CH 05 HW - Chapter 5 Physics Homework for Mastering PDF

Preview

Summary

Chapter 5 Physics Homework for Mastering
...

Description

CH 05 HW Due: 3:00pm on Monday, October 7, 2019 You will receive no credit for items you complete after the assignment is due. Grading Policy

An Object Accelerating on a Ramp Learning Goal: Understand that the acceleration vector is in the direction of the change of the velocity vector. In one dimensional (straight line) motion, acceleration is accompanied by a change in speed, and the acceleration is always parallel (or antiparallel) to the velocity. When motion can occur in two dimensions (e.g. is confined to a tabletop but can lie anywhere in the x-y plane), the definition of acceleration is in the limit

.

In picturing this vector derivative you can think of the derivative of a vector as an instantaneous quantity by thinking of the velocity of the tip of the arrow as the vector changes in time. Alternatively, you can (for small ) approximate the acceleration as . Obviously the difference between and is another vector that can lie in any direction. If it is longer but in the same direction, will be parallel to . On the other hand, if has the same magnitude as but is in a slightly different direction, then will be perpendicular to . In general, can differ from in both magnitude and direction, hence can have any direction relative to . This problem contains several examples of this.Consider an object sliding on a frictionless ramp as depicted here. The object is already moving along the ramp toward position 2 when it is at position 1. The following questions concern the direction of the object's acceleration vector, . In this problem, you should find the direction of the acceleration vector by drawing the velocity vector at two points near to the position you are asked about. Note that since the object moves along the track, its velocity vector at a point will be tangent to the track at that point. The acceleration vector will point in the same direction as the vector difference of the two velocities. (This is a result of the equation given above.)

Part A Which direction best approximates the direction of

when the object is at position 1?

Hint 1. Consider the change in velocity At this point, the object's velocity vector is not changing direction; rather, it is increasing in magnitude. Therefore, the object's acceleration is nearly parallel to its velocity.

ANSWER:

straight up downward to the left downward to the right straight down

Correct

PartTypesetting B math: 80%

Which direction best approximates the direction of

when the object is at position 2?

Hint 1. Consider the change in velocity At this point, the speed has a local maximum; thus the magnitude of is not changing. Therefore, no component of the acceleration vector is parallel to the velocity vector. However, since the direction of is changing there is an acceleration.

ANSWER:

straight up upward to the right straight down downward to the left

Correct Even though the acceleration is directed straight up, this does not mean that the object is moving straight up.

Part C Which direction best approximates the direction of

when the object is at position 3?

Hint 1. Consider the change in velocity At this point, the speed has a local minimum; thus the magnitude of is not changing. Therefore, no component of the acceleration vector is parallel to the velocity vector. However, since the direction of is changing there is an acceleration.

ANSWER: upward to the right to the right straight down downward to the right

Correct

A Mass on a Turntable: Conceptual A small metal cylinder rests on a circular turntable that is rotating at a constant rate, as illustrated in the diagram.

Typesetting math: 80%

Part A Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram?

Hint 1. The direction of acceleration can be determined from Newton's second law According to Newton's second law, the acceleration of an object has the same direction as the net force acting on that object.

ANSWER:

a b c d e

Correct

Part B Let be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location?

from the center

Check all that apply.

Hint 1. Find the speed of the cylinder Find the speed

of the cylinder at the new location. Assume that the cylinder makes one complete turn in a period of time

Express your answer in terms of

and

.

.

ANSWER: =

Correct Now compare your result with the speed of the cylinder before it is moved.

Hint 2. Find the acceleration of the cylinder Find the magnitude of the acceleration . Express your answer in terms of Typesetting math: 80%

of the cylinder at the new location. Assume that the cylinder makes one complete turn in a period of time

and

.

Hint 1. Centripetal acceleration Recall that the acceleration of an object that moves in a circular path of radius

with constant speed

has magnitude given by

. Note that both the velocity and radius of the trajectory change when the cylinder is moved.

