Worksheet #1 Free Body or Force diagrams Drawing Free-Body Diagrams Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams; these diagrams will be used throughout your study of physics. The size of the arrow in a free-body diagram is reflective of the magnitude of the force. The direction of the arrow reveals the direction in which the force acts. Each force arrow in the diagram is labeled to indicate the type of force. It is customary in a free-body diagram to represent the object by a box or a small circle and to draw the force arrow from the center of the box or circle outward in the direction in which the force is acting. One example of a free-body diagram is shown to the right. The free-body diagram above depicts four forces acting upon the object. Objects do not always have four forces acting upon them. There will be cases in which the number of forces depicted by a freebody diagram will be one, two, or three. There is no hard and fast rule about the number of forces which must be drawn in a free-body diagram. The only rule for drawing free-body diagrams is to depict all the forces which exist for that object in the given situation. Thus, to construct free-body diagrams, it is extremely important to know the types of forces. If given a description of a physical situation, begin by using your understanding of the force types to identify which forces are present. Then determine the direction in which each force is acting. Finally, draw a box and add arrows for each existing force in the appropriate direction; label each force arrow according to its type. Apply the method described in the reading to construct free-body diagrams for the situations described below. Use the symbols we discussed in class. Draw force vectors on the circle and label them. 1. A book is at rest on a table top. Diagram the forces acting on the book. 2. A girl is suspended motionless from the ceiling by a rope. Diagram the forces acting on the girl as she holds onto the rope. 3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it falls. 4. An egg is falling (not freely, do not neglect air resistance) from a nest in a tree. Diagram the forces acting on the egg as it falls.
5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. 6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. 7. A car is stopped at a stop light. 8. A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver. 9. A car is parked on a sloped street. 10. A hot air balloon is accelerating upward. 11. A car is coasting to the right and slowing down. Diagram the forces acting upon the car.
Name Date Worksheet 2, Drawing Force Diagrams Pd In each of the following situations, represent the object with a dot. Draw and label all the forces using standard force symbols as learned in class. 1. Object lies motionless on a surface. 2. Object slides at constant speed along a Smooth (frictionless) surface. 3. Object slows due to friction (rough surface). 4. Object slides on a smooth incline. 5. Friction on an incline prevents sliding. 6. An object is suspended from the ceiling. 7. An object is suspended from the ceiling. 8. The object is motionless. 9. The object is motionless. 10. The object is motionless. Worksheet, Drawing Force Diagrams 1 9/23/2009
11. The object is pulled by a force parallel to the surface. The surface is rough or has friction. 12. The object is pulled by a force at an angle to the surface. The surface is rough. 13. The object is pulled upward at constant speed. 13. A hot air balloon is held down to keep it From accelerating upward. 15. The object is falling (no air resistance). 16. The object is falling at constant (terminal) velocity. 17. The ball is rising in a parabolic trajectory. Do not neglect air resistance 18. A rocket is accelerating straight upward. 19. A skier is accelerating down a slope. There is friction and air resistance. 20.A big block of mass M is attached via a string to a smaller block of mass m. A student attaches a string to block M and pulls everything to the right along the rough surface. Both blocks travel at constant velocity. Do force diagrams for each block separately. Worksheet, Drawing Force Diagrams 2 9/23/2009
