Name: Unit 4 Newton s 1 st & 3 rd Law

Transcription

1 Name: Period: Table #: Unit 4 Newton s 1 st & 3 rd Law 1

2 UNIT IV: Reading - Force Diagrams The analysis of a problem in dynamics usually involves the selection and analysis of the relevant forces acting on some object under consideration. An important first step in this analysis process is to carefully select the object of interest that will be the focus of our analysis. This analysis process can often times be greatly simplified by utilizing a technique of constructing force diagrams to assists you in selecting the relevant forces and appropriately representing these forces with vector notations. These are the forces we will be considering: Ff Force of Friction (always opposite direction of motion) Fg Force of Gravity (always straight down) also called WEIGHT Fa Force applied to the object by a person or object Ft Force of tension from a string or rope F N Normal Force (always perpendicular to the surface it s touching) Consider the analysis of forces acting on a log as a tractor pulls it at a constant speed. (Figure 2 below) The analysis proceeds as follows: 1. Sketch the object and its surroundings. 2. Represent the object as a point at the center of coordinate axes with one axis parallel to the direction of motion. 3. Represent all relevant forces (across the system boundary) by a vector labeled with an appropriate symbol. Ex. 1: As an illustration of this process, consider the forces acting on a log being pulled by a tractor follows: Step 1 Sketch a diagram of the system and its surroundings as illustrated in Figure 2: Figure 2 2

3 Step 2 Since the shape of the object is unimportant, shrink it to a point. Place it at the intersection of a set of coordinate axes with one of the axes parallel to the direction of motion as shown in figure 4. f f Step 3 Proceed around the system boundary line and identify all points at which there is contact between the object (log) and its surroundings. Construct qualitative vectors (indicate directions and relative magnitudes) to represent these forces. Figure 4 The contact forces would be kinetic friction, F k (parallel to the supporting surface), the normal force, F N (the component of force that is perpendicular to the supporting surface), and the tension force of the rope, F T. The long range force(s), in this case would be only the force of gravity, F g. See Figure 4 at left. Now, it should be easy to determine the net force on the object. To do this, consider the force in each direction (x or y) separately. That is, x-axis F T and F f y-axis F g and F N In this case, the two forces in the x-direction are equal, but opposite, so they sum to zero. Also note that the two forces in the y-direction sum to zero. Therefore, you can conclude that this object will not accelerate in either direction. That leaves two possibilities: it is either motionless, or it is moving at constant velocity. Equation in the -direction F T = F f Equation in the Y-direction F N = F g 3

4 UNIT IV: Worksheet 1 In each of the following situations, sketch a qualitative position vs. time, velocity vs. time & acceleration vs. time graph. Also state whether or not this is a situation where forces are balanced or unbalanced. 1. Object lies motionless. 2. Object slides at constant speed without friction. V V A A Forces are: 3. Object slows due to Friction. Forces are: 4. Object slides down an incline without friction. V V A A Forces are: Forces are: 4

5 5. Friction prevents sliding. 6. An object is suspended from the ceiling. V V A A Forces are: 7. The object is pulled by a force parallel to the surface with NO friction. Forces are: 8. The object is pulled upward at constant speed. V V A A Forces are: Forces are: 5

6 9. The object is falling (no air resistance). 10. The object is falling at constant (terminal) velocity. V V A A Forces are: Forces are: 6

7 UNIT IV: Worksheet 2 In each of the following situations, represent the object with a particle. Sketch all the forces acting upon the object, making the length of each vector represent the magnitude of the force. 1. Object lies motionless. 2. Object slides at constant speed without friction. 3. Object slows due to kinetic friction. 4. Object slides without friction. 5. Static friction 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. 7

8 11. The object is pulled by a force parallel to the surface. 12. The object is pulled by a force at an angle to the surface. 13. The object is pulled upward at constant speed. 14. The object is pushed by a force applied downward at an angle 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. (the ball is in flight) 18. The ball is at the top of a parabolic trajectory. (the ball is in flight) 8

9 Force-Mass Pre-Lab Questions Purpose of the experiment: To determine what the relationship is between force and mass. 1) List possible independent variables that you think might affect the period of the pendulum (form hypothesizes). List as many as you can think of. 2) For each independent variable listed in #1, describe how you can change and/or measure that variable. 3) Can you now eliminate any of the variables in #1 which would not be possible to test due to equipment/lab limitations? 4) For each independent variable listed in #1, describe which factors would need to be kept constant? 5) What equipment will be needed to conduct this experiment? 9