ANSWER:

=

ANSWER: The speed of the cylinder has decreased. The speed of the cylinder has increased. The magnitude of the acceleration of the cylinder has decreased. The magnitude of the acceleration of the cylinder has increased. The speed and the acceleration of the cylinder have not changed.

Correct

Problem 5.04 You start an old record player and notice a bug on the surface close to the edge of the record. The record has a diameter of 12 inches and completes 33 revolutions each minute.

Part A What is the speed of the bug in SI units? Express your answer with the appropriate units. ANSWER: = 0.53

Correct

Part B What is the acceleration of the bug in SI units? Express your answer with the appropriate units. ANSWER: = 1.8

Correct

Part C Typesetting math: 80%

What would the bug's speed be if it were halfway between the center and the edge of the record?

Express your answer with the appropriate units. ANSWER: = 0.26

Correct

Part D What would the bug's acceleration be if it were halfway between the center and the edge of the record? Express your answer with the appropriate units. ANSWER: = 0.91

Correct

Problem 5.06 - Enhanced - with Feedback The Moon is an average distance of

from Earth. It circles Earth once each 27.3 days.

Part A What is its average speed? Express your answer with the appropriate units. ANSWER: = 1000

Correct

Part B What is its acceleration? Express your answer with the appropriate units. ANSWER: = 2.7×10−3

Correct

Part C How does this acceleration compare to the acceleration of free fall on Earth? ANSWER: It is comparable to the acceleration of free fall on Earth. It is much smaller than the acceleration of free fall on Earth. It is much bigger than the acceleration of free fall on Earth. Typesetting math: 80%

Correct

Problem 5.08 - Enhanced - with Feedback You are working in a biology lab and learning to use a new ultracentrifuge for blood tests. The specifications for the centrifuge say that a red blood cell rotating in the ultracentrifuge moves at 470 and has a radial acceleration of 150,000 's (that is, 150,000 times 9.8 ). The radius of the centrifuge is 0.15 . You wonder if this claim is correct.

Part A Determine the radial acceleration of the ultracentrifuge using calculations. Express your answer with the appropriate units. ANSWER: = 1.5×106

Correct

Part B Are the specifications for the centrifuge correct? ANSWER:

yes no

Correct

Problem 5.14 Three people are standing on a horizontally rotating platform in an amusement park. One person is almost at the edge, the second one is center, and the third is from the center.

from the

Part A Draw a force diagram for a person standing on a horizontally rotating platform. Draw the vectors starting at the black dot. The location, orientation, and relative length of the vectors will be graded. The exact length of your vectors will not be graded. ANSWER:

Typesetting math: 80%

No elements selected

Select the elements from the list and add them to the canvas setting the appropriate attributes.

All attempts used; correct answer displayed

Part B If the platform speeds up, who is more likely to have trouble staying on the platform? ANSWER:

A person who is

from the center.

A person who is

from the center.

A person who is at the edge of the platform. That doesn’t depend on the distance from the center of the platform.

Correct

Centripetal Force Ranking Task Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass and radius of orbit satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.

Typesetting math: 80%

. The

Part A Rank the net force acting on each satellite from their rockets. Rank from largest to smallest. To rank items as equivalent, overlap them.

Hint 1. Determine the satellite's speed Each satellite completes one orbit in the same amount of time. Based on this information, and the radius of the various orbits, which satellite is moving fastest? ANSWER:

The satellite of mass

orbiting with radius

.

The satellite of mass

orbiting with radius

The satellite of mass

orbiting with radius

.

The satellite of mass

orbiting with radius

.

The satellite of mass

orbiting with radius

.

The satellite of mass

orbiting with radius

.

.

Hint 2. Determine the centripetal acceleration Any object traveling along a circular path experiences a centripetal acceleration given by , where is the radius of orbit. This component of the object’s acceleration, directed inward toward the center of the circle, reflects a constant change in direction and keeps the object traveling in a circle. If the speed of each satellite is proportional to its radius, what power of the radius is the acceleration proportional to? ANSWER:

Correct The acceleration of each satellite is directly proportional to the size of its orbit. Basically, if the period of each orbit is constant, a satellite must have twice the acceleration to complete an orbit that is twice as long.

