# UNIT 2D. Laws of Motion

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1 Name: Regents Physics Date: Mr. Morgante UNIT 2D Laws of Motion

2 Laws of Motion Science of Describing Motion is Kinematics. Dynamics- the study of forces that act on bodies in motion. First Law of Motion (Inertial Mass) An object remains at rest or moves with uniform velocity unless it is acted upon by an unbalanced force. [Hard to prove this on earth because of all the forces such as gravity, friction, etc. Closest thing is an airhockey table. Ex. This law holds true in space.] This 1 st Law is also called the Law of Inertia. Examples: Ball on incline with and without Friction; Executive Desktoy Friction and Inertia Ground This does not obey 1 st Law. Why? Block moves but eventually slows down due to FRICTION (unbalanced force) Friction- The force that opposes the motion of one surface over another. Ex: on Earth? Friction Ex. 1. m=5 Kg Does the forces balance? Check it! a=3.0 m/s 2 F=20N [On Earth] Newton s 2 nd Law is F= ma F= 5kg x 3m/s 2 = 15N What is the missing force? Draw F.B.D. to find out that you are losing 5N to Friction in order for the forces to balance out! 2

3 F Net is equal to the NET force after you are done adding all the vectors in all directions. (If the net force =0 the it is at equilibrium, if not it is an unbalanced force) F f = Force of Friction a 15N=(F f ) 10 Kg 50N=(Fapplied) A) Find unbalanced force B) Find acceleration of object using F Net = ma A) F Net = Fapplied - F f = 50N 15N = 35N B) a = F Net / m = 35N/10kg = 3.5 m/s 2 Coefficient of Kinetic Friction μ K = Coeff. of Kinetic Friction [Applies to objects on Earth] F f (Friction Force) is directly proportional to F N (Normal Force) of an object. F N (Normal Force) is the force that results from the surface that the object is in contact with (a.k.a. Contact Force) Equation is F f = μ K * F N mu greek mew phonetics F N = m g = Fw F N Fw Example F f =5N m=5kg Direction of Sliding 3

4 a) What is μ K? b) Set up the FBD on your own F f = μ K * F N Where F f = 5N; F N = F w = mg = 5kg *9.8 m/s 2 = 49 N Note F N = F w here because F w creates the contact force on the surface Note there are NO UNITS FOR μ K!!!!!!!! (Newtons/Newtons = 1) Typical Block FBD F N F f F pull or F applied F W Again, where F N = Normal Force; F f = Friction Force; F pull = force pulling or applied; F w = Force due to weight. Above are the forces that occur on a block or other object that is on a HORIZONTAL SURFACE that has a force pulling it in the horizontal direction. Simplified Free Body Diagram (FBD) of the Diagram above F N F f F pull F w This is an FBD in its fundamental form. FBD s are intended to only show forces and the angles between them. What is a Newton? 1 Newton (N) is equal to the force that a 1 kilogram (kg) mass exerts. You should be able to develop the relationship with units to satisfy this statement based on F Net =ma. Acceleration and Freefall Every falling body experiences acceleration (g) which is equal to 9.81 m/s 2 on the earth. What force does a 10 kg mass fall with? The weight of the object is the force that it falls with! F=ma or W=mg in this case since we are talking about gravity as acceleration and is denoted as g. 4

5 Remember, sign convention is important here. _ + + What about your mass? We can find mass of an object using F Net =ma. X-direction - Y-direction From F Net =ma we can rearrange it to show F Net /a=m. If we know force and acceleration, we can get the mass. Gravitational mass is the mass with respect to gravity (g=9.81 m/s 2 ) Inertial mass is the mass with respect to acceleration applied to move an object. mass a F Newton s 2 nd Law of Motion F Net /a = m (m is constant, your mass doesn t change anywhere in the universe!!) What if we apply the same force to different masses? The acceleration of that object will change, but the mass will stay the same!! Newton s 2 nd Law When an unbalanced force acts upon a body, it accelerates the body in the direction of the force. The acceleration produced is directly proportional to the force applied. Newton s 3 rd Law of Motion For every action or force, there is an equal and opposite reaction or force. This statement is the basis for equating the normal force to the weight of an object that is on a horizontal surface. F N These are both Equal & opposite Forces! Fw We will use Newton s 3 rd Law extensively in the Inclined Planes Unit and other Mechanics units. 5

