Drawing and Using Free-Body Diagrams

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1 Name (First AND Last): Date: Goal: Drawing and Using Free-Body Diagrams Adapted from Minds on Physics Activity #51: Recognizing and Interpreting Free-Body Diagrams After completing this activity, you should be able to draw valid free-body diagrams. Also, you should be able to use free-body diagrams to write expressions for the components of the net force. Explanation of Activity and Examples: You will draw valid free-body diagrams for blocks in a variety of situations. PART A: Drawing Free-Body Diagrams For each block in each situation, draw and label a valid free-body diagram to describe the forces acting on it. (Note: You should ignore the forces of air resistance and buoyancy in this activity.) E1. A block of mass m is support from the ceiling by two ropes as shown. Notes: There are two ropes, so this object: The sketch of the block there are two tension forces, labeled FT1 and/or the and FT2. The force of gravitation points straight down. There are many ways to draw the free-body diagram for this object: The sketch of the block and/or be missing, or the be moved to one side.

2 Al. A block of mass m is suspended from the ceiling by a light string. A2. A block having mass m is pulled by a horizontal force F a in the positive x- direction along a rough, horizontal surface. A3. A block of mass ml is suspended from the ceiling by a rope. Attached to the bottom of m1 is a second rope, from which a second mass, m2, hangs.

3 A4. 100kg block is pushed up a smooth (frictionless) ramp by a horizontal force, F a = 2000N. The ramp makes an angle of 30 relative to the horizontal. A5. Two blocks, having masses m 1 = 5kg and m 2 = 10kg, are in contact and sit side-by-side on a smooth, horizontal surface. A force F a directed to the right is applied to ml and both blocks accelerate with a = 2m/s 2

4 A6. A 5kg block is at rest on a smooth ramp that makes an angle of 30 with the horizontal. The block is supported by a spring placed at the bottom of the ramp. A7. A block of mass m is attached to a string and released from rest when the string is horizontal. (Draw the free-body diagram for the block at the instant shown.)

5 Summary How are the forces in a free-body diagram related to the net force exerted on an object? The net force is the vector sum of all the external forces exerted on the object, and therefore, it should never appear in a free-body diagram. After all, it is in essence already there! How can I make my free-body diagrams as useful as possible? First of all, you should make sure that the directions of all your forces are accurately drawn. This will help you find the components of the forces, which will help you find the net force, and ultimately, the acceleration of the object. Then, if the sizes of the force vectors are also drawn accurately, often we can identify the direction of the net force F net. By Newton's second law, an object will always accelerate in the same direction as F net. Therefore, the net force implied by your free-body diagram should always be consistent with the magnitude and/or the direction of the object's acceleration (if either is known). For example, an object at rest or traveling with constant velocity has zero acceleration. In this instance, the vectors in your free-body diagram should add to zero, as closely as possible. What if the acceleration of the object is non-zero? Sometimes, we do not know the magnitude of the acceleration, particularly before we have solved the problem! Often we want to solve for the acceleration of an object. Even if we do not yet know the magnitude of the acceleration, sometimes we know its direction. For instance, if an object is sliding along a flat surface, we know that the velocity always points parallel to the surface. Therefore, all changes in velocity (as well as accelerations) also point parallel to the surface. Thus, the direction of the net force is known. Your free-body diagrams should be consistent with this fact. F net should point parallel to the surface; there should be no component of F net perpendicular to the surface.

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