Chapter 6 - Motion along a line

Question 1

what is mechanical equilibrium

Answer 1

For objects on which the net force is zero.

Model the object as a particle with no acceleration.

A particle at rest is in equilibrium.

A particle moving in a straight line at constant speed is also in equilibrium.

Mathematically: a⃗ =0⃗ in equilibrium; thus

Newton’s second law is F⃗ net=∑iFi→=0⃗ .

The forces are “read” from the free-body diagram,

Limitations: Model fails if the forces aren’t balanced.

Question 2

when looking at forces, you must consider the forces on the….

Answer 2

on the x axis and the y- axis
the sum of all y components must be zero
as well as the sum of all x components

Question 3

A car with a weight of 15,000 N is being towed up a 20∘ slope at constant velocity. Friction is negligible. The tow rope is rated at 6000 N maximum tension. Will it break?

Answer 3

1) identify all forces
2) do the free body diagram
there are 3 forces : n , w and T
3) identify all x and y components
Tx =T
nx = 0
wx = -wsin(theta)

ty = 0 
ny = n 
wy = - wcos(theta) 

T-w sin (theta) = 0
n - w cos (theta) = 0

4)
you can rewrite the first equation to isolate T
t = w sin (theta) 
  = 15,000 N sin (20)
  = 5100 N 

T < 6000N
therfore, the rope doesnt break

Question 4

What are the problem solving strategies for newtons second law problems

Answer 4

MODEL Model the object as a particle. Make other simplifications depending on what kinds of forces are acting.

VISUALIZE Draw a pictorial representation.

Show important points in the motion with a sketch, establish a coordinate system, define symbols, and identify what the problem is trying to find.

Use a motion diagram to determine the object’s acceleration vector a⃗ . The acceleration is zero for an object in equilibrium.

Identify all forces acting on the object at this instant and show them on a free-body diagram.

It’s OK to go back and forth between these steps as you visualize the situation.

SOLVE The mathematical representation is based on Newton’s second law:

F⃗ net=∑iF⃗ i=ma⃗
The forces are “read” directly from the free-body diagram. Depending on the problem, either

Solve for the acceleration, then use kinematics to find velocities and positions; or

Use kinematics to determine the acceleration, then solve for unknown forces.

ASSESS Check that your result has correct units and significant figures, is reasonable, and answers the question.

Question 5

To apply the step labeled solved , you must write the second law as 2 simultaneous equations

Answer 5

(Fnet)x = ∑Fx = ma *x
(Fnet)y = ∑Fy = ma *y

Question 6

A 1500 kg car is pulled by a tow truck. The tension in the tow rope is 2500 N, and a 200 N friction force opposes the motion. If the car starts from rest, what is its speed after 5.0 seconds?
(newtons second law)

Answer 6

check detail answer on ipad : physics chapter 6

ans: 7.7 m/s

Question 7

what is the constant force model ?

Answer 7

If all the forces acting on an object are constant, as in the last example, then the object moves with constant acceleration and we can deploy the uniform-acceleration model of kinetics. Now not all forces are constant—you will later meet forces that vary with position or time— but in many situations it is reasonable to model the motion as being due to constant forces. The constant-force model will be our most important dynamics model for the next several chapters

then you will be able to use the kinematics equations
which requires the acceleration to be constant

the particle will acccelerate in the direction of the net force

Question 8

A 500 g model rocket with a weight of 4.90 N is launched straight up. The small rocket motor burns for 5.00 s and has a steady thrust of 20.0 N. What maximum altitude does the rocket reach?

Answer 8

ans: 1540 m

check notability for detail answer

Question 9

what is mass ?

Answer 9

is a scalar quantity (only magnitude) that describes an object’s inertia. Loosely speaking, it also describes the amount of matter in an object. Mass is an intrinsic property of an object. It tells us something about the object, regardless of where the object is, what it’s doing, or whatever forces may be acting on it. from book

Question 10

what is newton law of gravity ?

