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**preview**shows half of the first page. to view the full**2 pages of the document.**7-1 Work Done by a Constant Force

● Force in the Direction of Displacement

○The greater the force, the greater the distance, the greater the work

○Work: W= Fd, when a constant force is in the direction of displacement

(N*m, J)

○Scalar quantity; a large force over a small distance is the same as small

force over a large distance

○1 J= 1 N*m= 1 (kg*m/s2)*m= 1 kg *m2/s2

○Work: W= F/d when the distance is vertical

○1 J of work lifts a gallon of milk about an inch

○W=0 if d=0 regardless of the size of the force

● Force at an Angle to the Displacement

○When F is at angle to the horizontal that is in the direction of motion, work is

the component of force in the direction of the displacement times the

magnitude of the displacement

○Work= (Fcos )d= Fdcos ; unit= J

○When the angle is 90 (when force and displacement are at right angles) the

work done by force F = 0

○The displacement equals dcos + dsin

■ Work is the component of force in the direction of the displacement

times the magnitude of displacement

■ Work is the component of displacement in the direction of the force

times the magnitude of the force

■ Mean the same thing; is an angle b/t the force vector and the

displacement vector placed tail-to-tail

○Dot product- the magnitude of one vector (in this case the force vector)

times the magnitude of the second vector (in this case the displacement

vector) times the cosine of the angle between them

● Negative Work and Total Work

○Work depends on the angle b/t the force, F, and the displacement (or

direction of motion), d which gives rise to three possibilities

■ Work is positive if the force has a component in the direction of

motion (-90 < < 90)

■ Work is zero if the force has no component in the direction of

motion ( + 90)

■ Work is negative if the force has a component opposite to the

direction of motion (90 < <270)

○When more than one force acts on an object the total work is the sum of the

work done by each separately

○Total work can also be calculated by first performing a vector sum of all the

forces acting on an object and then using the definition of work W= Ftotal

dcos

● 7-2 Kinetic Energy and the Work- Energy Theorem

● In general whenever the total work done on an object is positive, its speed

increases; when the total work done on an object is negative, its speed

decreases

● Wtotal= 1/2mvf2- 1/2mvi2

● Kinetic energy- the energy an object has due to its motion; KE= 1/2mv2;

unit= J

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