Unit 6: Forces II PRACTICE PROBLEMS

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1 Regents Physics Mrs. Long Unit 6: Forces II PRACTICE PROBLEMS Essential Understanding for the Unit: The net force can be determined by using force diagrams in order to show all forces acting, and thereby evaluate whether or not a system is in equilibrium (constant motion or at rest). YOU SHOULD BE ABLE TO EXPLAIN THESE IN DETAIL BY THE END OF THE UNIT Name 1

2 Assignment #1: Finding Forces in Equilibrium What exactly is meant by the terms balanced forces and unbalanced forces? 1.) First consider a physics book at rest on a table top. a.) What are the forces acting on the physics book? Label them in the picture to the right. b.) Is the book accelerating? How do you know? c.) If the book has a mass of 2 kg, what is its weight? d.) What must the magnitude of the normal force be, in order to balance out the weight? 2.) Next consider a physics book being pushed at a constant velocity against the force of friction. a.) What are the forces acting on the physics book? Label them in the picture to the right. b.) Is the book accelerating? How do you know? c.) If the book has a mass of 2 kg, determine the magnitude of the weight and the normal force. d.) If the applied force is 40 Newtons pushing to the right on the block, how much the frictional force be in order to balance out? Equilibrium When forces acting on an object are equal and opposite, they will balance out! There will be NO net force acting on the object and its motion will not change 2

3 1.) Which situation represents a person in equilibrium? (1) A child gaining speed while sliding down a slide (2) A woman accelerating upward in an elevator (3) A man standing still on a bathroom scale (4) A teenager driving around a corner in his car 2.) Two forces act concurrently on an object on a horizontal, frictionless surface, as shown in the diagram below. What additional force, when applied to the object, will establish equilibrium? (1) 16 N toward the right (2) 16 N toward the left (3) 4 N toward the right (4) 4 N toward the left 3.) Which body is in equilibrium? (1) A satellite moving around Earth in a circular orbit (2) A cart rolling down a frictionless incline (3) An apple falling freely toward the surface of the Earth (4) A block sliding at constant velocity across a tabletop 4.) Which diagram represents a box in equilibrium? 5.) Which graph best represents the motion of an object in equilibrium? 3

4 Assignment #2: Finding the Net Force (F NET ) Now consider a book sliding from left to right across a table top. Maybe someone pushed it or it slid down a ramp. As it slides there is NO force pushing it any more. What is the Net Force acting on the book in the y-direction? If the force of friction is 5 N, what is the Net Force acting on the book in the x-direction?? Forces acting in the same direction (0 O ) are added together. Forces in opposite directions (180 O ) are subtracted from each other Determine the Net Force (with direction) of the two problems below: Applied Forces Angle between Forces Net Force (with direction) 5 N 10 N 5 N 10 N 4

5 Depending on the information provided in the problem, sometimes you will solve for F NET using the equation F NET = ma. Sometimes you will solve for F NET using your force diagram. Decide which one to use in the following situations. Draw the force diagram for every question! 1. A 20 Kg mass is being pulled horizontally with a force of 250 N. The force of friction is equal to 150 N. a. Use vectors to draw a force diagram b. Solve for the net force. c. Find the acceleration of the mass. d. On your force diagram, draw vector a to represent the direction of the acceleration. 2. A block weighing 200 N is being lifted by a force of 500 N. a. Use vectors to draw a force diagram. b. Solve for the net force c. Find the acceleration of the block. d. On your force diagram, draw vector a to represent the direction of the acceleration. 5

6 3. Milo and Otis are both pulling a cart with a mass of 32 kilograms. Milo pulls with a force of 25 Newtons and Otis exerts a 42 Newton force in the same direction. A goat tied to the cart is pulling in the opposite direction with a force of 75 Newtons. a. Use vectors to draw a force diagram b. Solve for the net force. c. Find the acceleration rate of the cart. d. On your force diagram, draw vector a to represent the direction of the acceleration. 4. Four stooges are trying to move a 10 kg crate by pushing on each of the four sides. Joe pushes at 75 N north, Larry at 15 N east, Curly at 50 N south, and Moe at 25 N west. a. Use vectors to draw a force diagram b. Solve for the net force. c. Find the rate of acceleration of the crate. d. On your force diagram, draw vector a to represent the direction of the acceleration. 5. A mass is sitting on a horizontal surface. A force of 100 N is applied to the 5-kilogram mass and an acceleration rate of 6.0 m/s/s is produced. What is the net force acting on the mass? What is the force of friction? 6

