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Ninth Edition
Ninth Edition
Vector Mechanics for Engineers: Dynamics Introduction
CHAPTER
VECTOR MECHANICS FOR ENGINEERS:
• Newton’s first and third laws are sufficient for the study of bodies at rest (statics) or bodies in motion with no acceleration.
12 DYNAMICS
• When a body accelerates (changes in velocity magnitude or direction), Newton’s second law is required to relate the motion of the body to the forces acting on it.
Ferdinand P. Beer
E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler
Kinetics of Particles: Newton’s Second Law
• Newton’s second law: - A particle will have an acceleration proportional to the magnitude of the resultant force acting on it and in the direction of the resultant force.
Texas Tech University
study of the relations existing between the forces acting on a body, the mass of the body, and the motion of the body.
- The resultant of the forces acting on a particle is equal to the rate of change of linear momentum of the particle. - The sum of the moments about O of the forces acting on a particle is equal to the rate of change of angular momentum of the particle about O. © 2010 The McGraw-Hill Companies, Inc. All rights reserved.
© 2010 The McGraw-Hill Companies, Inc. All rights reserved.
Ninth Edition
Ninth Edition
Vector Mechanics for Engineers: Dynamics Newton’s Second Law of Motion
12 - 2
Vector Mechanics for Engineers: Dynamics Linear Momentum of a Particle
• Newton’s Second Law: If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of resultant and in the direction of the resultant.
• Replacing the acceleration by the derivative of the velocity yields   dv F  m dt  d  dL  m v   dt dt  L  linear momentum of the particle
• Consider a particle subjected to constant forces, F1 F2 F3      constant  mass, m a1 a2 a3
 • When a particle of mass m is acted upon by a force F , the acceleration of the particle must satisfy   F  ma
• Linear Momentum Conservation Principle: If the resultant force on a particle is zero, the linear momentum of the particle remains constant in both magnitude and direction.
• Acceleration must be evaluated with respect to a Newtonian frame of reference, i.e., one that is not accelerating or rotating. • If force acting on particle is zero, particle will not accelerate, i.e., it will remain stationary or continue on a straight line at constant velocity. © 2010 The McGraw-Hill Companies, Inc. All rights reserved.
Ninth Edition
Ninth Edition
Vector Mechanics for Engineers: Dynamics Systems of Units
12 - 4
Vector Mechanics for Engineers: Dynamics Equations of Motion
• Of the units for the four primary dimensions (force, mass, length, and time), three may be chosen arbitrarily. The fourth must be compatible with Newton’s 2nd Law. • International System of Units (SI Units): base units are the units of length (m), mass (kg), and time (second). The unit of force is derived, kg  m  m 1 N  1 kg 1 2   1 2  s  s • U.S. Customary Units: base units are the units of force (lb), length (m), and time (second). The unit of mass is derived, 1lb 1lb lb  s 2 1lbm  1slug  1 ft 32.2 ft s 2 1ft s 2 © 2010 The McGraw-Hill Companies, Inc. All rights reserved.
© 2010 The McGraw-Hill Companies, Inc. All rights reserved.
12 - 3
12 - 5
• Newton’s second law provides    F  ma • Solution for particle motion is facilitated by resolving vector equation into scalar component equations, e.g., for rectangular components,        Fx i  Fy j  Fz k  m a x i  a y j  a z k




 Fx  ma x  Fy  ma y  Fz  ma z  Fx  mx  Fy  my  Fz  mz • For tangential and normal components,
 F t  mat Ft  m
© 2010 The McGraw-Hill Companies, Inc. All rights reserved.
dv dt
 F n  ma n Fn  m
v2

12 - 6
1
Ninth Edition
Ninth Edition
Vector Mechanics for Engineers: Dynamics Sample Problem 12.1
Vector Mechanics for Engineers: Dynamics Sample Problem 12.1 SOLUTION: • Resolve the equation of motion for the block into two rectangular component equations.  Fx  ma :
SOLUTION: • Resolve the equation of motion for the block into two rectangular component equations.
A 200-lb block rests on a horizontal plane. Find the magnitude of the force P required to give the block an acceleration or 10 ft/s2 to the right. The coefficient of kinetic friction between the block and plane is mk  0.25.

