Unit 4 - Work, Energy, Power and Calculus

What is the definition of Work done by a constant force?

What is Work’s quantity, symbol, and UNITS???

Def: When a force F causes an object to be displaced by an amount d, the work done by F is equal to the dot product of F and d.

—> W = F⋅d = Fdcosθ

• Work is a SCALAR (work can be NEGATIVE!!!)

• Units = JOULES

• Symbol is just W

What are the 3 different directions of work, and what would work be in each?

1. Work to the right with an angle 0 <= θ <= 90

   1. W > 0

2. Work directly upwards (cos90 = 0)

   1. W = 0

3. Work to the left with an angle 0 <= θ <= 180

   1. W < 0 (WORK CAN BE NEGATIVE!!!)

What kind of work with friction ALWAYS produce?

Friction will ALWAYS produce negative work

What is the formula for Variable Work?

Look at picture

x_{a =} x_i

x_b = x_f

What MUST you remember about the derivatives and integrals of e, and ln?

The derivative of y = e^x does NOTHING

• the derivative of e^g(x) just means power rule —> = g’(x)e^g(x)

The integral of e^x does nothing but remember +c

|

The derivative of y = lnx is just y’ = 1/x (inverses anything)

• The derivative of ln(g(x)) is CHAIN RULE beacause ln is a function!!!!

The integral of 1/x is ln |x| + c (ABS VALUE!!!)

What is Hooke’s Law?

Hooke’s Law: The force exerted by a spring (F_s) is directly proportional to the extension or compression of the spring. (Spring gives Opposite reaction force to force applied on it)

F_s = -kx

(k = spring constant, x = disp, units are Nm)

In Hooke’s Law, when will F_s be pos and neg? Why?

F_{s =} force of spring = -kx

F_s is positive when you compress the spring cus x is negative

F_s is negative when you pull the spring cus in F_s = -kx, x is positive

How do you model the Hooke’s Law equation with calculus?

Why does the negative go away?

the reason why the negative disappears is because the the work of the spring is OPPOSITE to the work it takes to affect the Hooke’s Law Eq.

THINK:

The applied Work we give affects the equation F = -kx

—> the Work of the spring is the opposite of resulting Spring Force created by the Force we put in

What is Linear Mass Density?

We know that P = density = m/v

For Linear Mass Density, we have the symbol as lambda, and if the mass is distributed along length L, then λ = M/L (units are kg/m)