# Concept of Force Challenge Problem Solutions

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Concept of Force Challenge Problem Solutions Problem 1: Force Applied to Two Blocks Two blocks sitting on a frictionless table are pushed from the left by a horizontal force F, as shown below. a) Draw a free-body diagram for each of the blocks. b) What is the acceleration of the blocks? c) Express, in terms of the quantities given in the figure, the magnitude of the contact force between the two blocks. Briefly explain why your make sense. Suppose now a force of equal magnitude but opposite direction is applied to the block on the right. d) What is the acceleration of the blocks? e) What is the magnitude of the contact force between the two blocks in this case? Briefly explain why your make sense. Problem 1 Solutions: a) Take the positive direction to be to the right in the figure below. There is a contact force C of magnitude C C on each block; this force is directed to the left on block 1 and to the right on block 2. There is no friction; the vertical normal forces (between the table and the blocks) cancel the weights, and so vertical forces will be neglected. b) From Newton s Third Law, the acceleration of the block on the left is given by

2 and the acceleration of the block on the right is given by m a 1 = F C (1.1) 1 m a 2 = C. (1.2) 2 Note that the sign assigned to C is different for the different blocks. Adding Equations (1.1) and (1.2), and setting a 1 = a 2 = a (the blocks move together) yields (m 1 + m 2 )a = F F (1.3) a =. m 1 + m 2 It should not be surprising that when the blocks move together, the common acceleration is that of a single object of mass m 1 + m 2 subject to a single force of magnitude F. c) Substituting the result given in (1.3) into either of Equations (1.2) or (1.1) yields, after minor algebra, m C = F 2. (1.4) m + m 1 2 Note that if m 2 m 1, C / F 0 ; relatively little force is needed to accelerate the much smaller block. In the limit m 1 m 2, C F ; the presence of the small block does not affect the acceleration of the large block. d) The free body force diagrams onm each block for this case are shown below. Equations (1.1) and (1.2) become m 1 a 1 = F C m 2 a 2 = C F. (1.5) Adding these expressions and using a 1 = a 2 = a again yields a = 0 immediately; as expected, if there is no net force on the system, there is no acceleration.

3 e) Using a 1 = a 2 = a = 0 in either expression in Equation (1.5) gives C = F ; neither block accelerates, so there must be zero net force on each block.

4 Problem 2: Forces Responsible for Acceleration of Car When a car accelerates forward on a level roadway, which force is responsible for this acceleration? State clearly which body exerts this force, and on which body (or bodies) the force acts. Problem 2 Solution: The friction force of the road acting on the drive wheels accelerates the car forward. These days, virtually all cars are front-wheel drive, so the road acting on the front wheels causes the acceleration.

6 Problem 4: Hooke s Law Consider a spring with negligible mass that has an unstretched length l 0 = 8.8 "10 2 m. A body with mass m 1 = 1.5 "10 1 kg is suspended from one end of the spring. The other end (the upper end) of the spring is fixed. After a series of oscillations has died down, the new stretched length of the spring is l = 9.8 "10 2 m. Assume that the spring satisfies Hooke s Law when stretched. What is the spring constant? Problem 4 Solution: There are two forces acting on the body: the gravitational force between the body and the earth, F b. e = m1 g kˆ, and the force between the body and the spring, F b,s = F b,s kˆ. The interaction between the body and the spring stretches the spring a distance (l l 0 ) from its equilibrium length. By Hooke s Law the magnitude of this force is F b,s = k( l l 0 ). The force acting on the spring is thus F ˆ b,s = k( l l 0 ) k. The force diagram for the spring is shown below. Since the spring is in static equilibrium, the sum of the forces is zero, F = F + F = m g kˆ + k( l l ) kˆ = 0. (4.1) b,total b,e b,s 1 0 We can solve this equation for the spring constant,

7 1 2 m1 g (1.5"10 kg)(9.8 m # s ) k = = 2 2 l l "10 m 8.8 "10 m =147 N # m 1. (4.2)