6 NAME Regents Physics Friction Notesheet Define: 1. Friction: Date Mr. Morgante 2. Normal force: 3. Coefficient of friction: 4. Static friction: 5. Kinetic friction: Equation Variables/constants Units Can be used to find F f = μf N Algebra review Using F f = μf N ; solve for μ solve for F N Approximate Coefficients of Friction Kinetic Static Rubber on concrete (dry) Rubber on asphalt(dry) Wood on wood Free-body diagrams Label diagrams with F g,f N,F f, mass Case 1 Case 2 Case 3 Object on frictionless surface Wood on wood; Wood on wood; Object at rest incline; constant velocity F F Acceleration = Acceleration = Acceleration = Case 4 Wood on wood; object moving at constant velocity Acceleration = (OVER) 6

7 Graphs Friction vs. Normal Force graph Magnitude of friction as applied force graph Applied Force Normal force Applications Rubber car tire on dry asphalt Label diagrams with F g,f N,F f, mass Rubber car tire on wet asphalt Label diagrams with F g,f N,F f, mass Velocity Velocity Rolling friction and Fluid friction 1. Rolling friction: 2. Fluid friction: 3. How would fluid friction affect free-fall situations? Summary: F f = 1.Theoretically, should frictional force depend on surface area? 2. Theoretically, should frictional force depend on the speed of motion? 3. Theoretically, the frictional force should depend on : & 7

8 Name Regents Physics Notesheet: Forces Vocabulary- Define the Following Date Mr. Morgante 1. Dynamics: 2. Force: 3. Resultant: 4. Equilibrant: 5. Newton s 1st Law of Motion: 6. inertia: 7. mass: 8. weight: 9. kilogram: 10.Newton's 2nd Law of Motion: 11. Statics: 12. Newton(unit) 13. Newton s Third Law of Motion: 14. Net Force: 15. Contact Force: 16. Normal Force: 17. Static equilibrium: 18. Concurrent forces: 19. Equilibrium: 8

9 20.Free-body diagram: Regents Physics Reference Table Review: Use your Mechanics section to outline all equations that have an F term. Equation Variables Units Can be used to find: 9

10 Name: Date: Regents Physics Mr. Morgante Newton s Laws of Motion Practice Show all work to solve the problems below. Remember to use the correct units. Use the following formula and values: F = Force m = mass, a = acceleration dues to the Earth s gravity = 9.8 m/s/s Level I 1. What force is needed to give a mass at 50 kg an acceleration of 10 m/s/s? 2. A force of 12 N acts upon a 3 kg mass. What is the acceleration of the mass? 3. It takes a force of 25 N to give a body an acceleration of 5 m/s/s. What is the mass of the body? 4. What is the weight C on Earth of a 100 kg piece of lead? 5. What is the mass of an object that weighs 980N on Earth? 10

11 Name: Regents Physics Date Mr. Morgante Newton s Laws of Motion Practice 2 Level II 1. A 10 kg rocket fired horizontally encounters a force of air resistance of 8.0 N. The force supplied by the rocket s engine is 70.5 N. a) What is the net force accelerating the rocket? b) Calculate the acceleration of the rocket. 2. Find the gravitational force exerted on a photon at sea level whose mass is 1.7 X kg. 3. An electron is accelerated uniformly from rest to a speed of 4.0 x 10 6 m/s in 2.0 s. a) What is the acceleration of the electron? b) If the mass of the electron is 9.1 X kg what is the force producing this acceleration? (OVER) 11

12 Rocket Scientist Level 4. a) What is the mass of a rocket weighing 196 N? b) What force in excess of the weight of the rocket is needed to accelerate it upward of 4.0 m/s/s. c) What is the total force upward that must be exerted on the rocket to give it this acceleration? 5. a) What force in excess of the weight of a 500 kg rocket is needed to accelerate it upward at a rate equal to that of gravity (9.8m/s/s)? b) What is the total force acting on the rocket? 12

