Solucionario fisica serway 7 th. Solucionario Fisica De Serway Septima Edicion II by efac. Internet Archive HTML5 Uploader 1.6.3.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Download Link= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =Tacklife SDH13DC Cordless Screwdriver 3.6-Volt 2000mAh MAX Torque 4N.m - 3-Position. BLACK+DECKER LDX120C 20-Volt MAX Lithium-Ion Cordless Drill/Driver.
Tacklife SDP51DC Cordless Rechargeable Screwdriver 3.6-Volt 2000mAh Li-ion MAX. Black & Decker LDX120C 20-Volt MAX Lithium-Ion Cordless Drill/Driver w/ 15557 Drill Bit Set, 10.
Tacklife 12V Lithium-Ion Cordless Drill/Driver Set - PCD01B 3/8-inch All-Metal Chuck 2-Speed Max. The Black & Decker Ldx120C Comes With One 20-Volt Max Lithium Drill/Driver, 1. 20V Max Lithium Ion Compact Drill/Driver Kit. The DCD777C2 20V Max Lithium Ion Compact Drill/Driver Kit is lightweight and compact for working in tight spaces for long periods of time.
High-speed transmission delivers 2-Speed variations allowing users to choose the level of performance needed for various. The BLACK+DECKER LDX120C 20-Volt MAX Lithium-Ion Cordless Drill-Driver features lithium ion technology, making it lighter and more compact.
The 20-Volt MAX Lithium-Ion battery holds charges longer between use and has a longer life-cycle. The 11 position clutch provides precise control for drilling into wood, metal. Durable and powerful, this 20V MAX.
cordless drill features an 11-position clutch to help prevent stripped screws. A compact, lightweight design enables you to work in tight spaces with ease, and an LED light illuminates work surfaces.
Hang pictures, shelves and more in a snap with this compact, do-it-all drill/driver. Small and light than most, it fits in tight spaces (with an LED to light your way) while still delivering the power needed to complete most household tasks. Amazing deals on this 20V Lithium Drill Driver Kit at Harbor Freight.
Quality tools & low prices. Amazing deals on this 12V 3/8In Lithium-Ion Cordless Var Speed Drill at Harbor Freight. Quality tools & low prices. The 11-position clutch prevents stripping and overdriving screws. An LED work light illuminates the surface for easier drilling in dark places. A compact and lightweight design allows you to carry out drilling tasks in confined spaces. The kit includes: (1) 20-volt MAX drill/driver, (1) 20-volt MAX Lithium Ion battery, (1) charger.
The DCD771C2 20V MAX. Lithium Ion Compact Drill/Driver Kit is lightweight and compact for working in tight spaces for long periods of time. High-speed transmission delivers 2-Speed variations allowing users to choose the level of performance needed for various applications. Dewalt 20V Max Li-Ion Hammer Drill & Drill Driver Combo Kit Kit Includes:(1) 1/2' Hammerdrill (1) 1/4' Impact Driver (2) 20V MAX. Lithium Ion 3.0 Ah Batteries.
In praising these new Ryobi Li-Ion drill/drivers, it's important to remember that Ryobi was, until recently, a runt of the power tool litter. But it nailed the new screw-dropping 18-volt battery, both in this tool and our lime green value winner, the P203. The difference here is the AutoShift clutch, which lets the drill. Find great deals for Black & Decker LDX120C 20V Li-Ion 3/8' Cordless Drill/Driver. Shop with confidence on eBay!
Order online at Screwfix.com. Compact drill driver featuring a 2-speed, all-metal gearbox with reverse function. LED work light provides good visibility in poorly lit areas. Supplied with 2 x 1.5Ah Li-ion batteries, quick charger and carry case.
FREE next day delivery available, free collection in 5 minutes. 18 V Compact™ Cordless Drill/Driver - Tool Only. Lbs of torque - has enough torque to drive most common fasteners and drill bits; 7.6 In. Head length and 3.0 Lbs.
most compact and lightweight design available provides least amount of user fatigue; Drives 160 3 In. Screws per charge - strong run time keeps. Power in the Palm of Your Hand The Craftsman C3 19.2-Volt Lithium-Ion 3/8-in.
Drill/Driver Kit Why break the bank? The Craftsman C3 19.2-Volt Lithium-Ion 3/8-in. Drill/Driver Kit has all the bells and whistles at a great low price. With the power and technology of the included lithium-ion battery, experience. Maximum Torque, 260 in-lb. Chuck Size, 3/8'. Chemistry, Lithium-Ion.
Contents, Drill/Driver, (2) Batteries, Charger, Carrying Tote. Number of Clutch Settings, 17+1.