10 Force-Mass Lab Procedure: To graphically and mathematically determine the relationship between mass and force on an object. Using a spring scale with hanger (measured force in N) use 5 assorted masses (Kg) to collect 5 sets of data points. Continue to increase the mass for each trial. Measure the corresponding force with the spring scale. **For trial #1, your mass should be 0 kg (NO mass on the spring scale) Record all data collected! Table of Mass (kg) and Force (N) Trial # Mass ( Kg) Force (N) *Graph your data in Graphical Analysis. Remember to put the independent variable on the -axis! 10

11 Post Lab Questions 1. What was the independent variable and how did you change it? 2. What was the dependent variable and how did you measure it? 3. What was the mathematical equation from your graph? 4. What is the meaning of the slope in the above question (Look at the units of your slope and unit meanings below to help you. Don t say it s direct, that does not answer the question)? 5. What is the meaning of the y-int. in the above question (don t say it s where the line crosses the y- axis, that does not answer the question) 6. What is the general equation from #3 (substitute your answers of #4 and #5 into your mathematical equation) 7. Write 1 sentence relating the two variables (can only use direct if it was a straight line on the first graph). Explain what direct, inverse, or exponential means in your sentence. Unit meanings. m = displacement m/s = velocity m/s/s = acceleration m/s 2 = acceleration Kg = mass kg m/s 2 = Force Newton = Force N m = Joule= Energy N/kg = gravitational field constant N/m = spring constant 11

12 Worksheet 3 Directions: Use your knowledge of trigonometry to calculate the length of the unknown side. 1. SOH CAH TOA a 2 + b 2 = c o o o 12

13 UNIT IV: Worksheet 4 1. Determine the x and y components of the forces shown. 2. If the bricks weigh 25 N, what is the tension in the cable? 2a) Repeat if the angle is

14 In each of the following situations, draw a force diagram and calculate the requested value. Make sure to show all your work. 3. Calculate the tension in the horizontal part of the cable T 40 T =30.5 N 2 kg 4. Calculate the Frictional Force of the block that is being pulled at a constant velocity. The block is being pulled with a force of 40 N at an angle of 35 degrees. 5. Calculate the tension in the string if the box is being pulled at a constant velocity AND calculate the normal force. The weight of the box is 30 N. The frictional force is 10 N and the angle of the applied force is 30 degrees. (hint: the normal force is NOT 30 N) 14

15 UNIT IV: Worksheet 5 For each of the problems below, carefully draw a force diagram of the system before attempting to solve the problem. 1. Determine the tension in each cable in case A and case B. Case A Case B 5 kg 5 kg 2. Determine tension in each cable. 7 kg 4 kg 3. The object hung from the cable has a weight of 40 N. Write the equation for the sum of the forces in the y-direction. What is the tension in the cable which makes a 40 degree angle? Repeat the problem above with a 10 angle. How doe s the tension compare? 15

16 4. The cable at left exerts a 30 N force. 30 ο T 2 a. Write the equation for the sum of the forces in the x-direction. What is the value of T 2? T 1 b. 1)Write the equation for the sum of the forces in the y-direction. 2)What is the force of gravity acting on the ball? 5. The box (mass = 4 kg) is being pulled at a constant velocity. The box is pulled with a force of 50 N at an angle of 30 degrees. Calculate the frictional force. B) Calculate the value of the normal force? 16

17 6. A man pulls a 50 kg box at constant speed across the floor. He applies a 200 N force at an angle of 30. a. Sum the forces in the x-direction. What is the value of the frictional force opposing the motion? b. Sum the forces in the y-direction. What is the value of the normal force? 7. A man pushes a 2.0 kg broom at constant speed across the floor. The broom handle makes a 50 angle with the floor. He pushes the broom with a 5.0 N force. a. Sum the forces in the y-direction. What is the value of the normal force? b. Sum of the forces in the x-direction. What is the value of the frictional force opposing the motion? c. If the frictional force were suddenly reduced to zero, what would happen to the broom? 17

18 UNIT IV: Worksheet 6 1. Calculate the tension in the diagonal part of the cable AND the angle. T= 5 N? T =? 1 kg 2. The block of mass 2 kg is pushed at a constant velocity. The force applied is 40 N and is at an angle of 45 degrees. Determine the frictional force AND the normal force N 40N 3. Calculate the tension in the string if the box is being pulled at a constant velocity AND calculate the normal force. The mass of the box is 4 kg. The frictional force is 10 N and the angle of the applied force is 30 degrees. 18