7 Use the information below for Questions 1 4. Two forces act concurrently on an object on a horizontal surface, as shown in the diagram below. The 10 N force is the applied force, and the frictional force has a magnitude of 6 N. The object has a mass of 8 kg. Assignment #3: Equilibrium or Not? 1. What is the net force? N 2. What is the acceleration? [Show all work, including equation and substitution with units.] 3. What other force would be needed to bring the object into equilibrium? Give both magnitude and direction: N to the (direction) 4. Once the object is in equilibrium, what will be the object s net force and the acceleration? N and m/s 2 Use the diagram and information below to answer questions 5 7. A 10 kg mass slides to the right. The 50 N force may be considered to be the applied force. 5. If no other force acts, what is the net force? N 6. Give an example of a possible magnitude for the force of friction if: a. The block is accelerating to the right. N b. The block is moving with constant speed. N c. The block is in a state of equilibrium. N 7. If the applied of force of 50 N is removed while the block is still sliding to the right, and the friction force is 40 N, then what will be the magnitude and direction of the acceleration? [Show all work, including equation and substitution with units.] 7

8 Use the diagram below for Questions The diagram below shows a 5.00-kilogram block at rest on a horizontal table. 8. What is the force that the block exerts on the table? [Show all work, including equation and substitution with units.] 9. Which diagram best represents the force exerted on the block by the table? 10. As the block sits on the table, how do we know that the net force is zero newtons? 11. If the table exerted a force on the block that was greater than the force the block was exerting on the table, then what would happen to the block? 12. What would happen if the force exerted by the block on the table was greater? 8

9 Use the following information for Questions A block with a mass of 2 kg is moving across a horizontal surface. The applied force is 50 N to the left. The force of friction between the surface and the block is 35 N. 13. Calculate the weight of the block. [Show all work, including equation and substitution with units.] 14. Determine the normal force being exerted on the block. N 15. Draw a labeled force diagram that appropriately shows all four forces acting on the block. 16. Determine the magnitude and the direction of the net force on the block. N to the (direction) 17. Calculate the acceleration of the block. [Show all work, including equation and substitution with units.] to the (direction) 18. On your force diagram, draw a vector labelled a to represent the direction of the acceleration. 9

10 Assignment #4: Summary - Comparing Equilibrium Equilibrium Non-Equilibrium Definition Net Force (F NET ) Force Diagram Example(s) Acceleration Distance vs. Time Graph Velocity vs. Time Graph Acceleration vs. Time Graph 10

11 Assignment #5: Careful Reading! Directions: Read the following questions in Columns A and B. CIRCLE/Highlight the difference between the two questions. Then, answer each question. COLUMN A 1.) A book has a weight of 30 Newton s on the surface of Earth. What is the book s weight, if the book is moved to the moon, where the acceleration due to gravity is 1.6 m/s 2? COLUMN B 1.) A book has a weight of 30 Newton s on the surface of Earth. What is the book s mass, if the book is moved to the moon, where the acceleration due to gravity is 1.6 m/s 2? 2.) A 4 kg mass is dropped from a height of 30 meters on Earth s surface. What is its acceleration due to gravity? 2.) A 4 kg mass is dropped from a height of 30 meters on Earth s surface. What is its force due to gravity? 3.) A 10 kg box is accelerated upwards by an elevator at a rate of 3 m/s 2. What is the net force on the box? 3.) A 10 kg box is accelerated upwards by an elevator at a rate of 3 m/s 2. What force is applied to the box from the floor of the elevator? 4.) An 80 Newton applied force accelerates a mass of 5 kg with a rate of 10 m/s 2. Determine the net force acting on the mass. 4.) An 80 Newton applied force accelerates a mass of 5 kg with a rate of 10 m/s 2. Determine the frictional force acting on the mass. 11

