Three blocks of masses M 1 =2 kg, M 2 =4 kg, and M 3 =6 kg are connected by strings on a frictionless inclined plane of 60 o, as shown in the figure below.

Slides:

Advertisements

Similar presentations

M 1 and M 2 – Masses of the two objects [kg] G – Universal gravitational constant G = 6.67x N m 2 /kg 2 or G = 3.439x10 -8 ft 4 /(lb s 4 ) r – distance.

Advertisements

Physics 111: Mechanics Lecture 5

1 Chapter Four Newton's Laws. 2  In this chapter we will consider Newton's three laws of motion.  There is one consistent word in these three laws and.

Section 4-7 Solving Problems with Newton’s Laws; Free Body Diagrams

A ladder with length L weighing 400 N rests against a vertical frictionless wall as shown below. The center of gravity of the ladder is at the center of.

Newton’s 2nd Law some examples

Newton’s Laws of Motion. HFinks '072 6/2/2015 Basic Concepts  Force – push or pull on an object - Vector quantity  Mass – amount of matter in a body.

Chapter 5 Force and Motion (I) Kinematics vs Dynamics.

Lecture 4 Monday: 26 January 2004 Newton’s Laws of Motion.

Physics 101: Lecture 9, Pg 1 Physics 101: Application of Newton's Laws l Review of the different types of forces discussed in Chapter 4: Gravitational,

CHAPTER-5 Force and Motion-1.

Chapter 4 The Laws of Motion. Forces Usually think of a force as a push or pull Usually think of a force as a push or pull Vector quantity Vector quantity.

Solving Problems With Newton’s Laws. If object A exerts a force on object B, then object B exerts and equal and opposite force on object A. Examples:

Forces and The Laws of Motion

NEWTON'S LAWS OF MOTION There are three of them.

Dynamics – Ramps and Inclines

Chapter 4 Section 1 Changes in Motion Force.

Newton’s Laws - continued

Chapter 4 Preview Objectives Force Force Diagrams

Simplifying Problems. used to isolate a system of interest and to identify and analyze the external forces that act directly upon it Free-Body Diagrams.

A proton is shot with a velocity v at an angle  to a uniform magnetic field B, which is directed along the x-axis as shown below. Assume that the only.

Chapter 4 Changes in Motion Objectives

Forces Contact Forces - those resulting from physical contact between objects –Normal Force –Friction –Tension (spring/rope) –Compression Action at a Distance.

Free-body Diagrams To help us understand why something moves as it does (or why it remains at rest) it is helpful to draw a free-body diagram. The free-body.

© Houghton Mifflin Harcourt Publishing Company The student is expected to: Chapter 4 Section 1 Changes in Motion TEKS 4E develop and interpret free-body.

Newton’s Laws The Study of Dynamics.

I.Newton’s first law. II.Newton’s second law. III.Particular forces: - Gravitational - Gravitational - Weight - Weight - Normal - Normal - Tension - Tension.

1 4 Newton’s Laws Force, net-force, mass & inertia Newton’s Laws of Motion Weight, Contact Forces Labeling & Diagramming Hk: 37, 49, 53, 57, 59, 61, 65,

Newton’s Laws - continued Friction, Inclined Planes, N.T.L., Law of Gravitation.

Chapter 4 The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.

SECOND LAW OF MOTION If there is a net force acting on an object, the object will have an acceleration and the object’s velocity will change. Newton's.

Newton’s Laws - continued Friction, Inclined Planes, N3L, Law of Gravitation.

University Physics: Mechanics

Two blocks (m 1 =2.5kg, m 2 =1.8kg) are hanging from a pulley as shown in the figure below. The moment of inertia through the axis of rotation passing.

Chapter 4 The Laws of Motion. Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty space No physical.

A series of blocks is connected to a pulley in the manner depicted below. Find the minimum mass that block C must have in order to keep block A from sliding.