Hint 3. Determining the net force Typesetting math: 80%

Newton’s 2nd law is valid for any motion, whether the motion is along a straight line or a circular path. The net force acting on the satellite must be equal to the product of its mass and acceleration: .

ANSWER:

Reset

Help

The correct ranking cannot be determined.

Correct

Problem 5.24 A coin rests on a record 0.15 and the record is 0.24.

from its center. The record turns on a turntable that rotates at variable speed. The coefficient of static friction between the coin

Part A What is the maximum coin speed at which it does not slip? Express your answer with the appropriate units. ANSWER: = 0.59

Correct

Problem 5.28 A 18.0- ball is attached to a 130-

Typesetting math: 80%

-long string and moves in a horizontal circle (see the figure). The string exerts a force on the ball that is equal to 0.220

.

Part A What is the angle

?

Express your answer with the appropriate units. ANSWER: = 53.3

Correct

Problem 5.30 A car traveling at 10

passes over a hill on a road that has a circular cross section of radius 30

.

Part A What is the magnitude of the force exerted by the seat of the car on a 60-

passenger when the car is passing the top of the hill?

Express your answer with the appropriate units. ANSWER: = 390

Correct

Problem 5.34 You need to design a banked curve at the new circular Super 100 Raceway. The radius of the track is 800

and cars typically travel at speed 160

Part A What feature of the design is important so that all racecars can move around the track safely in any weather? ANSWER:

the angle of the embankmet should be zero the angle of the embankmet should be such that the sum of normal force and gravitational force were equal to the angle of the embankment does not influence the safety of the racers

Correct

Typesetting math: 80%

at 160

.

Part B What embankment angle should be to hold a car travelling at 160

if there were no friction between its wheels and the track?

Express your answer in degrees. ANSWER: = 33

Correct

± Banked Frictionless Curve, and Flat Curve with Friction A car of mass = 1400 traveling at 50.0 between the road and the car's tires as shown in . Use

enters a banked turn covered with ice. The road is banked at an angle , and there is no friction = 9.80 throughout this problem.

Part A What is the radius \texttip{r}{r} of the turn if \texttip{\theta }{theta} = 20.0 {\rm ^\circ} (assuming the car continues in uniform circular motion around the turn)? Express your answer in meters.

Hint 1. How to approach the problem You need to apply Newton's 2nd law to the car. Because you do not want the car to slip as it goes around the curve, the car needs to have a net acceleration of magnitude v^2/r pointing radially inward (toward the center of the curve). Hint 2. Identify the free-body diagram and coordinate system Which of the following diagrams represents the forces acting on the car and the most appropriate choice of coordinate axes?

ANSWER:

Typesetting math: 80%

Figure A Figure B Figure C

Hint 3. Calculate the normal force Find \texttip{n}{n}, the magnitude of the normal force between the car and the road. Take the positive x axis to point horizontally toward the center of the curve and the positive y axis to point vertically upward. Express your answer in newtons.

Hint 1. Consider the net force The only forces acting on the car are the normal force and gravity. There must be a net acceleration in the horizontal direction, but because the car does not slip, the net acceleration in the vertical direction must be zero. Use this fact to find \texttip{n}{n}. Hint 2. Apply Newton's 2nd law to the car in the y direction Which equation accurately describes the equation for the net force acting on the car in the y direction? ANSWER:

\sum F_y = n\cos\theta + Mg \sum F_y = n\sin\theta + Mg \sum F_y = n\cos\theta - Mg \sum F_y = n\sin\theta - Mg

ANSWER: \texttip{n}{n} = 1.46×104 \rm N

Hint 4. Determine the acceleration in the horizontal plane Take the y axis to be vertical and let the x axis point horizontally toward the center of the curve. By applying \sum F_x = Ma_x in the horizontal direction, determine \texttip{a}{a}, the magnitude of the acceleration, using your result for the normal force. Express your answer in meters per second squared.