Name Class Date Concept-Development Practice Page 6-1 Friction 1. A crate filled with delicious junk food rests on a horizontal floor. Only gravity and the support force of the floor act on it, as shown by the vectors for weight W and normal force n. a. The net force on the crate is (zero) (greater than zero). b. Evidence for this is. 2. A slight pull P is exerted on the crate, not enough to move it. a. The force of friction f acting on the crate is (less than) (equal to) (greater than) P. b. The net force on the crate is (zero) (greater than zero). 3. Pull P is increased until the crate begins to move. It is pulled so that it moves with constant velocity across the floor. a. Friction f is (less than) (equal to) (greater than) P. b. Constant velocity means acceleration is (zero) (greater than zero). Pearson Education, Inc., or its affi liate(s). All rights reserved. c. The net force on the crate is (less than) (equal to) (greater than) zero. 4. Pull P is further increased and is now greater than friction f. a. The net force on the crate is (less than) (equal to) (greater than) zero. b. The net force acts toward the right, so acceleration acts toward the (left) (right). 5. If the pulling force P is 150 N and the crate doesn t move, what is the magnitude of f? 6. If the pulling force P is 200 N and the crate doesn t move, what is the magnitude of f? 7. If the force of sliding friction is 250 N, what force is necessary to keep the crate sliding at constant velocity? 8. If the mass of the crate is 50 kg and sliding friction is 250 N, what is the acceleration of the crate when the pulling force is 250 N? 300 N? 500 N? CONCEPTUAL PHYSICS Chapter 6 Newton s Second Law of Motion Force and Acceleration 25
Falling and Air Resistance Bronco skydives and parachutes from a stationary helicopter. Various stages of fall are shown in positions (a) through (f). Using Newton s second law, find Bronco s acceleration at each position (answer in the blanks to the right). You need to know that Bronco s mass m is 100 kg so his weight is a constant 1000 N. Air resistance R varies with speed and cross-sectional area as shown. Circle the correct answers. 1. When Bronco s speed is least, his acceleration is (least) (most). 2. In which position(s) does Bronco experience a downward acceleration? (a) (b) (c) (d) (e) (f) 3. In which position(s) does Bronco experience an upward acceleration? (a) (b) (c) (d) (e) (f) 4. When Bronco experiences an upward acceleration, his velocity is (still downward) (upward also). 5. In which position(s) is Bronco s velocity constant? (a) (b) (c) (d) (e) (f) 6. In which position(s) does Bronco experience terminal velocity? (a) (b) (c) (d) (e) (f) 7. In which position(s) is terminal velocity greatest? (a) (b) (c) (d) (e) (f) Pearson Education, Inc., or its affi liate(s). All rights reserved. 8. If Bronco were heavier, his terminal velocity would be (greater) (less) (the same). CONCEPTUAL PHYSICS 26 Chapter 6 Newton s Second Law of Motion Force and Acceleration
Name Class Date Chapter 6 Newton s Second Law of Motion Force and Acceleration Newton s Second Law A large mining dump truck has a mass of 40,000 kg. If its engine produces 20,000 N of force, how fast will the truck accelerate? 1. Read and Understand What information are you given? Mass of truck = 40,000 kg Force applied = 20,000 N 2. Plan and Solve What unknown are you trying to calculate? Acceleration of truck =? Pearson Education, Inc., or its affiliate(s). All rights reserved. What formula contains the given quantities and the unknown? Acceleration = force mass or a = F m Replace each variable with its known value and solve. a= 20, 000 N 40, 000 kg 20, 000 kg m/s = 40, 000 kg 2 = 0.5 m/s 2 3. Look Back and Check Is your answer reasonable? Yes, the number calculated is the quotient of force and mass and the units are those of acceleration. Math Practice On a separate sheet of paper, solve the following problems. 1. The truck described above dumps its load and its mass is reduced to 10,000 kg. What is the acceleration of the truck? Assume its engine still produces the same amount of force. 2. How much force must the engine of the dump truck described above develop to achieve an acceleration of 3.5 m/s 2? 3. A toy car has a mass of 1500 g. If a 3-N force is applied to the car, what will its acceleration be? Conceptual Physics Reading and Study Workbook Chapter 6 45
Name Class Date Force and Acceleration Concept-Development Practice Page 6-2 1. Skelly the skater, total mass 25 kg, is propelled by rocket power. a. Complete Table I (neglect resistance) b. Complete Table II for a constant 50-N resistance. 2. Block A on a horizontal friction-free table is accelerated by a force from a string attached to Block B. B falls vertically and drags A horizontally. Both blocks have the same mass m. (Neglect the string s mass.) Circle the correct answers. a. The mass of the system (A + B) is (m) (2m). b. The force that accelerates (A + B) is the weight of (A) (B) (A + B). c. The weight of B is (mg/2) (mg) (2mg). Pearson Education, Inc., or its affi liate(s). All rights reserved. d. Acceleration of (A + B) is (less than g) (g) (more than g). e. Use a = to show the acceleration of (A + B) as a fraction of g. CONCEPTUAL PHYSICS Chapter 6 Newton s Second Law of Motion Force and Acceleration 27