13 Name: Date: Mr. Morgante Regents Physics Worksheet Newton s Laws 1. An object with a mass of 0.5 kilogram starts from rest and achieves a maximum speed of 20 meters per second in 0.01 seconds. What average unbalanced force accelerates this object? (1 ) 1,000 N (2 ) 10 N (3 ) 0.1 N (4 ) N 2. A force of 50. newtons causes an object to accelerate at 10. meters per second squared. What is the mass of the object? (1 ) 500 kg (2 ) 60. kg (3 ) 5.0 kg (4 ) 0.20 kg 3. What is the essential characteristic of an object at equilibrium. (1 ) Zero velocity (2 ) zero acceleration (3 ) zero potential energy (4 ) zero kinetic energy 4. Each diagram below shows a different block being pushed by a force across a surface at a constant velocity. In which two diagrams is the force of friction the same (Hint look at Reference Tables for )? (1 ) A and B (2 ) B and D (3 ) A and D (4 ) C and D 5. A bird feeder with two birds has a total mass of 2.0 kilograms and is supported by wire as shown in the diagram on the next page. (OVER) The Force in the top wire is approximately (1 ) 10. N (2 ) 14 N (3 ) 20. N (4 ) 39 N 13

14 6. A horizontal force is used to pull a 5.0-kilogram cart at a constant speed of 5.0 meters per second across the floor, as shown in the diagram. If the force of friction between the carts and the floor is 10. newtons, the magnitude of the horizontal force along the handle of the cart is (1 ) 5.0 N (2 ) 10. N (3 ) 25 N (4 ) 50. N 7. A 60 kilogram astronaut weighs 96 newtons on the surface of the moon. The acceleration due to gravity on the moon is (1 ) 0.0 m/s 2 (2 ) 1.6 m/s 2 (3 ) 4.9 m/s 2 (4 ) 9.8 m/s 2 14

15 Name: Regents Physics Questions to ask after reading the problem? FRICTION PROBLEMS Date: Mr. Morgante a) Is there constant speed (rest) or acceleration? b) If there is an unbalanced force what is the acceleration? Balanced force implies constant speed. The force due to friction can be read on the weight scale. Unbalanced force implies acceleration? Note: If the question is vague but asks for the calculation of acceleration then there is an unbalanced force!!!!!! Example A - Constant speed A 1200g block is moved across a table at a constant speed. It is carrying a 350g object. The scale thats pulling the block and the object reads 4.5N. Draw a diagram and use arrows to show the forces on the block. a) What is the weight of the block? The Block and the Mass? b) What is the Normal force? c) What is the force due to friction? d) Calculate the coefficient of friction. e) Suppose your calculation of the coefficient of friction were 1.85? Could this be possible? Sketch the friction/normal force graph for constant speed. Sketch the coefficient of friction /Normal force graph for constant speed. 15

16 Name Date Regents Physics Mr. Morgante Force Vector Toolkit Review Objective: Review the various methods to solve force vector, free-body diagrams Reminders: Vectors should have arrowhead, scale, use colored pencil/pen for resultant Triangle Method of Adding Concurrent Forces Show head to tail method P F 1 F 2 F 1 P F 2 Describe steps in head to tail method: Parallelogram Method of Adding Concurrent Forces Show the steps on the concurrent vectors below: F 1 P F 2 Specific Methods to Add Vectors at Right Angles to each other SOHCAHTOA: R F 2 Pythagorean Theorem: θ F 1 (over) 16

17 Show coordinate systems!!!! 1. Two vectors, 8 N & 10 N are placed concurrently at point P. a)sketch ;solve the MAXIMUM resultant b) Sketch; solve the minimum resultant + + P P 2. What is the resultant of 55N in the +x direction and 75 N in the y direction acting at point X? Reference your resultant direction to the + x axis: + X 3. Can two vectors of magnitude 5N each ever have a Resultant of : a) 7N (show sketch & angles) b) 5N (show sketch & angles) c) 4N (show sketch & angles) d) 0 N (show sketch and angles) e) 12 N (show sketch and angles) 4. What is the equilibrant of 7 N North and 10 N South (show sketch and angles) 5. A vector of 16 N pulls at an angle of 37 to the horizontal. Show x and y comps. 17