Speed Settings, 2. Amps, 2.0 Ah. Style, Compact. Handle Type, Pistol Grip.
Speed, 0 - 380 / 1260 rpm. Type, Drill/Driver.
Length, 6-31/32'. Find DeWALT 20V MAX Lithium-Ion Drill Driver/Impact Driver Combo Kit, 1.3Ah in the Power Impact Wrenches category at Tractor Supply Co.The DeWAL. The WORX 20V Drill Driver is a must-have tool for every household.
The efficient, lightweight design makes it easy to control and fit in tight places. The 1.5Ah Lithium ion battery provides plenty of runtime, and holds its charge up to 18 months. Part of the Worx Powershare family, this drill shares batteries with popular WORX. Drill and fasten up to 35% faster with the Milwaukee® M12 3/8in. Cordless drill/driver, the only tool in its class with an all-metal chuck. This powerful 12V cordless lithium-ion drill/driver delivers 275 in.-lbs. Of torque, up to 25% more torque than the competition, and 0–400/0–1500 RPM.
Its compact, lightweight and durable. Looking for DEWALT Cordless Drill/Driver Kit,20.0V,1/2in. Grainger's got your back.
Easy ordering & convenient delivery. Log-in or register for your pricing. DEWALT 20-Volt Max 1/2-in Cordless Drill at Lowe's. The DCD771C2 20 V MAX lithium ion compact drill/driver kit is lightweight and compact for working in tight spaces for long periods of time. Buy Guild 1.3AH Li-Ion Cordless Drill Driver - 18V at Argos.co.uk, visit Argos.co.uk to shop online for Drills, DIY power tools, DIY tools and power tools, Home and garden. This 18V Lithium 1/2' Drill/Driver kit has a powerful 2-speed motor that delivers high output for managing diverse projects. Depend on this 18V Lithium 1/2' Drill/Driver for durability and reaching hard angles.
The Rockwell® 20-volt lithium-ion cordless drill is great for HVAC, electrical, plumbing, remodeling, wood working and more. A brushless motor offers up to 10 times longer motor life, 50% more run-time and up to 25% more power. It is equipped with a 1/2' heavy-duty keyless metal chuck to securely hold all types of bits. Why break the bank? The Craftsman C3 19.2-Volt Lithium-Ion 3/8-in.
Drill/Driver Kit has all the bells and whistles at a great low price. With the power and technology of the included lithium-ion battery, experience fade-free tool performance throughout the charge of the battery. Save that arm strength, lithium-ion batteries also.
Drill and fasten up to 35% faster with the only tool in its class that has an all-metal locking chuck. The powerful M12TM cordless lithium-ion 3/8” drill/driver delivers 275 in-lbs of torque – up to 25% more torque than the competition – and 0-400/0-1,500 RPM. Its compact, lightweight and durable design means greater comfort. GSR 120-LI Bosch Quality, High Power, Affordable Price! Cocraft HD 18-LI Drill/Driver - COCRAFT Clas Ohlson Simple and easy to use 18 V drill/driver Keyless. Shop for a DeWalt 20V MAX Cordless Lithium Ion Drill Driver and Impact Driver Kit (DCK240C2) at Sears Outlet today!
We offer low prices and great service.Unable to ship to South Carolina. The ideal combo kit to handle your cordless drilling and fastening tasks.
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The power to get more done + the cordless convenience of Lithium-ion battery technology. The 20V MAX. 2 tool combo kit includes Drill/Driver, ¼ Impact Driver, 20V MAX.
Battery and Charger. Product Features. Find Makita 12V Li-ion Drill Driver and Impact Driver Combo Kit at Bunnings Warehouse.
Visit your local store for the widest range of tools products. The Makita drill set comes with a 18v cordless drill/Hammer drill, and impact driver. I must say that the Makita impact driver packs one hell of a punch with solid control and drive. Best of all, the 10 minute quick charge is exactly that, QUICK! Both of these drills are Brushless and the batteries are Lithium-ion. Includes: R82005 Drill, R82230 Impact Driver, (1) R82049 and (1) R82059 Hyper™ Lithium-ion Batteries, Charger, Bag, (2) Belt Hooks, Hex Shank Phillips Bit and Operator's Manuals.
Press Releases. New PORTER-CABLE® 20 Volt MAX. Lithium Ion System Features High-Performance Drill/Driver and Impact. (January 3, 2013) – PORTER-CABLE announces the launch of its 20 Volt MAX. Lithium Ion Compact Drill/Driver (PCCK600LB) and 20 Volt MAX. Lithium Ion Impact Driver.