3. Suppose A is still a 1-kg block, but B is a low-mass feather (or a coin). a. Compared to the acceleration of the system in 2, previous page, the acceleration of (A + B) here is (less) (more) and is (close to zero) (close to g). b. In this case the acceleration of B is (practically that of free fall) (constrained). 4. Suppose A is a feather or coin, and B has a mass of 1 kg. a. The acceleration of (A + B) here is (close to zero) (close to g). b. In this case the acceleration of B is (practically that of free fall) (constrained). 5. Summarizing 2, 3, and 4, where the weight of one object causes the acceleration of two objects, we see the range of possible accelerations is (between zero and g) (between zero and infinity) (between g and infinity). 6. A ball rolls down a uniform-slope ramp. a. Acceleration is (decreasing) (constant) (increasing). b. If the ramp were steeper, acceleration would be (more) (the same) (less). c. When the ball reaches the bottom and rolls along the smooth level surface it (continues to accelerate) (does not accelerate). Pearson Education, Inc., or its affi liate(s). All rights reserved. CONCEPTUAL PHYSICS 28 Chapter 6 Newton s Second Law of Motion Force and Acceleration
Name Class Date Racing Day with a = F/m Concept-Development Practice Page 6-3 In each situation below, Cart A has a mass of 1 kg. Circle the correct answers (A, B, or Same for both). 1. Cart A is pulled with a force of 1 N. Cart B also has a mass of 1 kg and is pulled with a force of 2 N. Which undergoes the greater acceleration? (A) (B) (Same for both) 2. Cart A is pulled with a force of 1 N. Cart B has a mass of 2 kg and is also pulled with a force of 1 N. Which undergoes the greater acceleration? (A) (B) (Same for both) 3. Cart A is pulled with a force of 1 N. Cart B has a mass of 2 kg and is pulled with a force of 2 N. Which undergoes the greater acceleration? (A) (B) (Same for both) 4. Cart A is pulled with a force of 1 N. Cart B has a mass of 3 kg and is pulled with a force of 3 N. Which undergoes the greater acceleration? (A) (B) (Same for both) Pearson Education, Inc., or its affi liate(s). All rights reserved. 5. This time Cart A is pulled with a force of 4 N. Cart B has a mass of 4 kg and is pulled with a force of 4 N. Which undergoes the greater acceleration? (A) (B) (Same for both) 6. Cart A is pulled with a force of 2 N. Cart B has a mass of 4 kg and is pulled with a force of 3 N. Which undergoes the greater acceleration? (A) (B) (Same for both) CONCEPTUAL PHYSICS Chapter 6 Newton s Second Law of Motion Force and Acceleration 29
Drop and Pull 1. Consider a 1-kg cart being pulled by a 10-N applied force. According to Newton s second law, acceleration of the cart is a = F = 10 N = 10 m/s 2. m 1 kg 2. Consider the acceleration of the cart when the applied force is due to a 10-N iron weight attached to a string draped over a pulley. Will the cart accelerate as before, at 10 m/s 2? The answer is no, because the mass being accelerated is the mass of the cart plus the mass of the piece of iron that pulls it. Both masses accelerate. The mass of the 10-N iron weight is 1 kg so the total mass being accelerated (cart + iron) is 2 kg. Then, a = F = 10 N = 5 m/s 2. m 2 kg a. Find the acceleration of the 1-kg cart when two identical 10-N weights are attached to the string. a = F = applied force = = m/s 2 m total mass Pearson Education, Inc., or its affi liate(s). All rights reserved. CONCEPTUAL PHYSICS 30 Chapter 6 Newton s Second Law of Motion Force and Acceleration
Name Class Date Drop and Pull continued b. Find the acceleration of the 1-kg cart when three identical 10-N weights are attached to the string. a = F = applied force = = m/s 2 m total mass c. Find the acceleration of the 1-kg cart when four identical 10-N weights (not shown) are attached to the string. a = F = applied force = = m/s 2 m total mass d. This time 1 kg of iron is added to the cart, and only one iron piece dangles from the pulley. Find the acceleration of the cart. a = F = applied force = = m/s 2 m total mass Pearson Education, Inc., or its affi liate(s). All rights reserved. e. Find the acceleration of the cart when it carries two pieces of iron and only one iron piece dangles from the pulley. a = F = applied force = = m/s 2 m total mass CONCEPTUAL PHYSICS Chapter 6 Newton s Second Law of Motion Force and Acceleration 31