Answer 10

shows two objects with masses m1 and m2 separated by distance r. Each object pulls on the other with a force given by Newton’s law of gravity:

(6.3)
F1 on 2=F2 on 1=Gm1m2r2(Newton’s law of gravity)

where G=6.67×10−11Nm2/kg2, called the gravitational constant, is one of the basic constants of nature. Notice that gravity is not a constant force—the force gets weaker as the distance between the objects increases.

Question 11

the gravitational force between 2 human size object is ….

Answer 11

The gravitational force between two human-sized objects is minuscule, completely insignificant in comparison with other forces. That’s why you’re not aware of being tugged toward everything around you. Only when one or both objects are planet-sized or larger does gravity become an important force.

Question 12

what is free fall ?

Answer 12

recall that free fall is motion under the influence of gravity only.
no other forces are acting on it

Question 13

what is weight ?

Answer 13

weight = m x g (acceleration due to gravity)

Weight is a force that acts at all times on all objects near Earth. The Earth pulls on all objects with a force of gravity downward toward the center of the Earth.

weight is another word for force of gravity (F_g)
always has units of N

in other words, there will be a gravitational force of magnitude mgmgm, g exerted downward on all objects near the Earth whether they are falling down, flying up at an angle, sitting at rest on a table, or accelerating upward in an elevator. There may be other forces that contribute to the acceleration of the object, but the force of gravity is always present.

Question 14

what happens to weight and mass of an object when you go on a different planet ?

Answer 14

The weight of an object will change if the object is brought farther away from Earth, or placed on a different planet, since the force of gravity on the object will change. However the mass of the object will remain the same regardless of whether the object is on Earth, in outer space, or on the Moon.

Question 15

An airplane of mass 4,500 kg, is taking off, flying through the air accelerating forward and upward. There is a thruster force of 6,700,, N on the plane in the direction of motion and an air resistance force of 4,300 N.

what is the force of gravity on the plane during takeoff?

Answer 15

The force of gravity is always nothing more nor less than mg regardless of any other forces or accelerations involved. So we can find the force of gravity on the plane (i.e. weight) by simply using,
F= mg
= 4500 x 9.8
44,100

Question 16

difference between mass and weight ?

Answer 16

Note Mass and weight are not the same thing. Mass, in kg, is an intrinsic property of an object; its value is unique and always the same. Weight, in N, depends on the object’s mass, but it also depends on the situation—the strength of gravity and, as we will see, whether or not the object is accelerating. Weight is not a property of the object, and thus weight does not have a unique value.

Question 17

when you weigh yourself on a scale that works with springs , what happens ?

what would happen if you weigh yourself on the scale at a different planet

Answer 17

Note that the scale does not “know” the weight of the object. All it can do is to measure how much its spring is compressed. On earth, a student with a mass of 70 kg has weight w = (70 kg)(9.80 m/s2) = 686 N because he compresses a spring until the spring pushes upward with 686 N. On a different planet, with a different value for g, the compression of the spring would be different and the student’s weight would be different.

Question 18

do you weigh more or less in the following situations

a) when the elevator accelerate upwards (person in on scale)
b) when the elevator accelerate downwards (person is on scale)

Answer 18

You do weigh more when accelerating upward (ay>0) because the reading of a scale—a weighing—increases. Similarly, your weight is less when the acceleration vector a⃗ points downward (ay<0) because the scale reading goes down. Weight, as we’ve defined it, corresponds to your sensation of heaviness or lightness.*

Question 19

what is the weigh of a stationary object ?

Answer 19

If an object is either at rest or moving with constant velocity, then ay=0 and w=mg. That is, the weight of a stationary object is the magnitude of the (effective) gravitational force acting on it. But its weight differs if it has a vertical acceleration.

Question 20

Suppose the elevator cable breaks and the elevator, along with the man and his scale, plunges straight down in free fall! What will the scale read?

Answer 20

When the free-fall acceleration ay=−g is used in Equation 6.10, we find w=0. In other words, the man has no weight!