12 Review Questions 1.) Which of the following has the greatest inertia? (a) 10 kg object (b) 15 kg object (c) 20 kg object (d) 25 kg object [d] 2.) Which of the following has the greatest inertia? (a) a 3 kg object moving at 2 m/s (b) a 0.5 kg object moving at 200 m/s (c) an 8 kg object moving at 0.1 m/s (d) a 10 kg object moving at 6 m/s [d] 3.) Which of the following statements MUST apply to an object with no net force acting on it? (1) The object must be accelerating. (2) The object must not be accelerating. (3) The object may be accelerating. (4) The object may be moving with a constant speed. (5) The object must be moving with a constant speed. (6) The object must be motionless. (7) The object cannot be motionless. (8) The object may be motionless. [2, 5, 8] 4.) A 20 newton net force acts on a 5.0 kilogram object. What rate of acceleration will this object experience? [4.0 m/s 2 ] 5.) An object of mass M experiences a net force F causing it to accelerate at rate A. At what rate would an object of mass M/2 accelerate if pushed with net force F? (a) 2A (b) A (c) A/2 (d) A/4 [a] 6.) What is the weight of a 5.0 kilogram object when it is near the surface of the Earth? [49.05 N] 7.) The acceleration due to gravity on Planet X is 6.0 N/kg. What is the weight of a 4.0 kilogram object on Planet X? 8.) A 2.5 kilogram object is transported from Earth to the Moon. When the object arrives on the Moon its weight is compared to that on Earth while its mass is compared to that on Earth. [less, the same] [24 N] 9.) Sketch a graph to show the relationship between mass and weight on the axes below. What does the slope of this graph represent? [accel due to gravity] weight mass 12

13 Assignment #6: Drawing Force Diagrams 1.) 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. 2.) A 65 kg skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver. a.) Determine the net force acting on the skydiver b.) Identify the magnitude of all of the forces acting on the skydiver. c.) Create a scaled force diagram. Scale Used: 3.) A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak. 13

14 4.) A 100 N force is applied to the right to drag a 15 kg sled across loosely-packed snow with a rightward acceleration of 5 m/s 2. Diagram the forces acting upon the sled. a.) Determine the net force acting on the sled b.) Identify the magnitude of all of the forces acting on the sled. c.) Create a scaled force diagram. Scale Used: 5.) A student is standing in an elevator that is accelerating downward. The force that the student exerts on the floor of the elevator must be (1) less than the weight of the student when at rest (2) greater than the weight of the student when at rest (3) less than the force of the floor on the student (4) greater than the force of the floor on the student 6.) A person is standing on a bathroom scale in an elevator car. If the scale reads a value greater than the weight of the person at rest, the elevator car could be moving (1) downward at constant speed (2) upward at constant speed (3) downward at increasing speed (4) upward at increasing speed 14

15 Assignment #7: REVIEW & NEW - Force as a Vector Information: Right Triangles (from p. 5 of your Reference Tables!) 1.) Given the following triangle, answer the following questions. Side A 38 o Side B 52.3 Angle X a) What is the value of Side A? b) Calculate the length of Side B. c) Find angle X. 15

16 Information: Resolving Vectors When a vector is at an angle, we may need to break the vector up into its horizontal and vertical parts. These horizontal and vertical parts are called the components of the vector. Finding the components is called resolution. Let s start resolving vectors! Given this vector: Draw a rectangle, making sure all angles are 90 o The sides of the rectangle form the x (horizontal) and y (vertical) components! Critical Thinking Questions: 2.) Resolve the following vector into its horizontal and vertical components by drawing a rectangle as done in the previous information section: Label the horizontal component x and the vertical component y. 3.) Resolve the following vectors into their components. Using trigonometry, determine the force and specify the direction of each component. a) 65 N at 30 o north of east b) 45 N, 20 o west of north 16