f. Find the acceleration of the cart when it carries 3 pieces of iron and only one iron piece dangles from the pulley. a = F = applied force = = m/s 2 m total mass g. Find the acceleration of the cart when it carries 3 pieces of iron and 4 pieces of iron dangle from the pulley. a = F = applied force = = m/s 2 m total mass a = F = applied force = = m/s 2 m total mass h. Draw your own combination of masses and find the acceleration. Pearson Education, Inc., or its affi liate(s). All rights reserved. CONCEPTUAL PHYSICS 32 Chapter 6 Newton s Second Law of Motion Force and Acceleration
Name Class Date Chapter 6 Newton s Second Law of Motion Force and Acceleration Exercises 6.1 Force Causes Acceleration (page 87) 1. When a hockey puck is struck with a hockey stick, a(n) acts on the puck and the puck. 2. Circle the letter of the type of force that causes acceleration. a. balanced b. negligible c. zero d. unbalanced 3. The combination of forces acting on an object is known as the force. 4. The acceleration of an object is directly proportional to the net force acting on it. This means that, as the net force acting on the object increases, the acceleration of the object. 5. Circle the letter of each statement about force and acceleration that is true. a. Balanced forces cause constant acceleration. b. The forces acting on an object at rest are unbalanced. c. A net force acting on an object causes acceleration. d. Force is not required for an object to accelerate. 6. Two shopping carts of equal mass are pushed by two different people. One cart accelerates three times as fast as the other cart. Describe the forces acting on each cart. Pearson Education, Inc., or its affiliate(s). All rights reserved. 6.2 Mass Resists Acceleration (page 87) 7. For a constant force, how does an increase in an object s mass affect its acceleration? 8. What does it mean for two quantities to be inversely proportional to one another? 9. Circle the letter showing how mass and acceleration are related. a. acceleration ~ mass b. acceleration ~ 1/mass c. acceleration ~ mass 2 d. acceleration ~ 1 2 mass 6.3 Newton s Second Law (pages 88 89) 10. Circle the letter of each quantity related by Newton s second law. a. mass b. force c. time d. acceleration Conceptual Physics Reading and Study Workbook Chapter 6 41
Name Class Date Chapter 6 Newton s Second Law of Motion Force and Acceleration 11. Circle the letter of each statement related to Newton s second law that is true. a. Acceleration is directly proportional to the net force. b. The direction of acceleration is the same as the net force. c. Acceleration is inversely proportional to mass. d. Net force and mass are always equal. 12. When using the equation for Newton s second law, if force is measured in newtons, then the unit for acceleration is and the unit for mass is. 13. Is the following sentence true or false? The acceleration of an object is equal to the net force acting on it divided by the object s mass. 14. A 100-N force is used to accelerate a large push cart across the floor. Circle the letter of the force required to accelerate the push cart twice as fast. a. 50 N b. 100 N c. 150 N d. 200 N 15. An object accelerates when a net force is applied to it. Circle the letter describing the conditions that would double the object s acceleration. a. doubling the mass b. halving the force c. doubling the mass and halving the force d. halving the mass 16. During a lab experiment, a net force is applied to an object and the object accelerates. The mass of the object is then doubled, and the net force applied to it also doubles. Describe the object s acceleration. 17. Circle the letter of the equation that describes Newton s second law of motion. a. a = F b. F = ma m 2 c. F = a d. F = 1 m 2 (am)2 6.4 Friction (page 90 91) 18. Describe what causes friction between two solid surfaces. Pearson Education, Inc., or its affiliate(s). All rights reserved. 19. Is the following sentence true or false? Friction does not depend on the types of materials in contact with each other. 20. Is the following sentence true or false? Friction depends on how much the materials in contact are pushed together. 42 Conceptual Physics Reading and Study Workbook Chapter 6
