their accelerations are the same. On the other hand, if you are asked for the force of one object on another, you must carry out the steps given above separately for each object. There is then an additional condition you must consider. Usually the condition is that the magnitudes of their accelerations are the same. You must then invoke Newton's third law: the force of the two objects on each other are equal in magnitude and opposite in direction. Use the same algebraic symbol to represent the magnitudes of these forces and draw their arrows in opposite directions on the free-body diagrams. 7. Identify the known quantities and solve for the unknowns. Question and Example Problems from Chapter 5 Question 1 The figure below shows overhead views of four situations in which forces act on a block that lies on a frictionless floor. If the force magnitudes are chosen properly, in which situations is it possible that the block is (a) stationary and (b) moving with a constant velocity?

3 Question 2 The body that is suspended by a rope in the figure below has a weight of 75 N. Is T equal to, greater than, or less than 75 N when the body is moving downward at decreasing speed? Question 3 In the figure below, two forces F 1 and F 2 are applied to a lunchbox as it slides at constant velocity over a frictionless floor. We are to decrease the angle θ of F 1 without changing the magnitude of F 1. (a) To keep the lunch box sliding at constant velocity, should we increase, decrease, or maintain the magnitude of F 2? (b) What happens to the normal force as we decrease the angle θ of F 1? Question 4 The figure shows four choices for the direction of a force of magnitude F to be applied to a block on an inclined plane. The directions are either horizontal or vertical. (For choices a and b, directions are either horizontal or vertical. (For choices a and b, the force is not enough to lift the block off the plane.) Rank the choices according to the magnitude of the normal force on the block from the plane, greatest first.

4 Problem 1 The helicopter in the drawing is moving horizontally to the right at a constant velocity. The weight of the helicopter is 53,800 N. The lift force L generated by the rotating blade makes an angle of 21.0 o with respect to the vertical. (a) What is the magnitude of the lift force? (b) Determine the magnitude of the air resistance R that opposes the motion. Problem 2 Accelerometer. A small mass m hangs from a thin string and can swing like a pendulum. You attach it above the window of your car as shown in the figure below. When the car is at rest, the string hangs vertically. What angle does the string make (a) when the car accelerates at a constant rate of 1.20 m/s 2, and (b) when the car moves at a constant velocity, v = 90 km/h?

5 Problem 3 In the figure below, two forces, F 1 and F 2, act a 50.0 kg crate that sits on a frictionless floor. The magnitude of F 1 is 255 N and it is applied at a 40 o angle. The magnitude of F 2 is 55N. (a) What is the normal force exerted on the crate? (b) What is the crate s acceleration? Problem 4 The figure below shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). The arrangement is know as Atwood s machine. One block has a mass m 1 = 1.30 kg; the other has mass m 2 = 2.80 kg. What are (a) the magnitude of the block s acceleration and (b) the tension in the cord?

6 Problem 5 In the figure below, let the mass of the block be 8.5 kg and the angle θ be 30. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the resulting acceleration of the block.

7 Problem 6 In the figure below, a block of weight w 1 = N on a frictionless inclined plane of angle 15 o is connected by a cord over a massless, frictionless pulley to a second block of weight w 2 = 30.0 N. (a) What are the magnitude and direction of the acceleration of each block? (b) What is the tension in the cord?

8 Problem 7 The figure below shows a box of mass m 2 = 1.0 kg on a frictionless plane inclined at angle θ = 30. It is connected by a cord of negligible mass to a box m 1 = 3.0 kg on a horizontal frictionless surface. The pulley is frictionless and massless. (a) If the magnitude of the horizontal force F is 2.3 N, what is the tension in the connecting cord? (b) What is the largest value the magnitude of F may have without the cord becoming slack?

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