17 Base your answers to questions 1 and 2 based on the diagrams below. A B C 5.0 kg 60. N 5.0 kg 60. N 15 o 5.0 kg 60. N 30 o 1.) Calculate the rightward acceleration for each of the 5.0-kilogram blocks. [Neglect friction.] [Show all work, including equation and substitution with units.] A B C 2.) What is the relationship between increased angle above the horizontal, horizontal net force, and resulting acceleration? 3.) A 2 kg box is being pulled horizontally across a level surface with a constant velocity by a 5 N force that makes a 30 angle with the horizontal. a.) Determine the net force acting on the sled (both horizontal and vertical net force) b.) Identify the magnitude of all of the horizontal and vertical forces acting on the sled 17 Continued on next page

18 Continued from previous page c.) Create a scaled force diagram. Scale Used: Regents Questions: 4.) Two forces act concurrently on an object. Their resultant force has the smallest magnitude when the angle between the forces is (1) 0 (2) 30 (3) 90 (4) ) As the angle between two concurrent forces decreases, the magnitude of the force required to produce equilibrium (1) decreases (2) increases (3) remains the same Base your answers to questions 6 and 7 on the information and diagram below. A child pulls a wagon at a constant velocity along a level sidewalk. The child does this by applying a 22-newton force to the wagon handle, which is inclined at 35 to the sidewalk as shown below. 6.) Calculate the magnitude of the component of the 22.-newton force that is parallel to the horizontal surface. [Show all work, including the equation and substitution with units.] [2] 7.) Determine the magnitude of the frictional force acting on the sled. [1] 18

19 Assignment #8: Friction Problems Show ALL work and be sure to include units! Information: Every substance has a different coefficient of friction. The coefficient of friction is a constant that depends on the surface properties of the substance. Because of its rough surface sand paper has a much larger coefficient of friction than ice the frictional force is stronger when something slides on sand paper than on ice. The following equation relates the force friction (F f ), the normal force (F N ), and the coefficient of friction (µ): F f = µf N 1) Define friction. What are the factors that influence the force of friction between 2 objects? 2) Define coefficient of friction. What are the factors that influence the coefficient of friction between 2 objects? 3) What is the coefficient of static friction between 2 wood surfaces? What is the coefficient of kinetic friction between rubber and dry concrete? What is the combination of surfaces with the lowest μ on the Ref Tables? 4) A 2.3 kg book is setting on a flat table. Calculate the frictional force between the book and the table if the coefficient of friction is (Hint: first calculate the normal force, then use the equation above.) 5) Unbeknownst to the students, every time the school floors are waxed, Mrs. Long likes to slide down the hallway in her socks. Mrs. Long weighs 500 N and the coefficient of kinetic friction between her socks and the floor is What is the force of friction that opposes Mrs. Long s motion down the hall? 19

20 6) Lola is pushing a 2 Kg copper pot across her stainless steel counter. How hard must Lola push to move the pot with a constant speed? 7.) In the diagram below, a force pulls a crate across a surface with a constant velocity. 15 kg v = 20m/s (constant) a.) What is the weight of the crate shown above? b.) What is the normal force acting on the crate? c.) If the force pulling the crate is 50 Newtons, what is the force of friction? d.) What is the coefficient of friction (kinetic) between the crate and the surface? 20

21 Assignment #9: Regents Exam Problems (Pretest) 1.) A 2.00-kilogram object weighs 19.6 newtons on Earth. If the acceleration due to gravity on Mars is 3.71 meters per second 2, what is the object s mass on Mars? (1) 2.64 kg (2) 19.6 N (3) 2.00 kg (4) 7.42 N 2.) A force of 1 newton is equivalent to 1 3.) A 6.0-newton force and an 8.0-newton force act concurrently on a point. As the angle between these forces increases from 0 to 90, the magnitude of their resultant (1) decreases (2) increases (3) remains the same 4.) Which object has the greatest inertia? (1) a 5.0-kg object moving at a speed of 5.0 m/s (2) a 10.-kg object moving at a speed of 3.0 m/s (3) a 15-kg object moving at a speed of 1.0 m/s (4) a 20.-kg object at rest 5.) What is the magnitude of the force needed to keep a 60.-newton rubber block moving across level, dry asphalt in a straight line at a constant speed of 2.0 meters per second? (1) 40. N (3) 60. N (2) 51 N (4) 120 N 6.) A cart travels with a constant (nonzero) acceleration along a straight line. Which graph best represents the relationship between the distance the cart travels and time of travel? 7.) Which body is in equilibrium? (1) a satellite moving around Earth in a circular orbit (2) a cart rolling down a frictionless incline (3) an apple falling freely toward the surface of Earth (4) a block sliding at constant velocity across a tabletop 21