This 20-volt drill driver is more than just a cordless drill. With Black+Decker's MATRIX QuickConnect system, you can purchase attachments like sanders, circular saws, reciprocating saws, and more, which will all be compatible to this drill's motor. At just over three and a quarter pounds, this drill is relatively lightweight, and it. FREE SHIPPING AVAILABLE! Buy DeWALT 20-Volt MAX Lithium Ion Compact Drill/Driver Combo Kit at JCPenney.com today and enjoy great savings. Available Online Only!
Product Information; Technical Information; Bench Builder. Two speed transmission provides optimal speed and torque control.
LED lights up dark areas. Powered by 12V MAX™ lithium battery pack. Max power: 189UWO; Max rpm: 1, 500; 15 3/8' chuck settings. Chuck type: one sleeve. Includes: 3/8' drill/driver, two 12V. The new RYOBI 12V Lithium-Ion Drill/Driver gives you optimal performance in a compact size. The reduced size and new ergonomic grip make it extremely easy to handle, and it's perfect for tight spaces.
With a battery that is 33% lighter weight and 30% more compact, you will always have the power to complete your home. A Compact, Lightweight, and Powerful Drill, powered by Lithium-Ion Technology; More Power and Double the Run Time of Ni-Cad Drills; Battery Holds its Charge up to 18 months in Storage; High-Performance Motor Produces up to 250 in.
Of Torque; Two Variable Speed Ranges for Versatility; Build-In LED Work Light. Volts: 20 volts; Chuck Size: 3/8 in.
Product Type: Cordless Drill/Driver Kit; Battery Type: Lithium-Ion; 115 in-lbs. Torque; Lithium-Ion battery always ready, holds a charge up to 18 months; Provides an extra level of control, the 11 position clutch prevents stripping and overdriving screws; LED work light illuminates the surface. Update: No longer available for shipping, however you may opt for in-store pickup. Site may be loading slow so please try again later Fry's.com has Bosch 12V Max Lithium-Ion Drill/Driver &.
Compact size and light weight with 142 in-lbs (16 Nm) max. ○ Quick released 1/4' Hex bit holder and auto spindle lock for efficient bit change. ○ 11 torques settings + drill mode. ○ Variable speed with reversible control and electric bra. Shop Big R's huge selection of DeWALT® brand products, like the 12V MAX. Cordless Li-Ion Drill/Driver/Impact Driver Combo Kit.
Shop Big R online or find a store nearest you. Important Notice: Lithium-Ion Item - Express Delivery option not available due to transportation regulations.SAVE hundreds of dollars when you buy a combo kit versus buying tools individually!Kit includes 18V Cordless M18 1/4 in.
Hex High Performance Impact Driver (2650-20) and the 18V Cordless M18 High Performace. Shop Cordless Compact Li-Ion Drill/Driver Kit by DeWalt (DCD760KL) at Graybar, your trusted resource for Impact Drivers and other DeWalt products. The Worx 20V MaxLithium Drill/Driver gives you more power - always a welcome asset when staring down a tough job. Take on wood, steel, metal and plastic and have the run time to get it done. IKEA - FIXA, Screwdriver/drill, lithium-ion, 1-speed cordless screwdriver/drill for general driving or simple drilling work.15 torque settings for driving allows. DEWALT 20 V MAX. XR Li-ion compact brushless drill/driver kit.
Metal 1/2 In. Ratcheting chuck for superior bit gripping strength. 3-Mode LED provides lighting in dark work environments up to 20X brighter than previous model.
Additional Features DEWALT brushless motor delivers up to 57% more run time over brushed. Remember when you weren't bound by cords? Drill whatever you want, whenever you want with the WEN 20V MAX Lithium-Ion Cordless Drill & Driver. Boasting 19 different clutch positions and an additional high torque setting, you'll have the versatility and power needed to handle a multitude of projects.A while back; we invested in a set of Makita's 18V LXT Li-ion impact driver + hammer drill driver set.
After trying out DeWalt's offerings (we were lured away by the much lower prices) we came away unimpressed. Dewalt's power tools don't have as much control as Makita's (4 pole motor vs. Dewalt's 2 pole. 20V MAX Cordless Lithium-Ion 1/2 in.
Compact Drill Driver - DCD771B; High speed transmission delivers two speeds (0 - 450 / 0 - 1,500 RPM) for a range of fastening and drilling applications; Compact, lightweight design fits into tight areas; Ergonomic handle delivers comfort and control; Heavy duty 1/2 in. Ratcheting chuck. Hitachi 12V 3/8-Inch Cordless Drill/Driver. Best 12V Cordless Drill - Hitachi DS10DFL2 Lo Res. Model: Hitachi DS10DFL2; Power Source: Hitachi 12V Lithium-ion Battery; Batteries Included: (2) 15 watt hour; No Load Speed: 0-350/1,300 RPM; Maximum Torque: 300 in-lbs.