19 4. You place a watermelon on a spring scale at the supermarket. If the mass of the watermelon is 4 kg, what is the reading on the scale (calculate the weight) (the scale measures in Newtons)? 5. A block has a mass of 1.2 kg and the sphere has a mass of 3 kg. What are the readings on the two scales? scale 1.2kg scale 3kg 19

20 20

21 21

22 Unit 4 Worksheet 7: Reading Questions From your reading on Newton s 3 rd Law, answer the following questions 1. In the interaction between a hammer and the nail it hits, Is a force exerted on the nail? Is a force exerted on the hammer? How many forces occur in this interaction? 2. When a hammer exerts a force on a nail, how does the amount of force compare with that on the nail on the hammer? 3. When you walk along a floor, what pushes you along? 4. When swimming, you push the water backward call this action. What is the reaction force? 5. If the action is a bowstring acting on an arrow, identify the reaction force? 6. When you jump up, the world really does recoil downward. Why can t this motion of the world be noticed? 7. When a rifle is fired... How does the size of the force on the rifle on the bullet compare with the force of the bullet on the rifle? How does the acceleration of the rifle compare with that of the bullet? 8. A bug gets splattered on the windshield of your car Who got hit with a larger force (bug or car)? Who underwent a larger acceleration (bug or car)? 22

23 UNIT IV: Review Sheet For questions 1 & 2, it is possible to have MORE THAN ONE correct answer. 1. A hockey puck is resting on frictionless ice. It is given a brief push. A moment later (after the push), which of the following forces act on the block? a. the force of the push b. a normal force c. friction d. the force of gravity 2. Which of the following describes the motion of the hockey puck in the previous problem? a. The block moves at constant speed b. The block slows down gradually to a stop. c. The block continues at constant speed for a while, then slows down d. The block accelerates constantly. 3. A student attaches a string to the block on a table, and pulls steadily on the block. The block moves with a constant velocity. Draw a Force Diagram on the forces acting on the block. 4. Describe the motion of the block on the table. 5. In each of the following situations, sketch all the forces acting upon the object, making the length of each vector represent the magnitude of the force. A. Static friction prevents sliding. B. Object slides at constant speed without friction. D. Object slows due to kinetic friction. C. Object slides without friction. 23

24 E. The object is pulled upward at constant speed. F. The ball is rising in a parabolic trajectory. G. An object is suspended from the ceiling. H. The object is falling at constant (terminal) velocity. I. The object is pulled by a force parallel to the surface with no friction. J. The object is pulled by a force at an angle to the surface at a constant speed. Problems 6. If the mass of the object in letter H above was 10 kg, what is the force of Air Resistance acting on the block? 7. If the mass of the object in letter A above is 5 kg and the angle of the incline is 30 what is the force of friction and the normal force acting on the block? 8. A horse exerts a 250 N force on a heavy wagon, causing it to accelerate. What force does the wagon exert on the horse? 24

25 9. If the tension in T 2 is 100 N. answer the following questions. a. Write the equation for the sum of the forces in the x-direction. 30 ο T 2 b. What is the value of T 1? T 1 c. Write the equation for the sum of the forces in the y direction? d. What is the force of gravity acting on the ball and what is its mass? 10.A person pulls on a 75 kg desk with a 300-N force acting at 60 angle above the horizontal. The desk does not budge. Draw a force diagram for the desk. a. Write the equation that describes the forces which act in the x-direction. b. Write the equation which describes the forces which act in the y-direction. c. Determine the x and y components of the force of tension. d. Determine the value of the frictional force. Do the same for the normal force. 11. Ben Dover is pulling 30 N on a crate causing it to accelerate. What force does the crate pull on Ben? Does your answer change if it s going at a constant velocity or not at all? Explain? 25

26 Calculation Answers for Unit 4 Packet Since you have the answers to these questions, your teacher will be looking for the work as to how you got to the answers to receive credit. Be sure to ALWAYS show ALL of your work for ANY calculations!! Worksheet 3 Worksheet 4 1. = 6N Y = 10.4 N = 14.1 N Y = 5.1 N N, N N N N, 24.2 N Worksheet 5 1. Case A: 49 N Case B: 24.5 N N, N N, N 4A. 60 N 4B. 52 N 5A N 5B N 6A N 6B. 390 N 7A N 7B. 3.2 N Worksheet N 2. Ff=28.3N FN = 47.9 N N, 33.4 N N N, 29.4 N 9B. 50 N 9D N, 8.8 kg 10C N, 150 N 10D. 150 N, 475 N 11. Forces are equal Review Sheet 26