22 8.) The diagram below shows a 4.0-kilogram object accelerating at 10. meters per second 2 on a rough horizontal surface. What is the magnitude of the frictional force F f acting on the object? (1) 5.0 N (2) 20. N (3) 10. N (4) 40. N 9.) Which graph best represents the motion of an object in equilibrium? 10.) A 4.0-kilogram object is accelerated at 3.0 meters per second 2 north by an unbalanced force. The same unbalanced force acting on a 2.0-kilogram object will accelerate this object toward the north at (1) 12 m/s 2 (2) 6.0 m/s 2 (3) 3.0 m/s 2 (4) 1.5 m/s 2 11.) What is the weight of a 2.00-kilogram object on the surface of Earth? (1) 4.91 N (2) 2.00 N (3) 9.81 N (4) 19.6 N 12.) A container of rocks with a mass of 65.0 kilograms is brought back from the Moon s surface where the acceleration due to gravity is 1.62 meters per second 2. What is the weight of the container of rocks on Earth s surface? (1) 638 N (2) 394 N (3) 105 N (4) 65.0 N 13.) A person weighing 785 newtons on the surface of Earth would weigh 298 newtons on the surface of Mars. What is the magnitude of the gravitational field strength on the surface of Mars? (1) 2.63 N/kg (2) 3.72 N/kg (3) 6.09 N/kg (4) 9.81 N/kg 22

23 14.) A 40.-kilogram mass is moving across a horizontal surface at 5.0 meters per second. What is the magnitude of the net force required to bring the mass to a stop in 8.0 seconds? (1) 1.0 N (2) 5.0 N (3) 25 N (4) 40. N 15.) A bicycle and its rider have a combined mass of 80. kilograms and a speed of 6.0 meters per second. What is the magnitude of the average force needed to bring the bicycle and its rider to a stop in 4.0 seconds? (1) N (2) N (3) N (4) N 16.) A 110-kilogram bodybuilder and his 55-kilogram friend run up identical flights of stairs. The bodybuilder reaches the top in 4.0 seconds while his friend takes 2.0 seconds. Compared to the power developed by the bodybuilder while running up the stairs, the power developed by his friend is (1) the same (3) half as much (2) twice as much (4) four times as much 17.) How much work is required to lift a 10.-newton weight from 4.0 meters to 40. meters above the surface of Earth? (1) 2.5 J (2) 3.6 J (3) J (4) J 18.) A person is standing on a bathroom scale in an elevator car. If the scale reads a value greater than the weight of the person at rest, the elevator car could be moving (1) downward at constant speed (3) downward at increasing speed (2) upward at constant speed (4) upward at increasing speed 19.) A 40.-kilogram mass is moving across a horizontal surface at 5.0 meters per second. What is the magnitude of the net force required to bring the mass to a stop in 8.0 seconds? (1) 1.0 N (2) 5.0 N (3) 25 N (4) 40. N 20.) Which situation will produce the greatest change of momentum for a 1.0-kilogram cart? (1) accelerating it from rest to 3.0 m/s (3) applying a net force of 5.0 N for 2.0 s (2) accelerating it from 2.0 m/s to 4.0 m/s (4) applying a net force of 10.0 N for 0.5 s Base your answers to questions 21 and 22 on the diagram, which shows a 1.0-newton metal disk resting on an index card that is balanced on top of a glass. 21.) What is the net force acting on the disk? (1) 1.0 N (2) 2.0 N (3) 0 N (4) 9.8 N 22.) When the index card is quickly pulled away from the glass in a horizontal direction, the disk falls straight down into the glass. This action is a result of the disk s (1) inertia (2) charge (3) shape (4) temperature 23

