4Net Work The sum of all the work done by all forces is If the person lifts the box with the same force as the weight of box, the box will move at constant speed. Net work is zero. Why?
5Perpendicular Force and Work A car is traveling on a curved highway. The force due to friction points toward the center of the circular path.How much work does the frictional force do on the car?
6Example:A rope inclined upward at 45o pulls a 15kg suitcase through the airport. The tension on the rope is 85N.a) How much work does the tension do if the suitcase is pulled 50m?b) How much work does the normal force do on suitcase?c) If uk= 0.25 between the suitcase and floor, find the net work done on the suitcase.
7Force vs Distance Graph Find the work done by the force from 0-6.0m
8ENERGYEnergy isWork can also be definedEnergy is a
9Work-Energy theoremIf the net work done on an object
11Example:A 2200 kg truck encounters an average friction force of 785N at interstate speeds. Suppose the truck accelerates from 25m/s to 35m/s over a distance of 350m. Determine the amount of force generated by the truck’s drive-train in order to produce this result.
12A paratrooper fell 370m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1m deep, but survived with only minor injuries. Assuming the paratrooper‘s mass was 80kg and his terminal velocity was 50m/s, estimate __________.a) the net work done on the paratrooper as the crater was created (beginning with his striking the snow)b) the work done by the snowc) the average force exerted on him by the snow to stop himd) the work done on him by air resistance from plane to initial contact with snow. DO NOT assume terminal v for entire fall.Part d) Wg + Wair = KE
13A 230-kg load is lifted 18.0m vertically upward with an acceleration of a = 0.180g by a single cable.Determine the __________.a) tension in the cableb) net work done on the loadc) work done by the cable on the loadd) work done by gravity on the loade) final speed of the load assuming it started from rest.
18As a spring is stretched or compressed FmaxxBut since spring force
19Force versus Stretch of 3 different Springs What is the significance of the slopes of the 3 graphs?
20EXAMPLEA block of mass kg is free to move on a horizontal surface where μ = As shown in the diagram below, the block is placed against a spring with constant k = 83.0 N/m. The spring is compressed 0.20 m and then the block is released. Find the speed of the block just as it leaves the spring.
21EXAMPLE: A 350-g mass is hung from a 32 EXAMPLE: A 350-g mass is hung from a 32.5cm long vertical spring causing its length to increase to 41.75cm.Determine the elastic potential energy of the system after the mass has stretched the spring and reached equilibrium.Calculate the change in total potential energy of the system at this point. Refer to equilibrium as zero point.Assume someone pulls the mass down, stretching the spring an additional 9.25cm and releases the mass.c) Determine the speed of mass when it returns to the original equilibrium point.
22Conservative & Non-Conservative Forces A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken…only matters on initial and final positions. ie; Gravity & spring force.A non-conservative force is a force with the property that the work done in moving a particle between two points DOES depend on the path taken. ie; frictionFor example, moving ball along the vertical path or curvey path still results in the same PEg gained or work done by gravity. However the work done by air friction would be different for the 2 different paths.
23Conservation of Mechanical Energy The total energyEnergy isIf friction is present
26Example1A kid throws a 4.90N rock off a bridge that is 25.0m above the water. The initial velocity is 13.0m/s at 0°.Find the rock's speed as it hits the water.Example2A girl with mass 28kg climbs a ladder to the top of a slide, 4.8m high. She slides down the slide and reaches a speed of 3.2m/s at the bottom. Determine the work done by friction.
27Example3A spring with constant k = 2500 N/m is mounted vertically and then compressed 10.0 cm. A 250 gram ball is placed on top of the spring and then the ball and spring are released. At what height above equilibrium will the ball be moving at 4.0m/s?Example4A block of wood with mass 0.50 kg is initially at rest on an incline of 30o where μk = 0.30. A person gives the block a quick push up the incline, parallel to surface, and lets go. The block slides a total distance of 2.0 m from beginning to end before stopping. Find the speed of the block at release.½ kx2 + mg(-0.1) = mgh + ½ mv21/2kx^2 + - mgh = 1/2mv^2 + mgh
28Example5An engine moves a boat through the water at a constant speed of 15m/s. The engine must develop a thrust of 6.0kN to balance the force of drag from the water acting on the hull. Determine the power output of the engine. Example6A dart gun has a spring with a spring constant of N/m and is positioned 3.0m above the floor. A 35.0-g dart depresses the spring 6.50 cm and is locked into place until the trigger releases it. The gun is pointed fired horizontally. How high above the ground will the speed of the dart be 8.4m/s?