Ch 07: Work & EnergyWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Work Done by a Constant Force

Practice: You pull a 5-kg object vertically up with a constant 100-N for 2 m. How much work do you do?

Example #1: Work by a Constant Force

Practice: A water skier is pulled by a boat (shown). Both move north with a constant 10 m/s. The tension on the rope is 150 N, and makes an angle of 53° with the horizontal. How much work is done by the rope in 5 seconds?

Concept #2: Zero Work, Negative Work & Work by Friction

Practice: A 3-kg box sits on a level surface. The box-surface coefficient of friction is 0.4. You pull on the box with 20 N at 37o above the horizontal for 5 meters. Calculate the work done by: 

(a) you;
(b) friction;
(c) weight; and
(d) normal.

How much energy was dissipated? Where did this energy “go” ?

Additional Problems
A 50 kg crate is at rest on the floor, and you need to move it across a room. The floor you are moving it across has a coefficient of static friction of 0.5 and a coefficient of kinetic friction of 0.3. In order to move it across the room, first you need to move it 5 m to the left, then 7 m forward, then finally 3 m to the right. How much work do you do on the box in order to move it across the room?
An object moves along a floor with some coefficient of kinetic friction. Which of the following statements is true? a. The work done by friction is positive, and doesn’t depend upon the path taken b. The work done by friction is positive, and does depend upon the path taken c. The work done by friction is negative, and doesn’t depend upon the path taken d. The work done by friction is negative, and does depend upon the path taken  
A fisherman reels in 12.0 m of line while pulling in a fish that exerts a constant resisting force of 25.0 N.If the fish is pulled in at constant velocity, how much work is done on it by the tension in the line?
You and three friends stand at the corners of a square whose sides are 8.0 m long in the middle of the gym floor, as shown in the figure . You take your physics book and push it from one person to the other. The book has a mass of 1.6 kg , and the coefficient of kinetic friction between the book and the floor is k= 0.26.The book slides from you to Beth and then from Beth to Carlos, along the lines connecting these people. What is the work done by friction during this displacement?You slide the book from you to Carlos along the diagonal of the square. What is the work done by friction during this displacement?You slide the book to Kim who then slides it back to you. What is the total work done by friction during this motion of the book?Is the friction force on the book conservative or nonconservative?Explain.
A 30.0-kg packing crate in a warehouse is pushed to the loading dock by a worker who applies a horizontal force. The coefficient of kinetic friction between the crate and the floor is 0.20. The loading dock is 15.0 m southwest of the initial position of the crate.If the crate is pushed 10.6 m south and then 10.6 m west, what is the total work done on the crate by friction?If the crate is pushed along a straight-line path to the dock, so that it travels 15.0 m southwest, what is the work done on the crate by friction?
A 0.60-kg book slides on a horizontal table. The kinetic friction force on the book has magnitude 1.6 N .How much work is done on the book by friction during a displacement of 2.7 m to the left?The book now slides 2.7 m to the right, returning to its starting point. During this second 2.7-m displacement, how much work is done on the book by friction?What is the total work done on the book by friction during the complete round trip?On the basis of your answer to part C, would you say that the friction force is conservative or nonconservative?
A large crate sits on the floor of a warehouse. Paul and Bob apply constant horizontal forces to the crate. The force applied by Paul has magnitude 51.0 N and direction 61.0 south of west.How much work does Pauls force do during a displacement of the crate that is 12.0 m in the direction 22.0 east of north.
On a farm, you are pushing on a stubborn pig with a constant horizontal force with magnitude 30.7 N and direction 37.0+x counterclockwise from the +x-axis.How much work does this force do during a displacement of the pig that is =(5.00 m)?How much work does this force do during a displacement of the pig that is =-(6.00 m)? How much work does this force do during a displacement of the pig that is =-(2.00 m)+(4.00 m)?
A child is pulling a wagon down the sidewalk. For 9.0 m the wagon stays on the sidewalk and the child pulls with a horizontal force of 23 N . Then one wheel of the wagon goes off on the grass so the child has to pull with a force of 38 N at an angle of 13 to the side for the next 5.5 m . Finally the wagon gets back on the sidewalk so the child makes the rest of the trip, 13.0 m , with a force of 23 N .How much total work did the child do on the wagon?
A boat with a horizontal tow rope pulls a water skier. She skis off to the side, so the rope makes an angle of 15.015.0 with her direction of motion, and then continues in a straight line. The tension in the rope is 180 N.</noba>How much work is done on the skier by the rope during a displacement of 300 m?
Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.8×106 N , one an angle 15 west of north and the other an angle 15 east of north, as they pull the tanker a distance 0.76 km toward the north.What is the total work they do on the supertanker?
Two men, Joel and Jerry, push against a concrete wall that is 3 meters thick. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. How does the work that Joel does on the wall compare to the work that Jerry does on the wall?A) Both men do positive work, but Jerry does 50% more work than Joel.B) Both men do positive work, but Joel does 25% more work than Jerry.C) Both men do positive work, but Joel does 50% more work than Jerry.D) Both men do positive work, but Joel does 75% more work than Jerry.E) Neither of them does any work.
The three ropes shown in the birds-eye view of the figure are used to drag a crate 3.6 m across the floor. How much work is done by each of the three forces?
Using a cable with a tension of 1310 N, a tow truck pulls a car 5.00 km along a horizontal roadway. How much work does:(a) the cable do on the car if it pulls horizontally(b) the cable do on the car if it pulls at 35.0° above the horizontal(c) gravity do on the car in part A(d) the cable do on the tow truck if it pulls horizontally(e) the cable do on the tow truck if it pulls at 35.0° above the horizontal
A 2400 N crate rests on the floor. How much work is required to move it at constant speed:(a) 4.1 m along the floor against a drag force of 240 N(b) 4.1 m vertically
An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.30 m deep, but survived with only minor injuries. Assuming the pilots mass was 88.0 kg and his terminal velocity was 46.0 m/s, estimate the:(a) work done by the snow in bringing him to rest (b) force exerted on him by the snow to stop him(c) work done on him by air resistance as he fell
A shopper in a supermarket pushes a cart with a force of 35.0 N directed at an angle of 25.0° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed. (a) Find the work done by the shopper on the cart as she moves down a 50.0-m-long aisle. (b) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the friction force doesn’t change, would the shopper’s applied force be larger, smaller, or the same?(c) What about the work done on the cart by theshopper?
A raindrop of mass 3.35 x 10-5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. As it falls 100 m, what is the work done on the raindrop (a) by the gravitational force and (b) by air resistance?
  ↵An object moves in the xy plane in Figure P7.43 and experiences a friction force with constant magnitude 3.00 N, always acting in the direction opposite the object’s velocity. Calculate the work that you must do to slide the object at constant speed against the friction force as the object moves along (a) the purple path O to Ⓐ followed by a return purple path to O, (b) the purple path O to Ⓒ followed by a return blue path to O, and (c) the blue path O to Ⓒ followed by a return blue path to O. (d) Each of your three answers should be nonzero. What is the significance of this observation?