Suppose, as the elevator falls, the man inside releases a ball from his hand. In the absence of air resistance, as Galileo discovered, both the man and the ball would fall at the same rate. From the man’s perspective, the ball would appear to “float” beside him. Similarly, the scale would float beneath him and not press against his feet. He is what we call weightless. Gravity is still pulling down on him—that’s why he’s falling—but he has no sensation of weight as everything floats around him in free fall.

Question 21

An elevator that has descended from the 50th floor is coming to a halt at the 1st floor. As it does, your weight is

More than mg.

Less than mg.

Equal to mg.

Zero.

Answer 21

more than mg

You are descending and slowing, so your acceleration vector points upward and there is a net upward force on you. The floor pushes up against your feet harder than gravity pulls down.

Question 22

without friction, what would happen ?

Answer 22

Friction is absolutely essential for many things we do. Without friction you could not walk, drive, or even sit down (you would slide right off the chair!).

Question 23

defined static friction ?

Answer 23

defined static friction fs→ as the force on an object that keeps it from slipping.

Question 24

how to determine the direction of static friction ?

Answer 24

To determine the direction of fs→ decide which way the object would move if there were no friction. The static friction force f⃗ s points in the opposite direction to prevent the motion.

Question 25

the size of static friction depends on what

Answer 25

the size of the static friction force depends on how hard you push or pull. The harder the rope in Figure 6.11 pulls, the harder the floor pulls back. Reduce the tension, and the static friction force will automatically be reduced to match. Static friction acts in response to an applied force.

shown in figure 6.12

Question 26

when does a object remains at rest in terms of static friction

Answer 26

An object remains at rest as long as fs

Question 27

what happens when fs is equal to fsmax

Answer 27

the object slips when fs=fsmax.

Question 28

coefficient of static friction, what is it ?

Answer 28

fsmax=μsn
where the proportionality constant μs is called the coefficient of static friction.
The coefficient is a dimensionless number that depends on the materials of which the object and the surface are made.

Question 29

is this possible A static friction force fs>fsmax ?

Answer 29

no ,its not.

Question 30

what happens when the box starts to slide ?

Answer 30

Once the box starts to slide, as in Figure 6.13, the static friction force is replaced by a kinetic friction force f⃗ k.

Question 31

kinetic friction, tell me about its magnitude

Answer 31

Experiments show that kinetic friction, unlike static friction, has a nearly constant magnitude.

Question 32

is the size of kinetic friction force bigger , less or the same as the max static friction ?

Answer 32

Furthermore, the size of the kinetic friction force is less than the maximum static friction, fk

Question 33

how do you decide which direction kinetic friction points in the diagram ?

Answer 33

The direction of f⃗ k is always opposite to the direction in which an object slides across the surface.

Question 34

stop to think : question 6.3

check book

Answer 34

fb > fc = fd = fe > fa. Situations c, d, and e are all kinetic friction, which does not depend on either velocity or acceleration. Kinetic friction is smaller than the maximum static friction that is exerted in b. fa = 0 because no friction is needed to keep the object at rest.

Question 35

example 6.5 : Carol pushes a 25 kg wood box across a wood floor at a steady speed of 2.0m/s. How much force does Carol exert on the box? If she stops pushing, how far will the box slide before coming to rest?

Answer 35

answers:
49 N
1.0 m
check tablet to see how its done

Question 36

A 50 kg steel file cabinet is in the back of a dump truck. The truck’s bed, also made of steel, is slowly tilted. What is the size of the static friction force on the cabinet when the bed is tilted 20°? At what angle will the file cabinet begin to slide?

Answer 36

170 N

39 degrees

Question 37

A 1500 kg car is traveling at a speed of 30 m/s when the driver slams on the brakes and skids to a halt. Determine the stopping distance if the car is traveling up a 10∘ slope, down a 10∘ slope, or on a level road.

Answer 37

10 degrees : 47.7
0 degrees : 57 m
- 10 degree : 74.7 m

Question 38

6.10 A 100 kg box of dimensions 50 cm×50 cm×50 cm is in the back of a flatbed truck. The coefficients of friction between the box and the bed of the truck are μs=0.40 and μk=0.20. What is the maximum acceleration the truck can have without the box slipping?

Answer 38

3.9 m/s ^2