24 23-24.) A 0.50-kilogram frog is at rest on the bank surrounding a pond of water. As the frog leaps from the bank, the magnitude of the acceleration of the frog is 3.0 meters per second 2. Calculate the magnitude of the net force exerted on the frog as it leaps. [Show all work, including the equation and substitution with units.] [2] 25.) A 1500-kilogram car accelerates at 5.0 meters per second 2 on a level, dry, asphalt road. Determine the magnitude of the net horizontal force acting on the car. [1] Base your answers to questions 26 through 32 on the information below. A manufacturer s advertisement claims that their 1,250-kilogram (12,300-newton) sports car can accelerate on a level road from 0 to 60.0 miles per hour (0 to 26.8 meters per second) in 3.75 seconds. 26.) Determine the acceleration, in meters per second 2, of the car according to the advertisement. [1] ) Calculate the net force required to give the car the acceleration claimed in the advertisement. [Show all work, including the equation and substitution with units.] [2] N m/s 29.) What is the normal force exerted by the road on the car? [1] ) The coefficient of friction between the car s tires and the road is Calculate the maximum force of friction between the car s tires and the road. [Show all work, including the equation and substitution with units.] [2] N 32.) Using the values for the forces you have calculated, explain whether or not the manufacturer s claim for the car s acceleration is possible. [1] 24

25 Base your answers to questions 33 and 34 on the information and diagram below. A soccer ball is kicked from point P i at an angle above a horizontal field. The ball follows an ideal path before landing on the field at point P f. 33.) On the diagram above, draw an arrow to represent the direction of the net force on the ball when it is at position X. Label the arrow F net. [Neglect friction.] [1] 34.) On the diagram above, draw an arrow to represent the direction of the acceleration of the ball at position Y. Label the arrow a. [Neglect friction.] [1] Base your answers to questions 35 through 68 on the information below. The driver of a car made an emergency stop on a straight horizontal road. The wheels locked and the car skidded to a stop. The marks made by the rubber tires on the dry asphalt are 16 meters long, and the car s mass is 1200 kilograms. 35.) Determine the weight of the car. [1] ) Calculate the magnitude of the frictional force the road applied to the car in stopping it. [Show all work, including the equation and substitution with units.] [2] N ) Calculate the work done by the frictional force in stopping the car. [Show all work, including the equation and substitution with units.] [2] ) Assuming that energy is conserved, calculate the speed of the car before the brakes were applied. [Show all work, including the equation and substitution with units.] [2] 25

26 Base your answers to questions 42 through 47 on the information below. An ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice, causing the block to accelerate uniformly at 1.4 meters per second 2 to the right. After the skater stops pushing the block, it slides onto a region of ice that is covered with a thin layer of sand. The coefficient of kinetic friction between the block and the sand-covered ice is ) Calculate the magnitude of the force applied to the block by the skater. [Show all work, including the equation and substitution with units.] [2] 44.) On the diagram below, starting at point A, draw a vector to represent the force applied to the block by the skater. Begin the vector at point A and use a scale of 1.0 centimeter = 5.0 newtons. [1] 45.) Determine the magnitude of the normal force acting on the block. [1] ) Calculate the magnitude of the force of friction acting on the block as it slides over the sandcovered ice. [Show all work, including the equation and substitution with units.] [2] N 26

27 ENRICHMENT: Force Diagrams and More For each of the problems below, you must begin your solution with a force diagram. Some require more than one diagram. 1. A 4600 kg helicopter accelerates upward at 2.0 m/s 2. What lift force is exerted by the air on the propellers? 2. The maximum force that a grocery bag can withstand without ripping is 250 N. Suppose that the bag is filled with 20. kg of groceries and lifted with an acceleration of 5.0 m/s 2. Do the groceries stay in the bag? 3. A student, standing on a scale in an elevator at rest, sees that his weight is 840 N. As the elevator rises, his weight increases to 1050 N, then returns to normal. When the elevator slows to a stop at the 10th floor, his weight drops to 588 N, then returns to normal. Determine the acceleration at the beginning and end of the trip. 4. A sign in an elevator states that the maximum occupancy is 20 persons. Suppose that the safety engineers assume the mass of the average rider is 75 kg. The elevator itself has a mass of 500 kg. The cable supporting the elevator can tolerate a maximum force of 30, 000 N. What is the greatest acceleration that the elevator's motor can produce without snapping the cable? 27

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