Chuck (Keyless): 3/8″; Weight. Drill Driver Dual 18v Kit, 19. EY7840, Battery Powered Ham/, 64. EY7880, 28.8v Rotary Hammer, 82.
EY7940, Tough Ip Hammer Drill, 28. EY7950, Tough Ip /hammer Drill Dr, 22. EY7960, Hammer Drill 21.6v, 22. EYC102B, Combo Kit, 53. EYC103B, Combo Kit, 48. EYFGA1NR, Cordless Li-ion Pistol Sc, 58. EYFGA2N Buy 18V Li-Ion Impact Cordless Drill Driver from an Eclipse Tools retailer near you or become a distributor.
Eclipse Tools is your complete tool and accessory source. The Ryobi ONE+ platform delivers value and performance with the 18V Lithium Drill Kit. The drill features the exclusive MAGTRAY magnetic holder as well as onboard bit storage for keeping screws and bits conveniently in reach. Plus, the kit is powered by lithium-ion technology that provides extended runtime and reduced. DEWALT 20 V MAX.
Li-ion compact drill/driver kit has an ergonomic handle that delivers comfort and control. Compact, lightweight design fits into tight areas High performance motor delivers 300 unit watts out (UWO) of power ability completing a wide range of applications High speed transmission delivers 2 speeds (0-450.
An intelligent electronic control system and Syneon Chip give the PSR 18 LI-2 Ergonomic cordless drill driver maximum power transfer. This package combines a 1/2' Drill/Driver with a 1/4' hex-drive Impact Driver, two 1.3 Ah Li-Ion batteries, a charger and a contractor bag. Both drivers features a lightweight, compact profile that fits easily into tight spaces.
The drill/driver has a powerful motor with a 2-speed transmission, while the impact driver features a. Most cordless drills these days run on lithium-ion (Li-ion) batteries. After the calibrated tests, CR's experts use each drill to drive screws and drill holes like you would, taking note of aspects such as balance, feel, and ease. It takes both cutting bits for drilling holes and driving bits for screwing in fasteners. A high performing cordless drill driver is an essential part of any DIY tool kit. A BLACK+DECKER 18V lithium-ion drill driver provides the speed, torque and battery runtime you need to take on any drilling task in a variety of materials, including timber, metal and plastics.
The 10 position clutch and 2 gear variable speed. Lithium-Ion technology is lighter, more compact, and no memory; 20V MAX Lithium-Ion battery holds charges longer between use and has longer cycle life; 11 position clutch provides precise control for drilling into wood, metal, plastic, and all screwdriving tasks; Compact and lightweight means less fatigue and allows users. Compare Items. Free Ship-to-Store. DeWalt Cordless Drill/Driver, 1/2-In., 18-Volt XRP, 3-Speed, LED Worklight. Item # 116734.
18-Volt XRP™ Drill/Driver With 1/2-Inch Chuck. Compare Items. Free Ship-to-Store. DeWalt Compact Cordless Drill / Driver Kit, 1/2-In., 20-Volt Lithium-Ion Battery. 20V MAX Lithium Ion Compact Hammerdrill and Impact Driver Combo Kit (3.0 Ah), Model DCK285L2. 20V MAX Lithium Ion Compact Drill/Driver Kit (1.5 Ah), Model DCD780C2 Quick View.
20V MAX Lithium Ion Compact Drill/Driver Kit (1.5 Ah), Model DCD780C2. Kit includes: Two 20V Max compact lithium ion battery packs, compact charger, and contractor bag. Compact, lightweight design fits into tight areas. High performance motor delivers 300 unit watts out (UWO) of power ability completing a wide range of applications. DEWALT® Max.
12 V Lithium-Ion 2450 RPM Cordless Drill/Driver/Impact Driver Combination Kit (Includes Fast Charger, (2) 12 Volt Max. Lithium Ion Battery Packs, DCF710 3/8' Drill Driver, DCF815 1/4' Impact Driver, Bit Tip, (2) Belt Hooks And Contractor Bag). Airgas Part #:DEWDCK211S2. Manufacturer #. 18V LXT® Lithium‑Ion Brushless Cordless 4‑1/2” / 5' Paddle Switch Cut‑Off/Angle Grinder, with Electric Brake, Tool Only. 18V LXT® Lithium‑Ion Sub‑Compact Brushless Cordless 3/8' Sq. Drive Impact Wrench Kit (2.0Ah).