Name Class Date Chapter 6 Newton s Second Law of Motion Force and Acceleration 21. The figure above shows where an out-of-control car might strike a concrete road divider. In terms of friction, explain why the concrete barrier is superior to the steel barrier in the figure. 22. Substances that are liquids or gases are also called. 23. Is the following sentence true or false? When friction is present, an object can move with constant velocity even when an outside force is applied. 24. A is a diagram in which all of the forces acting on an object are shown. Pearson Education, Inc., or its affiliate(s). All rights reserved. 6.5 Applying Force Pressure (pages 91 92) 25. Circle the letter of each quantity related to pressure. a. time b. force c. weight d. area 26. Circle the letter that best describes pressure. a. the applied force that acts on an object b. force per unit of area c. the area to which a force is applied d. force times surface area 27. Imagine standing on a bathroom scale on two feet and then one foot. Describe the force and pressure exerted in each case. 28. As the area a force acts on increases, the force exerted on each unit of area. 29. What is the equation for pressure when the force is perpendicular to the surface area? 30. Circle the letter that describes the unit of pressure known as a pascal. a. newtons area b. newton meter c. newtons per square meter d. square meters per second Conceptual Physics Reading and Study Workbook Chapter 6 43
Name Class Date Chapter 6 Newton s Second Law of Motion Force and Acceleration 31. Look at the two books resting on a shelf in the illustration shown below. Assume the two books are identical. Circle the letter of each statement about the two books that is true. a. Both books have the same mass. b. Both books exert the same force on the shelf. c. Both books exert the same pressure on the shelf. d. Both books have the same weight. 6.6 Free Fall Explained (pages 93 95) 32. An object dropped in air that experiences no air resistance is said to be in. 33. A 1-kg river rock and a 10-kg small boulder are dropped from the back of a truck at the same time. Identify which rock will strike the ground first. 34. When an object is in free fall, the only force acting on the object is. 35. Circle the letter of each statement about freely falling objects that is true. a. They all fall with the same acceleration. b. The net force acting on them is their weight. c. Their weight-to-mass ratios are always the same. d. Their acceleration is g, the acceleration due to gravity. 6.7 Falling and Air Resistance (pages 95 97) 36. Identify the conditions needed for a feather and coin to fall at the same rate. 37. Circle the letter of each factor that affects the amount of air resistance experienced by an object. a. time in contact with the air b. speed of object through the air c. surface area of object d. weight of object 38. Circle the letter that describes the forces that are in balance when an object reaches its terminal speed. a. mass and air resistance b. air resistance and friction c. friction and mass d. weight and air resistance 39. Define terminal speed and terminal velocity. Pearson Education, Inc., or its affiliate(s). All rights reserved. 44 Conceptual Physics Reading and Study Workbook Chapter 6
Chapter 6 Study Guide of Physics 1. Why is there more pressure standing vs. lying on the ground? 2. With a constant force, what happens to a sliding block of ice if you double the mass? 3. With a sliding block of ice, what happens when you double the force? 4. With a sliding block of ice, what happens when you triple the mass AND triple the force? 5. According to Newton s 2 nd Law (F=ma), how is acceleration related to mass? 6. Give two examples of fluids. What do all fluids do? 7. What is a free-body diagram? 8. How would you show inversely and directly proportional? 9. What two things affect the amount of friction between two objects that are touching? 10. What is the unit for pressure? 11. Define free fall like a physics teacher would do it. 12. What two things affect the amount of air resistance on an object? Problems A. A 500N force is used to push a cart across a floor with an acceleration of 5 m/s 2. How could you double the acceleration? B. How much pressure is experienced by an arm when a 0.0012 m 2 hypodermic needle is pushed against it with a force of 2 N? C. How much acceleration is there when a 2,000 N force is applied to a 5 kg mass? Extra Credit: #69 on page 105. Take a picture. Be careful. Need at least two people. Other Extra Credit: Draw a comic like page 94, but do it for an air resistance example. You may also use Toondoo.com.