8 Problem 5: Force Hooke s Law A body of mass m is suspended from a spring with spring constant k in configuration (a) and the spring is stretched 0.1m. If two identical bodies of mass m / 2 are suspended from a spring with the same spring constant k in configuration (b), how much will the spring stretch? Explain your answer. Problem 5 Solution: In part (a), assume that the spring is directly connected to the body. There are two forces acting on the body: the gravitational force between the body and the earth, F b.e = mg kˆ, and the force between the body and the spring, F b.s = F b.s kˆ. (The spring is actually connected to the rope, but since the rope is massless, the tension in the rope is uniform and the spring force transmits through the rope so the tension in the rope is equal to the magnitude of the spring force). The interaction between the body and the spring stretches the spring a distance x from its equilibrium length. By Hooke s Law the magnitude of this force is F b,s = k x and so the force acting on the spring is F b,s = k x kˆ. The force diagram on the body is shown below Theses two forces on the body balance since the body is in equilibrium, and so F T = F + F = mg kˆ + k x kˆ = 0 (5.1) b b.e b.s Therefore the spring stretches a distance

9 x = mg / k. (5.2) In configuration (b), the forces acting on the body are the gravitational force between the body and the earth, and the force between the rope and the body. The force diagram is shown in the figure below. Since the body is in static equilibrium, T F = F + F = (mg / 2 )kˆ + F kˆ = 0. (5.3) b b.e b.r b,r Therefore the magnitudes of the force of the rope (tension in the rope) and the gravitational force on the body are equal; mg / 2 = F b,r. (5.4) Suppose the spring stretches by an amount x 1. Just as in part (a), the tension in the rope is uniform, so the tension in the rope is equal to the magnitude of the spring force. Combining Equations (5.4) and (5.5) yields F = k x. (5.5) b.r 1 k x 1 = (m / 2) g. (5.6) Thus the spring stretches by half the amount as in part (a), as given by Equation (5.2), x 1 = (m / 2) g / k = x / 2. (5.7)

10 Problem 6: Equivalent Spring Constants Find the effective spring constants for the two systems shown in figures (a) and (b). The block has mass m and the two springs having spring constants k 1 and k 2 respectively, The spring with spring constant k 1 is attached to the ceiling and one end of the spring with spring constant k 2, and the other end of the second spring is attached to the block (the springs are attached in series). a) Each spring is attached to the ceiling and the block (the springs are attached in parallel). Problem 6 Solution: a) Each spring is stretched by a (possibly) different extension. Let x 1 represent the extension of the upper spring and x 2 represent the extension of the lower spring. The total extension for both springs is x = x + x. (6.1) total 1 2 The magnitude of the spring force is the same in each spring; that is, the spring force can be considered as being transmitted uniformly through the two springs. The two springs can be considered as a single spring. The spring force is for a massless spring is then F = k x = k x (6.2) Note that this last equation implies that x 1 = F / k 1 and x 2 = F / k 2. Since the total extensions add, Equation (6.1) becomes

11 F F xtotal = x 1 + x 2 = +. (6.3) k 1 k 2 The equivalent spring is under the same tension (same spring force), F = k"x total, where k is the equivalent spring constant when the two springs are replaced by one. The total displacement is therefore F x total =. (6.4) k" Substitute Equation (6.4) for the total displacement into Equation (6.3), yielding F F F. (6.5) = + k k 1 k 2 The magnitude F of the common force cancels from Equation (6.5), and the equivalent spring constant k is given by (6.6) = + k k 1 k 2 The spring constants for springs connected in series add inversely. b) When springs are connected in parallel (side by side), each spring adds to the total force that an equivalent spring would apply, F = F + F. (6.7) total 1 2 Since both springs stretch the same amount x, spring 1 exerts a force F 1 = k 1 x and spring 2 exerts a force F 2 = k 2 x. Therefore the total force in Equation (6.7) becomes F total = k 1 x + k 2 x = (k 1 + k 2 )x. (6.8) The equivalent spring (by definition) would be held under the same spring force F stretched the same amount x, so the equivalent spring constant is found from total and F = k"x. (6.9) total

12 Substituting Equation (6.9) into Equation (6.8) yields k"x = k 1 "x + k 2 "x. (6.10) Therefore the equivalent spring constant for two springs connected in parallel adds; k = k 1 + k 2. (6.11)

