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Work. AP Physics C Mrs. Coyle. Work. The work done on an object by an external constant force: W = F r cos q  is the angle between the displacement, r, and the force F. Products of two Vectors A and B. Dot Product: A·B =A B cos q Scalar Cross Product:

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Work

Work

AP Physics C

Mrs. Coyle


Work

Work

  • The work done on an object by an external constant force:

    W = Frcosq

  •  is the angle between the displacement, r, and the force F.


Products of two vectors a and b

Products of two Vectors A and B

  • Dot Product:

    • A·B =A B cos q Scalar

  • Cross Product:

    • AxB = AB sin q Vector


Work is a dot product

Work is a dot product

  • Work is the dot product of Force and displacement.

    W= F·r


Units of work

Units of Work

  • Is a scalar quantity.

  • Unit: Joule1 J = 1 N∙m

  • James Prescott Joule, English, 19thCentury

  • Other units of work:

    • British system:

      • foot-pound

    • cgs system:

      • erg=dyne ·cm

    • Sub-atomic level:

      • electron-Volt (eV)


Meaning of sign of work

Meaning of Sign of Work

When the work done by an external force onto the system is:

+ : the system gains energy

- : the system loses energy


Work

  • When the force is in the direction of the

    displacement, =0o:

    cos 0= 1 => W= F r and work is positive

Which force acting on the sled does positive work?


Work

When the force acts opposite to the direction of

the displacement, =180o:

cos 180o = -1 => W= F r and work is negative

Which force acting on the sleddoes negative work?


Work

When the force acts perpendicular to the

displacement,

then the work done by that force is zero.

What force(s) acting on the sled does no work?


Question

Question

  • Does the centripetal force do work?


Example 1

How much work was done by the 30N applied tension force to move the 6kg box along the floor by 20m? (A: 300J)

How much work did the weight do in the same case?

If µ=0.2, how much work did the friction do? (Hint: Use Fxnetto calculate N)(A: -136J)

Example 1


Work done by resultant

Work done by Resultant

W= W1+ W2+ Wn

Since work is a scalar, the net work done by

a resultant force is equal to the sum of the

individual works done by each individual

force acting on the object.


Work is the area under an f vs d graph

Work is the area under an F vs d graph.


Work done by a variable force

Work Done by a Variable Force

  • For a small displacement, Dx, W ~ FDx

  • Over the total displacement:


Work done by a variable force1

Work Done by a Variable Force

  • The work done is equal to the area under the curve.


Work

Work

W = FDr cos q

W =  F(x) dx

W = F • dr


Example 2 work by a variable force

Example 2 – Work by a Variable Force

The force acting on a particle is F(x)= (9x2 +3) N.

Find the work done by the force on the particle as it moves it from x1 =1.5m to x 2=4m.

Ans: 199 J


Example 3 work as dot product of vectors

Example 3 Work as dot product of vectors

A particle is pushed by a constant force of

F=(4i +5j)N and undergoes a displacement of

Dr= (3i+ 2j)m.

Find the work done by the force.

Ans: (12 +10)J= 22J (Scalar Quantity)


Hooke s law

Hooke’s Law

Force exerted by spring: Fs = - kx

  • equilibrium position is x = 0

  • k : spring constant (force constant) (k increases as stiffness of the spring increases)


F s is a r estoring force

Fs is a Restoring Force

  • because it always acts to bring the object towards equilibrium

  • the minus sign in Hooke’s law indicates that the Fs always acts opposite the displacement form equilibrium.


Work done by a spring

Work Done by a Spring


Example 16

Example #16

An archer pulls her bowstring back 0.4m by exerting a force that increases uniformly from 0 to 230N.

  • What is the equivalent spring constant of the bow?

  • How much work does the archer do in pulling the bow?

    Ans: a) 575N/m, b) 46.0J


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