Newton 2nd Law problems - Atwood Machines -Incline Planes -Tension Problems -Other Object Connected problems.

Applications & Examples of Newton’s Laws. Forces are VECTORS!! Newton’s 2 nd Law: ∑F = ma ∑F = VECTOR SUM of all forces on mass m  Need VECTOR addition.

Chapter 4 The Laws of Motion. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.

1 Applying Newton’s Laws Assumptions Assumptions Objects behave as particles Objects behave as particles can ignore rotational motion (for now) can ignore.

Forces on Inclined Planes Unit 3, Presentation 3.

Lecture 9 Serway and Jewett : 5.7, 5.8

Resolving Forces Into Vector Components Physics Montwood High School R

Chapter 5 The Laws of Motion.

© Houghton Mifflin Harcourt Publishing Company Preview Objectives Force Force Diagrams Chapter 4 Section 1 Changes in Motion.

Physics 215 – Fall 2014Lecture Welcome back to Physics 215 Today’s agenda: More on free-body diagrams and force components Applying Newton’s laws.

University Physics: Mechanics

1 Chapter 4 The Laws of Motion Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty.

Weight = mass x acceleration due to gravity

“ Friendship is like peeing on yourself; everyone can see it, but only you get the warm feeling it brings.” Funnyquotes.com Course web page

Two blocks (m1 = 5kg, m2 = 2.5kg) are in contact on a frictionless table. A constant horizontal force FA = 3N is applied to the larger block as shown.

Newton’s Third Law If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force.

Inclined Plane Problems. Axes for Inclined Planes X axis is parallel to the inclined plane Y axis is perpendicular to the inclined plane Friction force.

4-8 Applications Involving Friction, Inclines

1 Chapter 5 The Laws of Motion. 2 Force Forces are what cause any change in the velocity of an object A force is that which causes an acceleration The.

Section 5.3 Section 5.3 Force and Motion in Two Dimensions In this section you will: Section ●Determine the force that produces equilibrium when.

Force Problems. A car is traveling at constant velocity with a frictional force of 2000 N acting opposite the motion of the car. The force acting on the.

FRICTION and Newton’s second law. The “Normal” Force, N When an object is pressed against a surface, the surface pushes back. (That’s Newton’s 3 rd Law)

Today: (Ch. 3) Tomorrow: (Ch. 4) Forces and Motion in Two and Three Dimensions Equilibrium and Examples Projectile Motion.

Unit is the NEWTON(N) Is by definition a push or a pull Can exist during physical contact(Tension, Friction, Applied Force) Can exist with NO physical.

Topic 2.2 Extended B – Applications of Newton’s second.

Force and Motion–I Chapter 5. Newton's First and Second Laws A force: o Is a “push or pull” acting on an object o Causes acceleration We will focus on.

Chapter 5 Force and Motion I. Classical Mechanics Describes the relationship between the motion of objects in our everyday world and the forces acting.

Newton’s third law of motion 1 Force 2

Inclined Plane Problems

Phys 270 Newton’s Laws.

Chapter 5 Force and Motion.

Motion on Inclined Planes

Step 1: Get Organized Draw a picture.

Presentation transcript:

Three blocks of masses M 1 =2 kg, M 2 =4 kg, and M 3 =6 kg are connected by strings on a frictionless inclined plane of 60 o, as shown in the figure below. A force of F=120N is applied upward along the incline, causing the system of three masses to accelerate up the incline. Consider the strings to be massless and taut. What is the acceleration of M 2 ? Find the tensions T 1 and T 2 in the two sections of string.

Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question 13 Question 14 Question 15 Paired Problem 1

Notes *For simplicity when analyzing this system, we choose the the x-axis to be parallel to the surface of the incline and the y-axis to be perpendicular to the surface. Let’s define the positive direction as “upward” for both x and y. *Vectors quantities will be in bold type

A : the same as the acceleration of the system as a whole.A B : less than the acceleration of the system as a whole.B C : greater than the acceleration of the system as a whole.C 1.Which one of these statements finishes the following sentence correctly? (there is no acceleration in the y-direction, so “a” refers to the acceleration in the x-direction throughout this tutorial) The acceleration of M 2 is expected to be…

Newton’s Second Law tells us: F=Ma where: M = M 1 +M 2 +M 3 (total mass of the system) F is the net force on the system a is the acceleration of the whole system F = ( M 1 +M 2 +M 3 )a = M 1 a+M 2 a+M 3 a Thus, each block accelerates with the same “a,” which is also the acceleration of the system as a whole. Choice: A Correct

Remember that the strings are all taut, which allows the masses to move together. Choice: B Incorrect

Remember that the strings are all taut, which allows the masses to move together. Choice: C Incorrect

2. Which one of the following free body diagrams is correct for the system of three blocks? Weight (W=Mg) Force of Friction (F f ) Normal Force (F N ) (the length of the arrows does not represent the magnitudes of the forces here) A:A: C:C: D:D: B:B: F MgMg F F F MgMg MgMg MgMg FNFN FNFN FNFN FfFf

It is necessary to include the normal force (F N ). Choice: A Incorrect

This diagram shows all of the forces acting on the system. Choice: B Correct

The gravitational force always acts perpendicular to the ground, not perpendicular to the surface of the plane. Also, there is no friction between the blocks and the inclined plane. Choice: C Incorrect

The gravitational force always acts perpendicular to the ground, not perpendicular to the plane of contact. Choice: D Incorrect

3. A good choice of coordinate axes may be to consider the x-axis parallel to the surface of the inclined plane and the y-axis perpendicular to it. (The positive x and y directions should be upwards.) Which forces are aligned with these axes? A: F N and WA B: F and WB C: F N and FC

F N is in the positive y-direction (always perpendicular to the surface), but W is not along either coordinate axis. Remember that W=Mg, where g is gravitational acceleration, which always points downward (towards Earth). Choice: A Incorrect

F is in the positive x-direction, but W is not along either coordinate axis. Remember that W=Mg, where g is the acceleration due to gravity, which always points downward (towards Earth). Choice: B Incorrect

Choice: C Correct F N is directed in the positive y- direction and F is directed in the positive x-direction.

4. When we resolve the gravitational force into its x and y components, we get which one of the following? (the length of the arrows does not represent the magnitudes of the forces here) A:A: C:C: D:D: B:B: Mgcos(  )Mgsin(  ) Mgcos  )Mgsin(  ) Mgcos(  ) Mgsin(  )Mgcos(  )

Mgcos(  ) should point in the negative y-direction. Choice: A Incorrect

Mgsin(  ) should point in the negative x-direction. Choice: B Incorrect

Here, the components are correctly resolved. Choice: C Correct

Choice: D Incorrect Check the directions of both components.

5. Which one of the following is the correct equation of motion (x-component) for the whole system (using Newton’s Second Law)? Remember M=M 1 +M 2 +M 3 A: F=MaA B: F-Mgsin(  )=0B C: F-Mgsin(  )=MaC

Choice: A Incorrect Don’t forget the effect of gravity

Choice: B Incorrect The original problem statement tells us that the applied force is causing upward acceleration. Therefore, there is a net force; it is not equal to zero.

Choice: C Correct This equation is correct according to Newton’s Second Law. The applied force on the system of blocks is in the opposite direction to the x-component of the weight of the blocks. We know from the original problem statement that the net force is not zero.