13 Problem 7: Pulling a Rope Attached to Two Trees Suppose a rope is tied rather tightly between two trees that are 30 m apart. You grab the middle of the rope and pull on it perpendicular to the line between the trees with as much force as you can. Assume this force is 1000 N (about 225 lb ), and the point where you are pulling on the rope is h = 1m from the line joining the trees. a) What is the magnitude of the force tending to pull the trees together? b) Give an example of a situation where you think this may be of practical use. Problem 7 Solutions: a) The various forces involved are shown in Figure 2. The î -direction is to the right in the figure, and the ĵ -direction is down in the figure, in the direction of the applied force F. Note that the figure is not to scale ( L / h 30 ). The equations for force equilibrium, at the point where the force is applied, are: î :T cos "T cos = 0 ĵ: 2T sin " F = 0. (7.1) From the second equation in (7.1), T = F /(2sin ). With, L = 30m and h = 1m, tan = h / (L / 2 )= 1/15 # = tan "1 (1/15 )= 3.81 # sin = (7.2) Note that the small angle approximation sin tan = h /( L / 2) is certainly valid in this situation. The tension in the rope is then given by F T = = (1000 N)"15/ 2 = 7500 N. (7.3) 2sin

14 b) If the applied force is vertically downward, you re walking a tightrope, and the trees should be big enough to hold up to roughly 7-8 times your weight. If the applied force is horizontal, maybe one of the trees will come down, and you might have firewood without having to resort to a chainsaw. If one end of the rope is attached to a large enough tree and the other to a car in a ditch, you can apply several times the pulling force to try to move the car.

15 Problem 8: Climbing a Rope A person clings to a rope (assumed massless) that passes over a pulley. The person is balanced by a block of mass m hanging at the other end of the rope. Initially both the person and block are motionless. The person then starts climbing the rope by pulling on it with a constant force in order to reach the block. The person moves a distance L relative to the rope. Does the block move as a result of the person s climbing? If so, in which direction and by how much? Problem 8 Solution:

16 y=0 T T y 1 ĵ y 2 T T m b g BLOCK m p g PERSON The force diagrams are shown in the above figure. As the person pulls up on the rope, there is a force down on the rope, creating a tension in the rope. This tension is transmitted through the rope, and so is also the force on the object. Both the person and block satisfy Newton s Second Law, m g T = ma y ; (8.1) the person and the block accelerate upwards with the same acceleration. The length of the rope between the person and the block is l = y 1 + R + y 2, (8.2) where R is the radius of the pulley. As the person climbs, y 1 and y 2 change by the same (negative) amount. So, if a length of rope L passes through the person s hands, both the person and the object rise a distance L / 2.

### LECTURE 12 FRICTION, STRINGS & SPRINGS. Instructor: Kazumi Tolich

LECTURE 12 FRICTION, STRINGS & SPRINGS Instructor: Kazumi Tolich Lecture 12 2! Reading chapter 6-1 to 6-4! Friction " Static friction " Kinetic friction! Strings! Pulleys! Springs Origin of friction 3!!

### Chapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc.

Chapter 5 Newton s Laws of Motion Force and Mass Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The Vector Nature of Forces: Forces in Two Dimensions

### Equilibrium & Elasticity

PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block

### Exam 3 Practice Solutions

Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

### Dynamics; Newton s Laws of Motion

Dynamics; Newton s Laws of Motion Force A force is any kind of push or pull on an object. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The magnitude

### Newton s 3 Laws of Motion

Newton s 3 Laws of Motion 1. If F = 0 No change in motion 2. = ma Change in motion Fnet 3. F = F 1 on 2 2 on 1 Newton s First Law (Law of Inertia) An object will remain at rest or in a constant state of

### 5. Forces and Free-Body Diagrams

5. Forces and Free-Body Diagrams A) Overview We will begin by introducing the bulk of the new forces we will use in this course. We will start with the weight of an object, the gravitational force near

### HATZIC SECONDARY SCHOOL

HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT VECTOR DYNAMICS MULTIPLE CHOICE / 45 OPEN ENDED / 75 TOTAL / 120 NAME: 1. Unless acted on by an external net force, an object will stay at rest

### Concept Question: Normal Force

Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical

### 4.2. The Normal Force, Apparent Weight and Hooke s Law

4.2. The Normal Force, Apparent Weight and Hooke s Law Weight The weight of an object on the Earth s surface is the gravitational force exerted on it by the Earth. When you weigh yourself, the scale gives

### Lecture 6 Force and Motion. Identifying Forces Free-body Diagram Newton s Second Law

Lecture 6 Force and Motion Identifying Forces Free-body Diagram Newton s Second Law We are now moving on from the study of motion to studying what causes motion. Forces are what cause motion. Forces are

### THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES

THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES Today s Objectives: Students will be able to: 1. Calculate the work of a force. 2. Apply the principle of work and energy to

### 66 Chapter 6: FORCE AND MOTION II

Chapter 6: FORCE AND MOTION II 1 A brick slides on a horizontal surface Which of the following will increase the magnitude of the frictional force on it? A Putting a second brick on top B Decreasing the

### AP Physics 1 Review. On the axes below draw the horizontal force acting on this object as a function of time.

P Physics Review. Shown is the velocity versus time graph for an object that is moving in one dimension under the (perhaps intermittent) action of a single horizontal force. Velocity, m/s Time, s On the

### Version PREVIEW Semester 1 Review Slade (22222) 1

Version PREVIEW Semester 1 Review Slade () 1 This print-out should have 48 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A

### Chapter 4: Newton s Second Law F = m a. F = m a (4.2)

Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.

### (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

1. A solid metal ball and a hollow plastic ball of the same external radius are released from rest in a large vacuum chamber. When each has fallen 1m, they both have the same (A) inertia (B) speed (C)

### Isaac Newton. What is a force? Newton s Three Laws of Motion. What is the acceleration of the car?

Aim: What did Isaac Newton teach us about motion? Do Now: 1. A 2009 Ford Mustang convertible is travelling at constant velocity on Interstate 95 south from Philadelphia to Wilmington Delaware. It passes

### Newton s Laws and Free-Body Diagrams General Physics I

Newton s Laws and Free-Body Diagrams In the next few sections, we will be exploring some of the most fundamental laws of our universe, laws that govern the relationship actions and motion. These laws are

### 1. A 7.0-kg bowling ball experiences a net force of 5.0 N. What will be its acceleration? a. 35 m/s 2 c. 5.0 m/s 2 b. 7.0 m/s 2 d. 0.

Newton's Laws 1. A 7.0-kg bowling ball experiences a net force of 5.0 N. What will be its acceleration? a. 35 m/s 2 c. 5.0 m/s 2 b. 7.0 m/s 2 d. 0.71 m/s 2 2. An astronaut applies a force of 500 N to an

### Chapter 5: Applications of Newton's laws Tuesday, September 17, :00 PM. General strategy for using Newton's second law to solve problems:

Ch5 Page 1 Chapter 5: Applications of Newton's laws Tuesday, September 17, 2013 10:00 PM General strategy for using Newton's second law to solve problems: 1. Draw a diagram; select a coördinate system

### 4) Vector = and vector = What is vector = +? A) B) C) D) E)

1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In

### Use the following to answer question 1:

Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to

### PHY218 SPRING 2016 Review for Exam#2: Week 9 Review: Newton s Laws, Work, Energy, and Power

Review: Newton s Laws, Work, Energy, and Power These are selected problems that you are to solve independently or in a team of 2-3 in order to better prepare for your Exam#2 1 Problem 1: Inclined Plane

### Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.

Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?

### Review 3: Forces. 1. Which graph best represents the motion of an object in equilibrium? A) B) C) D)

1. Which graph best represents the motion of an object in equilibrium? A) B) C) D) 2. A rock is thrown straight up into the air. At the highest point of the rock's path, the magnitude of the net force

### s_3x03 Page 1 Physics Samples

Physics Samples KE, PE, Springs 1. A 1.0-kilogram rubber ball traveling east at 4.0 meters per second hits a wall and bounces back toward the west at 2.0 meters per second. Compared to the kinetic energy

### Unforced Mechanical Vibrations

Unforced Mechanical Vibrations Today we begin to consider applications of second order ordinary differential equations. 1. Spring-Mass Systems 2. Unforced Systems: Damped Motion 1 Spring-Mass Systems We

### Physics 18 Spring 2011 Homework 3 Wednesday February 2, 2011

Physics 18 Spring 2011 Homework 3 Wednesday February 2, 2011 Make sure your name is on your homework, and please box your final answer. Because we will be giving partial credit, be sure to attempt all

### Lecture 6. > Forces. > Newton's Laws. > Normal Force, Weight. (Source: Serway; Giancoli) Villacorta-DLSUM-BIOPHY1-L Term01

Lecture 6 > Forces > Newton's Laws > Normal Force, Weight (Source: Serway; Giancoli) 1 Dynamics > Knowing the initial conditions of moving objects can predict the future motion of the said objects. > In

### July 19 - Work and Energy 1. Name Date Partners

July 19 - Work and Energy 1 Name Date Partners WORK AND ENERGY Energy is the only life and is from the Body; and Reason is the bound or outward circumference of energy. Energy is eternal delight. William

### W = 750 m. PHYS 101 SP17 Exam 1 BASE (A) PHYS 101 Exams. The next two questions pertain to the situation described below.

