Section 101 Energy and Work

Decoding QR Code In Objective-CUsing Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications.

Creating QR Code In Objective-CUsing Barcode creation for iPhone Control to generate, create QR Code JIS X 0510 image in iPhone applications.

Force and Displacement at an Angle A sailor pulls a boat a distance of 300 m along a dock using a rope that makes a 250 angle with the horizontal How much work does the sailor do on the boat if he exerts a force of 255 N on the rope

Read QR In Objective-CUsing Barcode scanner for iPhone Control to read, scan read, scan image in iPhone applications.

Making Barcode In Objective-CUsing Barcode drawer for iPhone Control to generate, create bar code image in iPhone applications.

Analyze and Sketch the Problem

QR Maker In C#Using Barcode drawer for .NET Control to generate, create QR-Code image in .NET applications.

Create QR In VS .NETUsing Barcode creation for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications.

Establish coordinate axes Sketch the situation showing the boat with initial conditions Draw a vector diagram showing the force and its component in the direction of the displacement Known:

Drawing QR In Visual Studio .NETUsing Barcode generation for .NET Control to generate, create QR Code JIS X 0510 image in Visual Studio .NET applications.

QR Generator In Visual Basic .NETUsing Barcode creation for .NET Control to generate, create QR-Code image in .NET framework applications.

F d 255 N 300 m 250

Create Barcode In Objective-CUsing Barcode creation for iPhone Control to generate, create barcode image in iPhone applications.

Encoding EAN / UCC - 13 In Objective-CUsing Barcode creation for iPhone Control to generate, create UCC-128 image in iPhone applications.

y x F 250 d F F cos 250

Draw Barcode In Objective-CUsing Barcode encoder for iPhone Control to generate, create bar code image in iPhone applications.

Drawing Code 128 Code Set B In Objective-CUsing Barcode creator for iPhone Control to generate, create Code-128 image in iPhone applications.

Unknown:

Generating EAN-8 In Objective-CUsing Barcode maker for iPhone Control to generate, create GS1 - 8 image in iPhone applications.

Code 39 Printer In Visual Studio .NETUsing Barcode maker for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications.

Solve for the Unknown

Print Data Matrix In JavaUsing Barcode drawer for Android Control to generate, create Data Matrix image in Android applications.

Print Data Matrix 2d Barcode In Objective-CUsing Barcode creator for iPad Control to generate, create Data Matrix ECC200 image in iPad applications.

Use the equation for work done when there is an angle between the force and displacement W Fd cos (255 N)(300 m)(cos 250 ) Substitute F 255 N, d 300 m, 693 103 J

Painting Barcode In JavaUsing Barcode generator for Java Control to generate, create barcode image in Java applications.

Drawing UPC-A Supplement 5 In VB.NETUsing Barcode generation for Visual Studio .NET Control to generate, create Universal Product Code version A image in VS .NET applications.

250

Barcode Creator In VS .NETUsing Barcode encoder for Reporting Service Control to generate, create bar code image in Reporting Service applications.

Print EAN128 In Objective-CUsing Barcode drawer for iPad Control to generate, create GS1 128 image in iPad applications.

Evaluate the Answer

Are the units correct Work is measured in joules Does the sign make sense The sailor does work on the boat, which agrees with a positive sign for work

Math Handbook

Trigonometric Ratios page 855

4 If the sailor in Example Problem 2 pulled with the same force, and along the same distance, but at an angle of 500 , how much work would he do 5 Two people lift a heavy box a distance of 15 m They use ropes, each of which makes an angle of 15 with the vertical Each person exerts a force of 225 N How much work do they do 6 An airplane passenger carries a 215-N suitcase up the stairs, a displacement of 420 m vertically, and 460 m horizontally a How much work does the passenger do b The same passenger carries the same suitcase back down the same set of stairs How much work does the passenger do now 7 A rope is used to pull a metal box a distance of 150 m across the floor The rope is held at an angle of 460 with the floor, and a force of 628 N is applied to the rope How much work does the force on the rope do 8 A bicycle rider pushes a bicycle that has a mass of 13 kg up a steep hill The incline is 25 and the road is 275 m long, as shown in Figure 10-4 The rider pushes the bike parallel to the road with a force of 25 N a How much work does the rider do on the bike b How much work is done by the force of gravity on the bike

25 Figure 10-4 (Not to scale)

10 Energy, Work, and Simple Machines

Finding work done when forces change A graph of force versus displacement lets you determine the work done by a force This graphical method can be used to solve problems in which the force is changing Figure 10-5a shows the work done by a constant force of 200 N that is exerted to lift an object a distance of 150 m The work done by this constant force is represented by W Fd (200 N)(150 m) 300 J The shaded area under the graph is equal to (200 N)(150 m), or 300 J The area under a force-displacement graph is equal to the work done by that force, even if the force changes Figure 10-5b shows the force exerted by a spring, which varies linearly from 00 to 200 N as it is compressed 150 m The work done by the force that compressed the spring is the area under the graph, which is the area of a triangle, 1 (base)(altitude), or 2 W 1 (200 N)(150 m) 150 J 2 Work done by many forces Newton s second law of motion relates the net force on an object to its acceleration In the same way, the work-energy theorem relates the net work done on a system to its energy change If several forces are exerted on a system, calculate the work done by each force, and then add the results