Thanks to lithium-ion batteries, compact drills that would have been laughably undersized a few years ago can now handle drilling and driving tasks once reserved for much larger, heavier tools. This Old House assistant editor Sal Vaglica put these ⅜-inch drills through their paces to find which ones have the best power. Hilti Cordless Drills - SFC 22-A - Compact class cordless 22V drill driver powered by Li-ion battery with 13 mm keyless chuck for light- and medium-duty applications. DR1 +IonDrill 10.8v cordless Drill/Driver - Bare/Naked Used but fully working - end of line stock. The M18 FUEL™ Drill/Driver is the Most Powerful 18-volt cordless drill on the market. The POWERSTATE™ Brushless Motor delivers up to 1,200 in-lbs of torque and up to 2,000 RPM, providing faster drilling speed under heavy load to increase productivity.
At only 7.50” in length, it is the Most Compact drill in its class. DeWalt DCD980M2 20V MAX Lithium Ion Premium 3-Speed Drill/Driver Kit. DeWalt DCD980M2 20V MAX Lithium Ion Premium 3-Speed Drill/Driver Kit. CordLess driLL/driVer WeiGht 2 lb 10 oz (1.2 kG). (Without BAtterY). BAtterY tYPe.
BAtterY VoLtAGe. ComPAtiBLe BAtteries.
1.3 Ah Li-ion (054-3124-0). 2.6 Ah Li-ion (054-3125-8). BAtterY ChArGer. 1-hour, diagnostic (054-3126-6).
Safety symbols in this Instruction Manual are used to. The world's first completely sealed, easy-to-sterilize drill/driver was designed for clean rooms, medical and pharmaceutical labs, and the electronics industries, meeting the. No air vents and non-porous surface for easy sanitizing; Features a stainless steel (3cr10) chuck; Comes with two 18V 3Ah lithium-ion batteries. The Makita FD02W 12V MAX Cordless Lithium-Ion 3/8 in. Drill Driver Kit is compact in size and able to fit into tool pouches for the tradesman and accommodate users that like a smaller lighter driver drill that will still get the work done. Makita's 12V MAX Lithium-Ion batteries provide longer run time and lower self-discharge. Engineered with a compact and lightweight design, Metabo's BS18 18V 2.0 Ah Cordless Lithium-Ion 3/8 in.
Drill Driver Kit is ideal for working overhead, in small spaces, and for extended periods of time. The tool features the Metabo Quick Removable Chuck for fast, tool-free accessory changes and a spindle with a 1/4 in. Manufacturer's Part Number: #DCK240C2 The DEWALT DCK240C2 Combo Kit is versatile enough to handle most drilling and driving applications. This kit includes a DEWALT DCD771 1/2 in. Drill/Driver and a DCF885 1/4 in. Impact Driver.
Both tools are part of the DEWALT 20-Volt Max system and are compatible with all. Strong, versatile, lightweight and forceful, these 20-Volt compact tools fit into tight spaces and deliver Ample power using brushless motor technology that's engineered to run longer and stay cooler than brushed. Included in this bundle is a 1/2 in. Drill/driver with an all-metal ratcheting chuck and 2-speed settings along with a. Cordless Drill/Drivers - ASCM 18 QX. The highest performance FEIN cordless screwdriver with brushless motor, 4-speed gearbox and interchangeable chuck. 4-speed all-metal gearbox.
Brushless FEIN PowerDrive motor with 30% greater efficiency. Li-ion battery with FEIN SafetyCell technology. A separate communication. Milwaukee Cordless Hammer Drill/Driver Kit, Series: M12, 12 V, Lithium-Ion Battery, 4 Ah Battery Capacity, 1/2 in Chuck, Keyless Chuck, 0 - 22500 bpm, 0 - 400/0 -1700 rpm, 2 Speeds, 350 in-lb Torque, Single Sleeve Ratcheting Metal Clutch, Red? Housing, T-Shaped Handle, 7-3/4 in Overall Length, UL Listed, CSA. The LDX120C Cordless Drill/Driver is the perfect choice for all of your basic DIY duties around your home. It is lightweight and compact, which makes it the ideal tool for working in tight and confined spaces.
The 20-volt max lithium-ion battery and 115 pounds of torque and 650 rpm gives you enough power to drill holes. Adjustable side handle — offers control for heavy-duty drilling. High-power, extended-life 20-volt lithium-ion battery is compatible with ALL IQV20 Series cordless tools (3.0 Ah). PURCHASE OPTIONS. Two Battery Kit: Includes (1) Bare tool, (2) 20V li-ion 3.0 Ah batteries, (1) IQ Charger, (1) Blow–molded case. Several manufacturers are offering “combo kits” that include an impact driver along with a traditional cordless drill, using the same Lithium Ion battery (as someone with a cabinet full of different chargers and batteries, I say battery standardization is a great thing). When I compare the prices of these tools.