Hint 1. Apply Newton's 2nd law to the car in the x direction Which equation accurately describes the equation for the net force acting on the car in the x direction? ANSWER: \sum F_x = n\cos\theta \sum F_x = n\sin\theta \large{\sum F_x = n\cos\theta + \frac{Mv^2}{r}} \large{\sum F_x = n\cos\theta- \frac{Mv^2}{r}}

ANSWER: \texttip{a}{a} = 3.57 \rm m/s^2

Typesetting math: 80%

ANSWER: \texttip{r}{r} = 54.1 \rm m

Correct

Part B Now, suppose that the curve is level (\theta = 0) and that the ice has melted, so that there is a coefficient of static friction \texttip{\mu }{mu} between the road and the car's tires as shown in . What is \texttip{\mu _{\rm min}}{mu_min}, the minimum value of the coefficient of static friction between the tires and the road required to prevent the car from slipping? Assume that the car's speed is still 50.0 {\rm km/hour} and that the radius of the curve is 54.1 {\rm m} . Express your answer numerically.

Hint 1. How to approach the problem You need to apply Newton's 2nd law to the car. Because you do not want the car to slip as it goes around the curve, the car needs to have a net acceleration of magnitude v^2/r pointing radially inward (toward the center of the curve). Hint 2. Identify the correct free-body diagram Which of the following diagrams represents the forces acting on the car as it goes around the curve? \texttip{F_{\rm fr}}{F_fr} represents the friction

force. ANSWER: Figure A Figure B Figure C Figure D

Hint 3. Calculate the net force What is the net force \texttip{F_{\rm net}}{F_net} that acts on the car? Express your answer in newtons. Typesetting math: 80%

Hint 1. How to determine the net force

Newton's 2nd law tells you that \sum \vec F = m \vec a. Because you do not want the car to slip as it goes around the curve, the car needs to have a net acceleration of magnitude v^2/r pointing radially inward (toward the center of the curve).

ANSWER: \texttip{F_{\rm net}}{F_net} = 4990 \rm N

Hint 4. Calculate the friction force If the coefficient of friction were equal to \texttip{\mu _{\rm min}}{mu_min}, what would be \texttip{F_{\rm fr}}{F_fr}, the magnitude of the force provided by friction? Let \texttip{m}{m} be the mass of the car and \texttip{g}{g} be the acceleration due to gravity.

Hint 1. Equation for the force of friction The force of friction is given by F_{\rm fr} = \mu n. Hint 2. Find the normal force What is the normal force \texttip{n}{n} acting on the car? Enter your answer in newtons.

Hint 1. Acceleration in the y direction Because the car is neither sinking into the road nor levitating, you can conclude that a_y = 0.

ANSWER: \texttip{n}{n} = 1.37×104 \rm N

ANSWER:

\large{F_{\rm fr}=\frac{\mu_{\rm min}}{Mg}} F_{\rm fr}=\mu_{\rm min}Mg

ANSWER: \texttip{\mu _{\rm min}}{mu_min} = 0.364

Correct

Problem 5.44

Part A Determine the magnitude of the gravitational force Mars would exert on man if he was on the surface of Mars. The mass of the man is 73.0 {\rm \; kg} . The mass of the Mars is 6.42 \times 10^{23} {\rm \; kg} and its radius is 3396 {\rm km}. Express your answer with the appropriate units. ANSWER: mg_{\rm M} = 271 {\rm N}

Typesetting math: 80%

Correct

Problem 5.50

Part A Determine the distance above Earth's surface to a satellite that completes three orbits per day. Express your answer to three significant figures and include the appropriate units. ANSWER: h = 1.39×107 {\rm m}

Correct

Problem 5.64 An old building is being demolished by swinging a heavy metal ball from a crane. Suppose that such a 100 {\rm kg} ball swings from a 20-...