# Work Done by a Constant Force

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Work Done by a Constant Force
The definition of work

Work for Force at an Angle
If the force is at an angle to the displacement:

Negative and Positive Work
The work done may be

Net 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?

Perpendicular 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?

Example: 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.

Force vs Distance Graph
Find the work done by the force from 0-6.0m

ENERGY Energy is Work can also be defined Energy is a

Work-Energy theorem If the net work done on an object

A) Kinetic Energy Kinetic Energy is the

Example: 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.

A 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 snow c) the average force exerted on him by the snow to stop him d) 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

A 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 cable b) net work done on the load c) work done by the cable on the load d) work done by gravity on the load e) final speed of the load assuming it started from rest.

B) Gravitational Potential Energy

Springs Springs can exert forces on objects. Pull on a spring, it pulls back. Push on a spring, it pushes back.

Force exerted by a spring is given by Hooke’s Law:

C) Elastic Potential Energy

As a spring is stretched or compressed
Fmax x But since spring force

Force versus Stretch of 3 different Springs
What is the significance of the slopes of the 3 graphs?

EXAMPLE A 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.

EXAMPLE: 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.

Conservative & 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; friction For 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.

Conservation of Mechanical Energy
The total energy Energy is If friction is present

Einitial = Efinal

Power Involves the rate

Example1 A 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. Example2 A 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.

Example3 A 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? Example4 A 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 mv2 1/2kx^2 + - mgh = 1/2mv^2 + mgh

Example5 An 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.  Example6 A 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?

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