DEWALT DCK240C2 20v Lithium Drill Driver/Impact Combo Kit for $199.00 at Amazon.com. Shop Lithium-Ion Cordless Drill Driver Powerful Screwdriver 18V 0-550 rpm 1300mAh 1.55kg 3-5h Battery Life with 15pc Drill and Bit Set. Free delivery on eligible orders of £20 or more. Results 1 - 30 of 40.
Festool Drills and Festool Drivers including festool power drill T15+3 at Highland Woodworking, authorized Festool Dealer. The Festool Centrotec Installer's Set includes a huge collection of Festool drill and driver bits. Festool Drills and Drivers offer an.
Festool Lithium Ion Cordless Drill - 18V. The Rockwell 20V MaxLithium Brushless Drill & Driver delivers more power, runtime, and longer motor life over a traditional drill/driver. Order yours today. The DEWALT® 20V MAX. Lithium-Ion Compact Drill/Driver / Impact Driver Combo Kit features two powerful tools in one durable carrying case. The set comes with two batteries and one charger, so you can use the tools right away.
The drill/driver comes with two speed settings, one that reaches up to 600 RPM and the faster. The DCK283D2 20V MAX. XR Lithium Ion Brushless Compact Drill / Driver and Impact Driver Combo Kit has a powerful motor to deliver maximum runtime. Features a lightweight, compact design to fit in tight spaces. 3-mode LED light gives users visibility in dark spaces.
Cordless Power Tool Kits Runnings. Today on Amazon you can grab this Black & Decker LD120VA 20-Volt MAX Lithium-Ion Drill / Driver Kit for only $39.99. This is a GREAT deal since it's usually around $52! Lithium Ion Battery – Always Ready, holds a charge up to 18 months; By providing extra level of control, the 24 postion clutch prevents.yqariti.
Solucionario serway cap 7.1.7Energy of a SystemCHAPTER OUTLINE7.2 Work Done by a Constant Force7.3 The Scalar Product of TwoVectors7.4 Work Done by a Varying Force7.5 Kinetic Energy and the Work-Kinetic Energy Theorem7.6 Potential Energy of a System7.7 Conservative andNonconservative Forces7.8 Relationship Between Conserva-tive Forces and Potential Energy7.9 Energy Diagrams and theEquilibrium of a SystemANSWERS TO QUESTIONSQ7.1 (a) Positive work is done by the chicken on the dirt.(b) The person does no work on anything in the environ-ment. Perhaps some extra chemical energy goes throughbeing energy transmitted electrically and is convertedinto internal energy in his brain; but it would be veryhard to quantify “extra.”(c) Positive work is done on the bucket.(d) Negative work is done on the bucket.(e) Negative work is done on the person’s torso.Q7.2 Force of tension on a ball moving in a circle on the endof a string. Normal force and gravitational force on anobject at rest or moving across a level floor.Q7.3 (a) Tension (b) Air resistance (c) The gravitational force does positive work in increasingspeed on the downswing.
It does negative work in decreasing speed on the upswing.Q7.4 Each dot product has magnitude 1⋅1⋅cosθ where θ is the angle between the two factors. Thus for(a) and (f) we have cos 0 = 1. For (b) and (g), cos 45° = 0.707. For (c) and (h), cos 180° = −1. For(d) and (e), cos 90° = 0.
The assembled answer is a = f b = g d = e c = h.Q7.5 The scalar product of two vectors is positive if the angle between them is between 0 and 90°. Thescalar product is negative when 90 180° ° a = b(iii) Now think about the product of mass times height. Answer: c b = d aQ7.20 There is no violation.
Choose the book as the system. You did work and the Earth did work on thebook. The average force you exerted just counterbalanced the weight of the book. The total workon the book is zero, and is equal to its overall change in kinetic energy.Q7.21 In stirring cake batter and in weightlifting, your body returns to the same conformation after eachstroke.
During each stroke chemical energy is irreversibly converted into output work (and inter-nal energy). This observation proves that muscular forces are nonconservative.154 Chapter 71379407ch07p153-174.indd 1541379407ch07p153-174.indd 154 12/2/06 1:46:45 PM12/2/06 1:46:45 PM.Energy of a System 155Q7.22 A graph of potential energy versus position is a straight horizontal line for a particle in neutralequilibrium.
The graph represents a constant function.Q7.23 (c) The ice cube is in neutral equilibrium. Its zero acceleration is evidence for equilibrium.Q7.24 The gravitational energy of the key-Earth system is lowest when the key is on the floor letter-side-down.