PHYS 101 Exams PHYS 101 SP17 Exa BASE (A) The next two questions pertain to the situation described below. A boat is crossing a river with a speed to the water. The river is flowing at a speed W = 750

### 2.1 Forces and Free-Body Diagrams

2.1 Forces and Free-Body Diagrams A is a push or a pull. Forces act on objects, and can result in the acceleration, compression, stretching, or twisting of objects. Forces can also act to stabilize an

### P8.14. m 1 > m 2. m 1 gh = 1 ( 2 m 1 + m 2 )v 2 + m 2 gh. 2( m 1. v = m 1 + m 2. 2 m 2v 2 Δh determined from. m 2 g Δh = 1 2 m 2v 2.

. Two objects are connected by a light string passing over a light frictionless pulley as in Figure P8.3. The object of mass m is released from rest at height h. Using the principle of conservation of

### Topic 4 Forces. 1. Jan 92 / M1 - Qu 8:

Topic 4 Forces 1. Jan 92 / M1 - Qu 8: A particle of mass m lies on a smooth plane inclined at α. It is held in equilibrium by a string which makes an angle θ with the plane. The tension in the string is

### Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities

Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities 1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the

### Recall: Gravitational Potential Energy

Welcome back to Physics 15 Today s agenda: Work Power Physics 15 Spring 017 Lecture 10-1 1 Recall: Gravitational Potential Energy For an object of mass m near the surface of the earth: U g = mgh h is height

### dt 2 x = r cos(θ) y = r sin(θ) r = x 2 + y 2 tan(θ) = y x A circle = πr 2

v = v i + at a dv dt = d2 x dt 2 A sphere = 4πr 2 x = x i + v i t + 1 2 at2 x = r cos(θ) V sphere = 4 3 πr3 v 2 = v 2 i + 2a x F = ma R = v2 sin(2θ) g y = r sin(θ) r = x 2 + y 2 tan(θ) = y x a c = v2 r

### WORK & ENERGY. Work W = Fdcosα 1. A force of 25.0 Newtons is applied so as to move a 5.0 kg mass a distance of 20.0 meters. How much work was done?

PHYSICS HOMEWORK #41 Work W = Fdcosα 1. A force of 25.0 Newtons is applied so as to move a 5.0 kg mass a distance of 20.0 meters. How much work was done? 2. A force of 120 N is applied to the front of

### LAB 4: FORCE AND MOTION

Lab 4 - Force & Motion 37 Name Date Partners LAB 4: FORCE AND MOTION A vulgar Mechanik can practice what he has been taught or seen done, but if he is in an error he knows not how to find it out and correct

### LECTURE 12 FRICTION & SPRINGS. Instructor: Kazumi Tolich

LECTURE 12 FRICTION & SPRINGS Instructor: Kazumi Tolich Lecture 12 2 Reading chapter 6-1 to 6-2 Friction n Static friction n Kinetic friction Springs Origin of friction 3 The origin of friction is electromagnetic

### 1301W.600 Lecture 18. November 15, 2017

1301W.600 Lecture 18 November 15, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:30-8:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program

### Inertia and Mass. 7. Mass and velocity values for a variety of objects are listed below. Rank the objects from smallest to greatest inertia.

Inertia and Mass Read from Lesson 1 of the Newton's Laws chapter at The Physics Classroom: http://www.physicsclassroom.com/class/newtlaws/u2l1a.html http://www.physicsclassroom.com/class/newtlaws/u2l1b.html

### Investigating Springs (Simple Harmonic Motion)

Investigating Springs (Simple Harmonic Motion) INTRODUCTION The purpose of this lab is to study the well-known force exerted by a spring The force, as given by Hooke s Law, is a function of the amount

### Problem-Solving Strategies

Connexions module: m42076 1 Problem-Solving Strategies OpenStax College This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License Abstract Understand and

### Physics 202 Homework 1

Physics 202 Homework Apr 3, 203. A person who weighs 670 newtons steps onto a spring scale in the bathroom, (a) 85 kn/m (b) 290 newtons and the spring compresses by 0.79 cm. (a) What is the spring constant?

