Chapter 7

Question 1

tell me examples of interaction

and what interaction is ?

Answer 1

In fact, any time an object A pushes or pulls on another object B, B pushes or pulls back on A. When you pull someone with a rope in a tug-of-war, that person pulls back on you. Your chair pushes up on you (the normal force) as you push down on the chair. These are examples of an interaction, the mutual influence of two objects on each other.

Question 2

what is a reaction action pair

Answer 2

To be more specific, if object A exerts a F⃗ A on B force on object B, then object B exerts a force F⃗ B on A on object A. This pair of forces, shown in Figure 7.2, is called an action/reaction pair. Two objects interact by exerting an action/reaction pair of forces on each other. Notice the very explicit subscripts on the force vectors. The first letter is the agent; the second letter is the object on which the force acts. F⃗ A on B is a force exerted by A on B.

Question 3

what is the system ?

Answer 3

Let’s define the system as those objects whose motion we want to analyze

Question 4

what is the environment

Answer 4

the environment as objects external to the system.

Question 5

interaction diagram ? what is it?

Answer 5

a schematic diagram.
where the system is enclosed in a square
and the interaction between objects are shown through lines

Question 6

external forces ?

Answer 6

interaction of the system with the environment

Every force is one member of an action/reaction pair, so there is no such thing as a true “external force.” What we call an external force is simply an interaction between an object of interest, one we’ve chosen to place inside the system, and an object whose motion is not of interest.

Question 7

example 7.1 : Pushing a crate

Answer 7

Figure 7.4 shows a person pushing a large crate across a rough surface. Identify all interactions, show them on an interaction diagram, then draw free-body diagrams of the person and the crate.

Question 8

what is propulsion ?

Answer 8

It is the force that a system with an internal source of energy uses to drive itself forward. Propulsion is an important feature not only of walking or running but also of the ­forward motion of cars, jets, and rockets. Propulsion is somewhat counterintuitive, so it is worth a closer look.

Question 9

gives example of propulsion

Answer 9

If you try to walk across a frictionless floor, your foot slips and slides backward. In order for you to walk, the floor needs to have friction so that your foot sticks to the floor as you straighten your leg, moving your body forward. The friction that prevents slipping is static friction. Static friction, you will recall, acts in the direction that prevents slipping. The static friction force f⃗ P has to point in the forward direction to prevent your foot from slipping backward. It is this forward-directed static friction force that propels you forward! The force of your foot on the floor, the other half of the action/reaction pair, is in the opposite direction.

check book for more examples.
the car and the rocket

Question 10

example 7.2
A tow truck uses a rope to pull a car along a horizontal road, as shown in Figure 7.8. Identify all interactions, show them on an interaction diagram, then draw free-body diagrams of each object in the system.

Answer 10

answer in book

Question 11

stop to think - 7.1 :
A rope of negligible mass pulls a crate across the floor. The rope and crate are the system; the hand pulling the rope is part of the environment. What, if anything, is wrong with the free-body diagrams?

Answer 11

check book for answer

Question 12

WHAT IS NEWTON THIRD LAW ?

Answer 12

Every force occurs as one member of an action/reaction pair of forces.

The two members of an action/reaction pair act on two different objects.

The two members of an action/reaction pair are equal in magnitude but opposite in direction: F⃗ A on B=−F⃗ B on A.

Question 13

the action /reaction pair is always….

Answer 13

opposite in direction

Question 14

action /reaction pair will always have the same or different magnitude ?

Answer 14

But the most significant portion of the third law, which is by no means obvious, is that the two members of an action/reaction pair have equal magnitudes. That is, F A on B = F B on A. This is the quantitative relationship that will allow you to solve problems of interacting objects.

Question 15

what is the catchphrase for newton third law and why the book doesnt like it ?

Answer 15

Newton’s third law is frequently stated as “For every action there is an equal but opposite reaction.” While this is indeed a catchy phrase, it lacks the preciseness of our preferred version. In particular, it fails to capture an essential feature of action/reaction pairs—that they each act on a different object.

Question 16

Example 7.3 The forces on accelerating boxes

The hand shown in Figure 7.12 pushes boxes A and B to the right across a frictionless table. The mass of B is larger than the mass of A.

Draw free-body diagrams of A, B, and the hand H, showing only the horizontal forces. Connect action/reaction pairs with dashed lines.

Rank in order, from largest to smallest, the horizontal forces shown on your free-body diagrams.

Answer 16

Farm on H>FA on H=FH on A>FB on A=FA on B

check book

Question 17

Stop to Think 7.2
A small car is pushing a larger truck that has a dead battery. The mass of the truck is larger than the mass of the car. Which of the following statements is true?

The car exerts a force on the truck, but the truck doesn’t exert a force on the car.

The car exerts a larger force on the truck than the truck exerts on the car.

The car exerts the same amount of force on the truck as the truck exerts on the car.

The truck exerts a larger force on the car than the car exerts on the truck.

The truck exerts a force on the car, but the car doesn’t exert a force on the truck.