O
 Fy  0 :
x
N  P sin 30  200 lb  0
W 200 lb m  g 32.2 ft s 2
• Unknowns consist of the applied force P and the normal reaction N from the plane. The two equations may be solved for these unknowns. N  P sin 30  200 lb
lb  s 2 ft F  mk N
P cos 30  0.25 P sin 30  200 lb  62.1 lb
 0.25 N
12 - 8
Vector Mechanics for Engineers: Dynamics Sample Problem 12.2
SOLUTION: • Resolve the equation of motion for the bob into tangential and normal components. • Solve the component equations for the normal and tangential accelerations.
The bob of a 2-m pendulum describes an arc of a circle in a vertical plane. If the tension in the cord is 2.5 times the weight of the bob for the position shown, find the velocity and acceleration of the bob in that position.
Ninth Edition
Ninth Edition
Vector Mechanics for Engineers: Dynamics Sample Problem 12.2
P  151 lb
© 2010 The McGraw-Hill Companies, Inc. All rights reserved.
12 - 7

 62.1lb
 6.21
© 2010 The McGraw-Hill Companies, Inc. All rights reserved.

P cos 30  0.25 N  6.21lb  s 2 ft 10 ft s 2
y
• Unknowns consist of the applied force P and the normal reaction N from the plane. The two equations may be solved for these unknowns.
• Solve for the velocity in terms of the normal acceleration.
SOLUTION: • Resolve the equation of motion for the bob into tangential and normal components. • Solve the component equations for the normal and tangential accelerations. mg sin 30  mat  Ft  mat : at  g sin 30
 Fn  man :
an  g 2.5  cos 30
an  16.03 m s 2 • Solve for velocity in terms of normal acceleration.
an  © 2010 The McGraw-Hill Companies, Inc. All rights reserved.
at  4.9 m s 2
2.5mg  mg cos 30  ma n
12 - 9
v2

© 2010 The McGraw-Hill Companies, Inc. All rights reserved.
v  an 
2 m 16.03 m s 2  v  5.66 m s 12 - 10
2

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Part 1: Best 1080P HD Movie Player for HD Videos and Blu-Ray Movies

Whether you need to play Blu-ray movies, or HD videos of any media format, Free Blu-ray Player is the best HD video player to enjoy the movies with the original quality. Moreover, you can also enjoy the movies with different screen modes and capture features.

1. Play video formats up to 4K Ultra HD and Blu-ray disc/ISO/folder.

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5. Capture the favorite snapshots during the playback process.

How to Play HD Videos with the Original Quality

Launch the best HD media player

Download and install the free HD video player, launch the program on your computer. If you need to play 1080P videos from Blu-ray disc, insert the disc into Blu-ray drive beforehand.

Import HD video or Blu-ray movies

Click the “Open File” button to import the HD videos from your computer, or “Open Disc” button to load the 1080P Blu-ray movies from the Blu-ray disc into the program.

Playback the HD movies on computer

After that you can select the favorite audio track and subtitle. Go to “Audio” and “Video” settings to set up the best quality. Then control the playback with icons on the bottom.

Part 2: 4 Best HD Players to Enjoy 4K/1080P/HD Videos

Top 1: 5KPlayer

5KPlayer is a versatile HD movie player to watch HD movies from computer, online streaming sites, DLNA & AirPlay compatible devices and receive satellite radio.

1. Compatible with 5K, 4K, 1080P, 360 HD videos, DVDs and radio.

2. Support a wide range of formats like AVI, FLV, MKV, MP4, WebM, etc.

3. Equipped with a media library to manage local media files with ease.

4. Download and stream videos from YouTube, Vimeo, and more.

Top 2: QuickTime

QuickTime is the pre-installed free HD video player on Mac. Not only to play the high quality movies, you can also download trailer, make or edit movies or convert videos to QuickTime.

1. Play HD MOV and MP4 videos up to 1080P or 4K resolutions.

2. Lightweight and play HD videos without lagging or losing quality.

3. Compatible with full screen mode and multiple monitor setups.

4. Capture online videos and iPhone activities with screen recorder.

Top 3: SMPlayer

SMPlayer is another free HD media player for Windows 10 and earlier. It has an in-built codec for video playback on PCs, so you do not have to look for extra codec for the loaded video file.