### LECTURE 9 FRICTION & SPRINGS. Instructor: Kazumi Tolich

LECTURE 9 FRICTION & SPRINGS Instructor: Kazumi Tolich Lecture 9 2 Reading chapter 6-1 to 6-2 Friction n Static friction n Kinetic friction Springs Static friction 3 Static friction is the frictional force

### HATZIC SECONDARY SCHOOL

HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT CIRCULAR MOTION MULTIPLE CHOICE / 30 OPEN ENDED / 65 TOTAL / 95 NAME: 1. An object travels along a path at constant speed. There is a constant

### 1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant

1982B1. The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity

### ΣF = 0 and Στ = 0 In 2-d: ΣF X = 0 and ΣF Y = 0 Goal: Write expression for Στ and ΣF

Thur Sept 24 Assign 5 Friday Exam Mon Oct 5 Morton 235 7:15-9:15 PM Email if conflict Today: Rotation and Torques Static Equilibrium Sign convention for torques: (-) CW torque (+) CCW torque Equilibrium

### 5. The graph represents the net force acting on an object as a function of time. During which time interval is the velocity of the object constant?

1. A 0.50-kilogram cart is rolling at a speed of 0.40 meter per second. If the speed of the cart is doubled, the inertia of the cart is A) halved B) doubled C) quadrupled D) unchanged 2. A force of 25

### Fall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton

Fall 007 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton -3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.

### Lecture Presentation Chapter 14 Oscillations

Lecture Presentation Chapter 14 Oscillations Suggested Videos for Chapter 14 Prelecture Videos Describing Simple Harmonic Motion Details of SHM Damping and Resonance Class Videos Oscillations Basic Oscillation

### AP Physics Problems Simple Harmonic Motion, Mechanical Waves and Sound

AP Physics Problems Simple Harmonic Motion, Mechanical Waves and Sound 1. 1977-5 (Mechanical Waves/Sound) Two loudspeakers, S 1 and S 2 a distance d apart as shown in the diagram below left, vibrate in

### 5. REASONING AND SOLUTION An object will not necessarily accelerate when two or more forces are applied to the object simultaneously.

5. REASONING AND SOLUTION An object will not necessarily accelerate when two or more forces are applied to the object simultaneously. The applied forces may cancel so the net force is zero; in such a case,

### Recognizing Forces: Does the floor know when you put on weight?

Teacher Guide for BLOSSOMS Lesson: Recognizing Forces: Does the floor know when you put on weight? Based on Energizing Physics Lesson 3.04: What forces are acting on you? Overview Lesson Type: Interactive

### Practice Honors Physics Test: Newtons Laws

Name: Class: Date: Practice Honors Physics Test: Newtons Laws Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Acceleration is defined as the CHANGE in

### Energy Problem Solving Techniques.

1 Energy Problem Solving Techniques www.njctl.org 2 Table of Contents Introduction Gravitational Potential Energy Problem Solving GPE, KE and EPE Problem Solving Conservation of Energy Problem Solving

### This module requires you to read a textbook such as Fowles and Cassiday on material relevant to the following topics.

Module M2 Lagrangian Mechanics and Oscillations Prerequisite: Module C1 This module requires you to read a textbook such as Fowles and Cassiday on material relevant to the following topics. Topics: Hamilton

### Announcements. Equilibrium of a Particle in 2-D

nnouncements Equilibrium of a Particle in 2-D Today s Objectives Draw a free body diagram (FBD) pply equations of equilibrium to solve a 2-D problem Class ctivities pplications What, why, and how of a

### Distance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is:

Chapter 1 Kinematics 1.1 Basic ideas r(t) is the position of a particle; r = r is the distance to the origin. If r = x i + y j + z k = (x, y, z), then r = r = x 2 + y 2 + z 2. v(t) is the velocity; v =

### Forces and Newton s Second Law

Forces and Newton s Second Law Goals and Introduction Newton s laws of motion describe several possible effects of forces acting upon objects. In particular, Newton s second law of motion says that when

### Physics 351, Spring 2015, Homework #5. Due at start of class, Friday, February 20, 2015 Course info is at positron.hep.upenn.