Answer 17

check book for answers

Question 18

what is an acceleration constraint ?

Answer 18

For example, if two objects A and B move together, their accelerations are constrained to be equal: acceleration of A=acceleration of B. A well-defined relationship between the accelerations of two or more objects is called an acceleration constraint. It is an independent piece of information that can help solve a problem.

Question 19

Consider the car being towed in Figure 7.14.

what is the acceleration constraint ?

Answer 19

they’ll be the same acceleration

Because the accelerations of both objects are equal, we can drop the subscripts C and T and call both of them ax.

Question 20

will the acceleration of 2 objects connected together always the same ?
explain why or why not ?

Answer 20

Don’t assume the accelerations of A and B will always have the same sign. Consider blocks A and B in Figure 7.15. The blocks are connected by a string, so they are constrained to move together and their accelerations have equal magnitudes. But A has a positive acceleration (to the right) in the x-direction while B has a negative acceleration (downward) in the y-direction.

Question 21

Example 7.4 Keep the crate from sliding
You and a friend have just loaded a 200 kg crate filled with priceless art objects into the back of a 2000 kg truck. As you press down on the accelerator, force F⃗ surface on truck propels the truck forward. To keep things simple, call this just F⃗ T. What is the maximum magnitude F⃗ T can have without the crate sliding? The static and kinetic coefficients of friction between the crate and the bed of the truck are 0.80 and 0.30. Rolling friction of the truck is negligible.

Answer 21

answer : 17,000 N

check book

Question 22

Boxes A and B are sliding to the right across a frictionless table. The hand H is slowing them down. The mass of A is larger than the mass of B. Rank in order, from largest to smallest, the horizontal forces on A, B, and H.

FB on H=FH on B=FA on B=FB on A

FB on H=FH on B>FA on B=FB on A

FB on H=FH on BFA on B

Answer 22

check book for answer

Question 23

Tension revisited :

molecualr bond in the rope

Answer 23

introduced an atomic-level model in which tension is due to the stretching of spring-like molecular bonds within the rope. Stretched springs exert pulling forces, and the combined pulling force of billions of stretched molecular springs in a string or rope is what we call tension.

An important aspect of tension is that it pulls equally in both directions. To gain a mental picture, imagine holding your arms outstretched and having two friends pull on them. You’ll remain at rest—but “in tension”—as long as they pull with equal strength in opposite directions. But if one lets go, analogous to the breaking of ­molecular bonds if a rope breaks or is cut, you’ll fly off in the other direction!

example of rope tied to a safe and to the ceiling

Question 24

Example 7.5 Pulling a rope
Figure 7.18a shows a student pulling horizontally with a 100 N force on a rope that is attached to a wall. In Figure 7.18b, two ­students in a tug-of-war pull on opposite ends of a rope with 100 N each. Is the tension in the second rope larger than, smaller than, or the same as that in the first rope?

Answer 24

the same in both rope

Question 25

massless string approximation ?

Answer 25

In other words, if objects A and B interact with each other through a massless string, we can omit the string and treat forces F⃗ A on B and F⃗ B on A as if they are an action/reaction pair. This is not literally true because A and B are not in contact. Nonetheless, all a massless string does is transmit a force from A to B without changing the magnitude of that force. This is the real significance of the massless string approximation.

Question 26

massless string approximation ?

Answer 26

In other words, if objects A and B interact with each other through a massless string, we can omit the string and treat forces F⃗ A on B and F⃗ B on A as if they are an action/reaction pair. This is not literally true because A and B are not in contact. Nonetheless, all a massless string does is transmit a force from A to B without changing the magnitude of that force. This is the real significance of the massless string approximation.

For problems in this book, you can assume that any strings or ropes are massless unless the problem explicitly states otherwise. The simplified view of Figure 7.21 is appropriate under these conditions. But if the string has a mass, it must be treated as a separate object.

Question 27

Example 7.6 Comparing two tensions
Blocks A and B in Figure 7.22 are connected by massless string 2 and pulled across a frictionless table by massless string 1. B has a larger mass than A. Is the tension in string 2 larger than, smaller than, or equal to the tension in string 1?

Answer 27

The tension in string 2 is smaller than the tension in string 1.

Question 28

questions with pulleys :

do we take into account the friction on the pulley

Answer 28

shows a simple situation in which block B, as it falls, drags block A across a table. As the string moves, static friction between the string and pulley causes the pulley to turn. If we assume that

The string and the pulley are both massless, and

There is no friction where the pulley turns on its axle,

then no net force is needed to accelerate the string or turn the pulley. Thus the tension in a massless string remains constant as it passes over a massless, frictionless pulley.

Question 29

to resume For massless ropes or strings and massless, frictionless pulleys:

Answer 29

If a force pulls on one end of a rope, the tension in the rope equals the magnitude of the pulling force.

If two objects are connected by a rope, the tension is the same at both ends.

If the rope passes over a pulley, the tension in the rope is unaffected.