18 Name Regents Physics Forces Algebra Review + Practice Date Mr. Morgante 1. If F net = ma, solve for: m =, a = 2. If F net = ma, and a = v / t, F net = m v / t. Solve for: m =, v = t = 3. If F net = ma, and m = mass (kg) and a = acceleration (m/s 2 ), what are the units of Force? 4. A constant unbalanced force is applied to an object for a period of time. Which graph best represents the acceleration of the object as a function of elapsed time? a a a a t t t t (1) (2) (3) (4) Explain your reasoning: 5. What can the graph of F Net versus mass tell you? F Net (N) what type of relationship is shown? What are the units of the slope? Mass (kg) 6. Compare and contrast the equations a = F net / m and g = F g / m Similarities: Differences: (OVER) 18

19 7. Sketch and solve the following: a. Two forces are applied to a 5.0 kg block initially at rest on a frictionless horizontal surface: +y F 1 = 2 N F 2 =10 N +x Calculate the sum of the horizontal forces: Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: Calculate the normal force on the block: b. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface: F 2 = 25 N +y F 1 = 5 N +x θ = 35 Calculate the sum of the horizontal forces: Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: Calculate the normal force on the block: 19

20 Name Regents Physics Force Practice #1 Show all work Solve the following: Date Mr. Morgante 1. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface: F 2 = 50 N +y F 1 = 20 N +x θ = 35 Magnitude Calculate the sum of the horizontal forces: Direction Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: F g F N (OVER) 20

21 2. Scale: 1 cm = 2N. Calculate and draw the vectors and their resultant for the following vectors acting at the origin: +y +x Vector #1 8 N (-y) Vector #2 10 N (+x) What angle does the resultant make with the +x axis? 21

22 Name Regents Physics Newton s 3-Laws Level 2&3 Date Mr. Morgante Show all work Solve the following (Each problem on this page is worth one point): 1. Two forces are applied to a 8.0 kg block initially at rest on a frictionless horizontal surface: +y F 1 = 12 N F 2 =50 N +x Magnitude Calculate the sum of the horizontal forces: Direction Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: Calculate the normal force on the block: 2. Two forces are applied to a 10.0 kg block initially at rest on a frictionless horizontal surface: F 2 = 45 N +y F 1 = 15 N +x θ = 35 Magnitude Calculate the sum of the horizontal forces: Direction Calculate the acceleration of the block: Calculate the weight of the block: Show the F g and F N vectors on the drawing: Calculate the normal force on the block: (OVER) 22

23 3. A horizontal force of 70 N acts on a box of mass 15 kg resting on a smooth, frictionless floor. 70 N +x (2 pts) a) Calculate the weight of the box: a) (2 pts) b) Sketch the Weight vector on the sketch above: (2 pts) c) Calculate the Normal force on the box: c) (2 pts) d) Sketch the Normal force vector on the sketch above: (2pts) e) Calculate the Force in the horizontal direction: e) (2 pts) f) Calculate the acceleration in the horizontal direction: (2 pts) g) what is the horizontal displacement of the box at t = 4.5 secs f) g) (OVER) 23

24 4. 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 30 meters long and the car s mass is 2200 kilograms. Sketch Known values +x (2 pts) a) Calculate the weight of the car: (2 pts) b) Calculate the normal force exerted on the car by the road: a) b) (2 pts) c) Calculate the magnitude of the frictional force the road applied to the car in stopping it. c) (2 pts) d) If the car came to rest in 2.5 seconds, calculate the magnitude and direction of the acceleration the car underwent. (2 pts) e) On the Free-body diagram below, sketch the F g, F N, F f vectors d) +x Z:\Physics\Regents Physics\Class Material\Unit 2D Laws of Motion doc 24

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