6. The acceleration of the system of blocks can be expressed by which of the following equations? A:A B:B C:C

This equation is incorrect because it doesn’t take gravity into consideration. Choice: A Incorrect

This is what we get when we rearrange the equation that we found for force in question 6. Choice: B Correct

This is just the net force on the system. We are looking for the acceleration of the system. Choice: C Incorrect

7. Determine the value of the acceleration a of the blocks up the incline.

Reasoning: Where: F=120N M= M 1 +M 2 +M 3 = 2 kg +4 kg+6 kg= 12 kg g= 9.8 m/s 2

As discussed earlier, the acceleration of M 2 is the same as that of the system as a whole because the blocks move together. Now let’s focus on finding the tensions T 1 and T 2.

8. Which one of these is the free body diagram of M 2 ? (the length of the arrows does not represent the magnitudes of the forces here) A:A: C:C: D:D: B:B: M2gM2g T2T2 T1T1 FNFN M2gM2gT1T1 FNFN F+T 2 FNFN T2T2 M1gM1g M2gM2g T2T2 T1T1 M2gM2g FNFN

F only acts on M 3. Choice: A Incorrect

This diagram shows all of the forces acting upon M 2. Choice: B Correct

The gravitational force on M 1 does not act on M 2. Therefore, it does not belong in the free body diagram for M 2. Include T 1. Choice: C Incorrect

Choice: D Incorrect The force on an object from contact with a string in tension always acts in the direction away from the object. The directions of T 1 and T 2 should be switched.

9. Which of the following is the correct representation of the x-component of Newton’s second law? You must resolve the gravitational force into components. A :A B :B C :C

This expression does not include the gravitational force. Choice: A Incorrect

This expression is consistent with the free body diagram. Choice: B Correct

Gravitational force and tension T 1 should also be considered because they are acting on M 2. Choice: C Incorrect

10. We have two unknowns, T 1 and T 2. We need two equations. We have one equation from the free body diagram of M 2. Get the other one from the free body diagram of M 1. The free body diagram for M 1 is: (the length of the arrows does not represent the magnitudes of the forces here) A:A: C:C: D:D: B:B: T1T1 T1T1 F FNFN FNFN FNFN M1gM1g M1gM1g M1gM1g T1+T2T1+T2 M1gM1g FNFN

All of the forces are shown correctly. Choice: A Correct

T 2 doesn’t act on M 1. Choice: B Incorrect

F only acts on M 3. Choice: C Incorrect

The normal force acts perpendicular to the surface of the plane of contact. Choice: D Incorrect

11. Resolving the gravitational force into its components and applying Newton’s Second Law gives us which of the following as the x- component of the equation of motion for M 1 ? A :A B :B C :C

T 1 is not the net force. Remember the force in Newton’s Second Law is the net force. Gravity acts upon M 1. Choice: A Incorrect

This equation is consistent with the free body diagram for M 1. Choice: B Correct

This would be correct if the angle of inclination were 90 degrees. Choice: C Incorrect

12. Which equation should be solved first? A :A B :B

We start with the other equation because this one contains two unknowns. It is not possible to solve for two unknowns using a single equation. Choice: A Incorrect

This equation should be solved first since only T 1 is unknown. Choice: B Correct

13. After solving for T 1 you will get : If you plug this back into the equation of motion for M 2 ( ) and simplify, you get which of the following expressions for T 2 ? A :A B :B C :C

This expression omits several terms. Check your algebra. Choice: A Incorrect

This expression does not include the contribution of gravity. Choice: B Incorrect

We get this result using simple algebra and factoring out common variables. Choice: C Correct

Now all you have to do is insert the given values and calculate the numerical values of T 1 and T 2.

14) Find the value of T 1 Answer

The correct answer is:

15) Now find T 2. Answer

The correct answer is :

Paired Problem 1) Three blocks of masses M 1 =2 kg, M 2 =4 kg, and M 3 =6 kg are connected by strings on a frictionless inclined plane of 60 o, as shown in the figure below. A force of F=120N is applied upward along the incline, causing the system of three masses to accelerate up the incline. Consider the strings to be massless and taut. What is the acceleration of M 2 ? Find the tensions T 1 and T 2 in the two sections of string.