Physics 101: Lecture 13

Physics 101: Lecture 13, Pg 1

Physics 101: Physics 101: Lecture 13Lecture 13

Quick Review of Last Time, Example Problems Power, Work done by a variable force Reminders:

Exam I, Tuesday, September 30th at 5 PMSee PHY101 Web page for room assignmentsPlease do not forget to bring your UB ID card !

Chapter 6 : Work and Energy


Work done by a constant ForceWork done by a constant Force

Ekin = Wnet

• W = F s = |F| |s| cos = Fs s

|F| : magnitude of force |s| = s : magnitude of displacement Fs = magnitude of force in direction of displacement :

Fs = |F| cos

: angle between displacement and force vectors• Kinetic energy : Ekin= 1/2 m v2

• Work-Kinetic Energy Theorem:

F

s


Work Done by GravityWork Done by Gravity

Example 1: Drop ball

Yi = h

Yf = hf

Wg = (mg)(S)cos

S = h0-hf

Wg = mg(h0-hf) cos(00)

= mg(h0-hf)

= Epot,initial – Epot,final

mgS

y

x

Yi = h0

mgS

y

x



Example 2: Toss ball up

Wg = (mg)(S)cosS = h0-hf

Wg = mg(h0-hf)cos(1800) =

=-mg(h0-hf)

= Epot,initial – Epot,final

Yi = h0

Yf = hf

mgS

y

x



Example 3: Slide block down incline

Wg = (mg)(S)cos

S = h/cos

Wg = mg(h/cos)cos

Wg = mgh

with h= h0-hf

h

mgS

Work done by gravity is independent of path

taken between h0 and hf

=> The gravitational force is a conservative force.

h0

hf


Concept QuestionConcept Question

Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed?

1. Dropping2. Slide on ramp (no friction)3. Swinging down4. All the same

In all three experiments, the balls fall from the same height and therefore the same amount of their gravitational potential energy is converted to kinetic energy. If their kinetic energies are all the same, and their masses are the same, the balls must all have the same speed at the end.

1 2 3correct


Conservation of Mechanical EnergyConservation of Mechanical Energy

Total mechanical energy of an object remains constant provided the net work done by non-conservative

forces is zero: Etot = Ekin + Epot = constantor

Ekin,f+Epot,f = Ekin,0+Epot,0

Otherwise, in the presence of net work done bynon-conservative forces (e.g. friction):

Wnc = Ekin,f – Ekin,0 + Epot,f-Epot,i


Example ProblemExample Problem

Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces? 1. 0J 2. 50J 3. -50J 4. 225J 5. -225J

correct

Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies.

W = (300-75) + ((-25) - 250) = 225 - 275 = -50J.


Power Power

Average power is the average rate at which a net force

does work:

Pav = Wnet / tSI unit: [P] = J/s = watt (W)

Or Pav = Fnet s /t = Fnet vav


Work done by a Variable ForceWork done by a Variable Force

The magnitude of the force now depends on the

displacement: Fs(s)

Then the work done by this force is equal to the

area under the graph of Fs versus s, which can be

approximated as follows:

W = Wi Fs(si) s = (Fs(s1)+Fs(s2)+…) s

Physics 101: Lecture 13

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