1. Support HD videos in MP4, AVI, MKV, FLV, MOV and more others.

2. Search and download subtitle for the HD videos automatically.

3. Adjust and sync audio tracks and subtitles to remove any delay.

4. Play HD videos from YouTube with built-in YouTube live streams.

Top 4: Plex

Plex is not only a HD media player, but also a video streaming service. It brings together all the media files with a growing catalog of great web shows, news and podcasts.

1. Play HD videos, photos, music, and other media content with ease.

2. Construct playlists to manage your media files and enjoy them later.

3. Stream high quality videos from Apple, Android, Roku, Xbox, etc.

4. Compatible with the latest visual technology, including VR videos.

Part 3: 4 Best HD Players for Videos and Blu-ray Movies

Top 1: VLC Media Player

VLC Media Player is a versatile HD movie player available for Windows, Mac, Linux and mobile devices, which you can stream video, convert movies, edit files and more.

1. Integrate a wide array of video codecs including Blu-ray movies.

2. Play HD video and audio files from online videos to optical discs.

3. Convert some HD video and audio files to other file formats.

4. Offer extensive tools, such as DVD ripping, video conversion, etc.

Top 2: PotPlayer

PotPlayer is more than a free multimedia HD video player for computer. It also supports Digital TV devices, Webcams, Analogs, DXVA, live broadcasts, etc.

1. Built-in video codecs for playing all HD videos and Blu-ray movies.

2. Advanced hardware acceleration like CUDA, QuickSync and DXVA.

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3. Maximize the performance with advanced setting.

4. Contain a variety of tools, such as bookmark your favorite scenes.

Top 3: UMPlayer

Just double click any video file for all platforms, UMPlayer includes a long array of more than 270 codec to play audio, video, DVD discs, video files from the web address.

1. HD video player for media files, DVD discs and Blu-ray movies.

2. Automatically search and download subtitles from opensubtitles.org.

3. Repair and playback some decode damaged AVI video files.

Top 4: MPC-HC

MPC-HC is the best DVB player and HD media player for non-tech savvy. It supports all common video and audio formats available for playback without advertisements or toolbars.

1. Play common and HD videos and movies with the original quality.

2. Lightweight and very simple to use on Windows 10 or earlier.

3. Custom toolbar to fit almost any need to play HD videos on PC.

4. It can also be used as DVB player or DVD players.

Part 4: FAQs of Playing 1080p HD Videos

1. Which is the best media player for 1080p movies?

From the above 1080p HD player list, Free Blu-ray Player is the best media player for free, because it supports the common 1080p HD videos and audio, but also plays the 1080p Blu-ray files for free.

Its Pro version lets you play 4K UHD movies smoothly on your computer.

2. How to play 1080p videos smoothly on VLC?

Though 1080p HD videos are not played properly on computer in VLC, this problem can be fixed by changing the settings on computer.

➤ Change the power settings

Press 'Windows + X' to find Control Panel. Click the 'Hardware and Sound' category and then select 'Power Options'. Finally select the checkbox of 'High performance'.

'High Performance' will drain your battery fast, but it plays 1080p HD videos in VLC smoothly.

➤ Toggle hardware acceleration on VLC

Play the video in VLC, right-click to select 'Tools' and find 'Preferences'. Go to the 'Input / Codecs' tab to click the 'Hardware-accelerated decoding'. Select another option or Disable it entirely.

Then you can see the lagging 1080p HD videos playback will be smooth.

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3. Can you play 4k video on 1080p monitor?

Yes, you can.

But there is no visual difference, because the monitor only shows the 1080p. What's worse, the 4K video playback may be a lot slower on a 1080p HD display.

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Ultra Hd Blu Ray Movies

4. Can iPhone XR play 1080p videos?

Tamil Hd Bluray Movies Download Tamilrockers

Yes.

The video playback is up to 1080p high resolution on iPhone XR. It can record 1 4K UHD video at 24/30/60 fps or 1080p HD at 30/60 fps.

Conclusion

Best Buy Movies Blu Ray

The article shares the top 9 best HD video players available for Windows, MacOS and Linux. If you are looking for the best solution to enjoy HD videos and Blu-ray movies, Free Blu-ray Player should always be the first choice.