Physics 351, Spring 2015, Homework #5. Due at start of class, Friday, February 20, 2015 Course info is at positron.hep.upenn.edu/p351 When you finish this homework, remember to visit the feedback page

### t = g = 10 m/s 2 = 2 s T = 2π g

Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the

### DISPLACEMENT AND FORCE IN TWO DIMENSIONS

DISPLACEMENT AND FORCE IN TWO DIMENSIONS Vocabulary Review Write the term that correctly completes the statement. Use each term once. coefficient of kinetic friction equilibrant static friction coefficient

### Name Period. What force did your partner s exert on yours? Write your answer in the blank below:

Nae Period Lesson 7: Newton s Third Law and Passive Forces 7.1 Experient: Newton s 3 rd Law Forces of Interaction (a) Tea up with a partner to hook two spring scales together to perfor the next experient:

### the spring is compressed and x is the compression

Lecture 4 Spring problem and conservation of mechanical energy Hooke's Law The restoring force exerted by the spring is directly proportional to its displacement. The restoring force acts in a direction

### Static Equilibrium and Torque

10.3 Static Equilibrium and Torque SECTION OUTCOMES Use vector analysis in two dimensions for systems involving static equilibrium and torques. Apply static torques to structures such as seesaws and bridges.

### Work. 98N We must exert a force of 98N to raise the object. 98N 15m 1470Nm. One Newton- meter is called a Joule and the

ork Suppose an object is moving in one dimension either horizontally or vertically. Suppose a Force which is constant in magnitude and in the same direction as the object's motion acts on that object.

### The Spring: Hooke s Law and Oscillations

Experiment 7 The Spring: Hooke s Law and Oscillations 7.1 Objectives Investigate how a spring behaves when it is stretched under the influence of an external force. To verify that this behavior is accurately

### Chapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc.

Chapter 5 Newton s Laws of Motion Copyright 2010 Pearson Education, Inc. Force and Mass Copyright 2010 Pearson Education, Inc. Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion

### Exam Review and Friction

Exam Review and Friction Announcements: Exam Thursday at 7:30pm Bring a #2 pencil Will be long answer questions in addition to multiple choice Room assignments will be on web page (Exam info) Calculators

### 1 of 6 10/21/2009 6:33 PM

1 of 6 10/21/2009 6:33 PM Chapter 10 Homework Due: 9:00am on Thursday, October 22, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment

### Name Period Date A) B) C) D)

Example Problems 9.2 E1. A car rounds a curve of constant radius at a constant speed. Which diagram best represents the directions of both the car s velocity and acceleration? Explain: A) B) C) D) E2.

### Lecture 18: Work and Energy. Today s Agenda

Lecture 18: Work and Energy Work and Energy Definition of work Examples Today s Agenda Definition of Mechanical Energy Conservation of Mechanical Energy Conservative forces Physics 201: Lecture 10, Pg

### Isaac Newton. What is the acceleration of the car? "If I have seen further it is by standing on the shoulders of giants" Isaac Newton to Robert Hooke

Aim: What did Isaac Newton teach us about motion? Do Now: 1. A 2009 Ford Mustang convertible is travelling at constant velocity on Interstate 95 south from Philadelphia to Wilmington Delaware. It passes

### Second Semester Review

Second Semester Review Name Section 4.2 1. Define energy What is energy? Explain if it is scalar or vector in nature. 2. Explain what factors affect the speed of a rollercoaster. Whether a rollercoaster

### Circular Motion & Gravitation FR Practice Problems

1) A mass m is attached to a length L of string and hung straight strainght down from a pivot. Small vibrations at the pivot set the mass into circular motion, with the string making an angle θ with the

### Equation of Motion. Start with the definition of force (rate of change of momentum) and use what we know about momentum.