The average height of particles in the key is lowest in that configuration. As describedby F = −dUրdx, a force pushes the key downhill in potential energy toward the bottom of a graphof potential energy versus orientation angle. Friction removes mechanical energy from the key-Earth system, tending to leave the key in its minimum-potential energy configuration.Q7.25 Gaspard de Coriolis first stated the work-kinetic energy theorem. Jean Victor Poncelet, an engineerwho invaded Russia with Napoleon, is most responsible for demonstrating its wide practicalapplicability, in his 1829 book Industrial Mechanics. Their work came remarkably late comparedto the elucidation of momentum conservation in collisions by Descartes and to Newton’sMathematical Principles of the Philosophy of Nature, both in the 1600’s.SOLUTIONS TO PROBLEMSSection 7.2 Work Done by a Constant ForceP7.1 (a) W F r= = ( )( ) =∆ cos.
Cos.θ 16 0 2 20 25 0 31 9N m J°(b), (c) The normal force and the weight are both at 90° to the displacement in any time interval.Both do 0 work.(d) W∑ = + + =31 9 0 0 31 9.J JP7.2 (a) W mgh= = ×( )( )( ) = ×− −3 35 10 9 80 100 3 28 105 2.J J(b) Since R mg=, Wair resistance J= − × −3 28 10 2.P7.3 METHOD ONELet φ represent the instantaneous angle the rope makes with the vertical as it is swinging up fromφi = 0 to φf = °60. In an incremental bit of motion from angle φ to φ φ+ d, the definition ofradian measure implies that ∆r d= ( )12 m φ. The angle θ between the incremental displacementand the force of gravity is θ φ= +90°. Then cos cos sinθ φ φ= +( )= −90°. The work done by thegravitational force on Batman isW F dr mg dmgif= = −( )( )= −∫ ∫cos sinθ φ φφφ12060m°112 80 9 8 12060m kg m s m2( ) = −( )( )( ) −∫ sin.φ φd°ccoscos.φ( )= −( )( ) − +( ) = −°060784 12 60 1 4 70N m ° ××103JMETHOD TWOThe force of gravity on Batman is mg = ( )( )=80 9 8 784kg m s N2. Only his verticaldisplacement contributes to the work gravity does.
His original y-coordinate below the treelimb is −12 m. His final y-coordinate is −( ) ° = −12 60 6m mcos. His change in elevation is− − −( ) =6 12 6m m m.
The work done by gravity isW F r= = ( )( ) = −∆ cos cos.θ 784 6 180 4 70N m kJ°FIG. P7.31379407ch07p153-174.indd 1551379407ch07p153-174.indd 155 12/2/06 1:46:45 PM12/2/06 1:46:45 PM.156 Chapter 7.P7.4Yes. Object 1 exerts some forward force on object 2 as they move through the same displacement.By Newton’s third law, object 2 exerts an equal-size force in the opposite direction on object 1.
InW = F∆rcos θ, the factors F and ∆r are the same, and θ differs by 180°, so object 2 does −15.0 Jof work on object 1. The energy transfer is 15 J from object 1 to object 2, which can be countedas a change in energy of −15 J for object 1 and a change in energy of +15 J for object 2.Section 7.3 The Scalar Product of Two VectorsP7.5 A B i j k i j k⋅ = + +( )⋅ + +( )A A A B B Bx y z x y zˆ ˆ ˆ ˆ ˆ ˆA B i i i j i k⋅ = ⋅( )+ ⋅( )+ ⋅( )+A B A B A BAx x x y x zˆ ˆ ˆ ˆ ˆ ˆyy x y y y zz xB A B A BA Bˆ ˆ ˆ ˆ ˆ ˆˆj i j j j kk⋅( )+ ⋅( )+ ⋅( )+ ⋅ˆˆ ˆ ˆ ˆ ˆi k j k kA B( )+ ⋅( )+ ⋅( )⋅ = +A B A BA B A Bz y z zx x y yy z zA B+P7.6 A = 5 00.; B = 9 00.; θ = °50 0.A B⋅ = = ( )( ) =ABcos. Cos.θ 5 00 9 00 50 0 28 9°P7.7 (a) W F x F yx y= ⋅ = + = ( )( ) ⋅ + −( )F r∆ 6 00 3 00 2 00 1.N m 000 16 0( ) ⋅ =N m J.(b) θ =⋅⎛⎝⎜⎞⎠⎟ =( ) + −− −cos cos.1 12166 00 2 00F r∆∆F r (( )( ) ( ) +( )( )= °2 2 23 00 1 0036 9.P7.8 We must first find the angle between the two vectors.
