WORK

As far as Physics is concerned… When a force is applied to an object, over a distance, then work is done on that object.

Simply put… Work is done when a force is applied to move an object.

Work-Energy Relationship The net work done in a body is equivalent to Kinetic energy (Work-Kinetic Energy Theorem). This allows us to think of kinetic energy as the work an object can do while it changes speed.

Is Work Being Done? A boy pushes a lawn mower. – Yes The mower is being pushed by the boy. Energy is transferred in the process. The displacement of the object and the force are in the same direction.

Is work being done? A man digging a hole. Yes Lifting and moving the soil with the shovel should be thought of as work.

Is work being done? A waiter serving his customers. Yes and No. As he lifts the dishes he is doing work on them. As he holds them –no work is done Even if he is moving the dishes horizontally at constant speed, no work is done. More about that later…AND when he places them back down, negative work is done. More about that later…

Is work being done? A man pushes against a chair, but has not yet caused the chair to move. No –Not Yet. He has not done any work until the chair moves.

Is Work Being Done?

Yes

Is Work Being Done?

Yes

Is Work Being Done?

Yes

Is Work Being Done?

Yes

Work is a scalar quantity and has positive or negative displacement. Work is positive when the component of the force is the same direction as the displacement. For example, when you lift a box, the work done by the force you exert on the box is positive because the force is upward, in the same direction as the displacement. Physics Text (pg 156) - Serway/ Faughn

Work is negative when the force is in the direction opposite the displacement. For example, the force of kinetic friction between a sliding box and the floor is opposite the displacement of the box, so the work done by the force of friction on the box is negative. Physics Text (pg 156) - Serway/ Faughn

In order for positive work to occur, the force and displacement must be in the same direction.

Assume you forgot to set the parking break and your car starts rolling down a hill.  You try in vain to stop it by pulling as hard as you can on the bumper, but the car keeps on moving forward.  You exert a force on the car opposite to the direction of travel.  The distance traveled in the direction of the force is negative, you do negative work on the car.  But the car is pulling you in the direction of travel with a force of equal magnitude (Newton's third law).  The car is doing positive work on you.

Is work done slowing the object or increasing the objects speed? If the net work is positive, the object speeds up and work is done on the object. If the net work is negative, the object slows down and work is done by the object on something else. Physics Text (pg 157)- Serway/ Faughn

Physics Text (pg 156) - Serway/ Faughn

The road exerts a friction force on a speeding car skidding to a stop. For each of the following, indicate whether the work done on the second object will have a positive or negative value. The road exerts a friction force on a speeding car skidding to a stop. Work has a negative value because the work caused the moving car to slow down.

A rope exerts a force on a bucket as the bucket is raised up a well.

The work done by the force on the bucket is positive because the force is upward, in the same direction as the displacement.

Air exerts a force on a parachute as the parachutist falls to earth.

The work done by the air on the parachute is negative since it slows the parachute and opposes the motion.

Work Sign tips: Force is in direction of motion + work Force opposes motion - work Force is 90o to motion no work Object not in motion no work

Is Work done while carrying an object at constant speed? NO – The force acting on the object must be in the same, or opposite direction to the object’s displacement or at some angle less that 90o (perpendicular to the object).

http://hyperphysics.phy-astr.gsu.edu/hbase/work2.html

When you put it back down, you are still exerting an upward force to keep it from falling, but the displacement is downward and hence the work you do on the object is negative.

In Summary… When a force moves a body on which it acts in the direction of the force, we say it has done work.

Calculating Work W = Fd F = W/d d = W/F The work done by a force is found by multiplying the force by the distance it has moved the body in the direction of the force. Equations: W = Fd F = W/d d = W/F Units of Work: Joules 1J = 1 Newton-Meters Also Foot-Pound Joule = 0.737562149 foot pounds

Sample Work Calculations How much work is done when a 50N crate is pushed along a floor a distance of 10m? W = fd = (50N)(10m) = 500 N.m = 500 J

If a neighbor pushes a lawnmower four times as far as you do but exerts only half the force, which one of you does more work and by how much? Your neighbor does twice as much work as you do.

Let’s say that you cut 5m of your lawn with a force of 12 N and your neighbor cuts 20m of his lawn with a force of 6 N. W = Fd Your work = (12 N)(5m) = 60 N.m = 60 J Your Neighbor’s work = (6 N)(20m) = 120 N.m = 120 J

A student’s backpack weighs 30N A student’s backpack weighs 30N. She lifts it from the floor to a shelf 1.5m high. How much work is done on the pack full of books. Since the backpack weighs 30N, the force needed to lift it off the ground is equivalent to the 30N it weighs. (Lifting it requires a force equivalent to the force of gravity attracting it to the Earth.) F = 30N d = 1.5m W = F x d = (30N)(1.5m) = 45N.m = 45 J

A carpenter lifts a 45 kg beam 1.2m. How much work is done on the beam? First convert mass to weight. w = mg (45kg)(9.8m/s2) = 441N Next: W = fd = (441N)(1.2m) = 529.2 N.m = 529.2 J

Calculating work if the force is applied at an angle.