Notes Syllabus update: If you are >10 min late to a discussion section, you will not be counted as participating in the discussion. Results in 50% loss in the next group quiz score. Quiz 2: Next Friday,

### AP physics B - Webreview ch 13 Waves

Name: Class: _ Date: _ AP physics B - Webreview ch 13 Waves Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A large spring requires a force of 150 N to

### Exam. Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You want to swim straight across a river that is 76 m wide. You find that you can do

### AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is

### P211 Spring 2004 Form A

1. A 2 kg block A traveling with a speed of 5 m/s as shown collides with a stationary 4 kg block B. After the collision, A is observed to travel at right angles with respect to the initial direction with

### Upthrust and Archimedes Principle

1 Upthrust and Archimedes Principle Objects immersed in fluids, experience a force which tends to push them towards the surface of the liquid. This force is called upthrust and it depends on the density

### Physics 111. Lecture 10 (Walker: 5.5-6) Free Body Diagram Solving 2-D Force Problems Weight & Gravity. February 18, Quiz Monday - Chaps.

Phsics 111 Lecture 10 (Walker: 5.5-6) Free Bod Diagram Solving -D Force Problems Weight & Gravit Februar 18, 009 Quiz Monda - Chaps. 4 & 5 Lecture 10 1/6 Third Law Review A small car is pushing a larger

### 7. Two forces are applied to a 2.0-kilogram block on a frictionless horizontal surface, as shown in the diagram below.

1. Which statement about the movement of an object with zero acceleration is true? The object must be at rest. The object must be slowing down. The object may be speeding up. The object may be in motion.

### QUESTION TWO: BUNGY JUMPING. Acceleration due to gravity = 9.81 m s 2

6 QUESTION TWO: BUNGY JUMPING Acceleration due to gravity = 9.81 m s Standing on a platform that is 5.0 m above a river, Emma, of height.00 m and mass m, is tied to one end of an elastic rope (the bungy)

### Applying Newton s Second Law. 8.01T Sept 22, 2004

Applying Newton s Second Law 8.01T Sept 22, 2004 Reference Frame Coordinate system with an observer placed at origin is a reference frame in which the position, velocity, and acceleration of objects are

### 5. Two forces are applied to a 2.0-kilogram block on a frictionless horizontal surface, as shown in the diagram below.

1. The greatest increase in the inertia of an object would be produced by increasing the A) mass of the object from 1.0 kg to 2.0 kg B) net force applied to the object from 1.0 N to 2.0 N C) time that

### Physics 40 Chapter 7 Homework Solutions

Phsics 40 Chapter 7 Homework Solutions T = F 3 g (1) T sin θ + T sin θ = Fg () 1 1 T cosθ = T cosθ (3) 1 1 Eliminate T and solve for T 1 Fgcos θ T = = T 1 3 g ( sin θ cosθ + cosθ sin θ ) sin ( θ + θ )

### Forces and Motion. Holt Book Chapter 4

Forces and Motion Holt Book Chapter 4 Forces: A Video Introduction Misconceptions about Falling Bodies http://www.youtube.com/watch?v=_mcc-68lyzm What is the Magnus Force? (advanced) http://www.youtube.com/watch?v=23f1jvguwjs

### The Spring: Hooke s Law and Oscillations

Experiment 9 The Spring: Hooke s Law and Oscillations 9.1 Objectives Investigate how a spring behaves when it is stretched under the influence of an external force. To verify that this behavior is accurately

### Chapters 10 & 11: Energy

Chapters 10 & 11: Energy Power: Sources of Energy Tidal Power SF Bay Tidal Power Project Main Ideas (Encyclopedia of Physics) Energy is an abstract quantity that an object is said to possess. It is not

### EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS

Today s Objectives: Students will be able to: EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS a) Identify support reactions, and, b) Draw a free-body diagram. In-Class Activities: Check Homework Reading

### Physics 211 Week 10. Statics: Walking the Plank (Solution)

Statics: Walking the Plank (Solution) A uniform horizontal beam 8 m long is attached by a frictionless pivot to a wall. A cable making an angle of 37 o, attached to the beam 5 m from the pivot point, supports

### A force is could described by its magnitude and by the direction in which it acts.

8.2.a Forces Students know a force has both direction and magnitude. P13 A force is could described by its magnitude and by the direction in which it acts. 1. Which of the following could describe the

### Forces and Motion Forces Gravity Net Forces Free Body Diagrams

Forces and Motion Forces Gravity Net Forces Free Body Diagrams Misc. 200 200 200 200 200 400 400 400 400 400 600 600 600 600 600 800 800 800 800 800 1000 1000 1000 1000 1000 FINAL JEOPARDY Go To Score