It is:θ = − − − =360 118 90 0 132 20 0° ° ° ° °.ThenF v⋅ = = ( )( ) °Fvcos. Cos.θ 32 8 0 173 20 0N m sor F v⋅ =⋅=5 33 5 33.N msJsP7.9 (a) A i j= −3 00 2 00. ˆB i j= −4 00 4 00.
ˆ θ =⋅=+( )( )=− −cos cos.1 1 12 0 8 0013 0 32 01A BAB11 3. °(b) B i j k= − +3 00 4 00 2 00.
ˆA i j= − +2 00 4 00. ˆ cos.θ =⋅=− −( )( )A BAB6 00 16 020 0 29 0θ = 156°(c) A i j k= − +ˆ. ˆ2 00 2 00B j k= +3 00 4 00. ˆ θ =⋅⎛⎝⎜⎞⎠⎟ =− +⋅− −cos cos.1 1 6 00 8 009 00 25A BAB.082 3⎛⎝⎜⎞⎠⎟ = °FIG. P7.81379407ch07p153-174.indd 1561379407ch07p153-174.indd 156 12/2/06 1:46:46 PM12/2/06 1:46:46 PM.Energy of a System 157P7.10 A B i j k i j k− = + −( )− − + +( )3 00 2 00 5 00. ˆA B i j kC A B j− = − −⋅ −( )= −4 00 6 002 00 3 0. 00 4 00 6 00 0 2 00 18 0ˆ.
ˆ.k i j k( )⋅ − −( )= + −( )+ +( ) 16 0.P7.11 Let θ represent the angle between A and B. Turning by 25° makes the dot product larger, so theangle between C and B must be smaller. We call it θ − 25°. Then we haveA 5 cos θ = 30 and A 5 cos (θ − 25°) = 35Then A cos θ = 6 and A (cos θ cos 25° + sin θ sin 25°) = 7Dividing, cos 25° + tan θ sin 25° = 7ր6 tan θ = (7ր6 − cos 25°)րsin 25° = 0.616θ = 31.6°.
Then the direction angle of A is 60° − 31.6° = 28.4°Substituting back, A cos 31.6° = 6 so A = 7.05 m at 28.4°Section 7.4 Work Done by a Varying ForceP7.12 F xx = −( )8 16 N(a) See figure to the right(b) Wnetm N m N=−( )( )+( )( )= −2 00 16 021 00 8 002.112 0. JP7.13 W Fdxif= =∫ area under curve from xi to xf(a) xi = 0 xf = 8 00.
MW = area of triangle ABC AC=⎛⎝⎞⎠×12altitude,W0 8128 00 6 00 24 0→ =⎛⎝⎞⎠× × =.m N J(b) xi = 8 00. MW = area of ∆CDE CE=⎛⎝⎞⎠×12altitude,W8 10122 00 3 00 3 00→ =⎛⎝⎞⎠×( )× −( ) = −.m N J(c) W W W0 10 0 8 8 10 24 0 3 00 21 0→ → →= + = + −( ) =. JP7.14 W d x y dxif= ⋅ = +( ) ⋅∫ ∫F r i j i4 305ˆ ˆ ˆNm4 0 4250 005 205N m N m Jm m( ) + = ( ) =∫ xdxx.FIG. P7.131379407ch07p153-174.indd 1571379407ch07p153-174.indd 157 12/2/06 1:46:47 PM12/2/06 1:46:47 PM.158 Chapter 7P7.15 W F dxx= ∫and W equals the area under the Force-Displacement curve(a) For the region 0 5 00≤ ≤x. M,W =( )( )=3 00 5 0027 50.N mJ(b) For the region 5 00 10 0.≤ ≤x,W = ( )( ) =3 00 5 00 15 0.N m J(c) For the region 10 0 15 0.≤ ≤x,W =( )( )=3 00 5 0027 50.N mJ(d) For the region 0 15 0≤ ≤x.W = + +( ) =7 50 7 50 15 0 30 0.J JP7.16 (a) Spring constant is given by F kx=kFx= =( )( )=2300 400575NmN m.(b) Work = = ( )( ) =F xavg N m J12230 0 400 46 0.P7.17 kFyMgy= = =( )( )×= ×−4 00 9 802 50 1.NmN m(a) For 1.50 kg mass ymgk= =( )( )×=1 50 9 801 57 100 9383. Cm(b) Work =122kyWork = × ⋅( ) ×( ) =−121 57 10 4 00 10 1 253 2 2.N m m J.P7.18 In F = −kx, F refers to the size of the force that the spring exerts on each end.