Transcript Chapter 5 - Brookville Local Schools

Work
CHAPTER 5
WORK

The product of the magnitudes of the
component of a force along the direction of
displacement and the displacement.

Units-Force x Length
N

x m = Nm = J (Joules)
W=Fd (force times displacement)
WORK
If an object is not moved, NO WORK is done.
 If you hold a heavy object, your body has work
being done inside, but no work is done on the
object.
 For W = Fd, the force must be the component
in the same direction as the displacement.

EXAMPLE

You push on a van directly horizontal
W

= (your force) x (distance moved horizontally)
You push down on a bumber at an angle
 Find
the force of the horizontal component
 Use cos θ ; so W = Fd cosθ
SAMPLE PROBLEM


You pull a crate by attaching a rope at an angle of 25⁰.
You then pull with 100 N, and it moves 10m. Calculate
the work done?
Given:




Work:




F=100 N
Θ=25⁰
d=10 m
W = Fd cosθ
W = (100 N)(10 m) cos(25⁰)
W=900 J
Homework: Practice 5A Page 162 #1-4
PRACTICE 5A

Problem #1
 Given:
F= 5.00 x 103N
d= 3.00Km=3000 m
 Work:
W=Fd
W=(5.00 x 103N)(3000m)
W=1.50 x 107J
PRACTICE 5A

Problem #2
 Given:
F= 350 N
d= 2.00m
 Work:
W=Fd
W=(350 N)(2.00 m)
W=7.0 x 102 J
PRACTICE 5A

Problem #3
 Given:
F= 35 N
d= 50.0 m
Θ= 25⁰
 Work:
W=Fd cosθ
W=(35 N)(50.0 m)cos(25⁰)
W=1.6 x 103J (1600 J)
SIGN OF WORK







Not what you might think
 Scalar, but can be + or –
Positive-component force in same direction as
displacement.
Negative- If opposite (Kinetic Friction Force)
Cos θ is negative for angles greater than 90⁰ but less
than 270⁰
When speed is changed by work:
 If sign is positive, increases
 If sign is negative, decreases
Positive Work - work done ON the object
Negative Work -work done BY the object
KINETIC ENERGY

Energy associated with an objects motion
 Does
not depend on direction; scalar
 Depends on mass and speed
 KE = (1/2) mv2
 m=mass
 v=velocity
 Units
 Kg
(m/s)2
 Kg m2/s2 = Joule (J)
POTENTIAL ENERGY
Stored energy; depends on properties of the
object AND it position (reference to
environment)
 Two Types

 Gravitational
(PEg)
 Elastic (PEelastic)

Total PE= PEg + PE (elastic)
GRAVITATIONAL
The energy associated with an object due to the
object’s position relative to a gravitational source.
 PEg = mgh
 m=mass
 g=9.81m/s2
 h=height (In measuring height, choose arbitrary zero
level.)
 Units=Joules (J)
 Note: Gravity and Free-fall acceleration are not
properties of the object

ELASTIC
Potential energy in a stretched or compressed
elastic object.
 PE (elastic) = (1/2) Kx2
 k-spring constant, specific to the elastic object
unit N/m
 x-distance stretched/compressed from resting
 Unit-N/m

SAMPLE PROBLEM

A 700kg stuntman is attached to a bungee
cord with an unstretched length of 15.0m. He
jumps off a bridge from a height of 50.0m.
When he finally stops, the cord has a stretched
length of 44.0m. Disregard weight of cord
K = 71.8 N/m. What is total PE relative to the
water when the man stops falling?
SAMPLE PROBLEM

Given:
 m=70.0
Kg
 h=50.0 m – 44.0 m = 6.0m
 x=44.00 m - 15.0 m = 29.0 m
 PE = 0 at River Level

Work:
 PEg
= mgh = (70.0)(9.81)(6.0) = 4100 J
 PE(elastic) = (1/2)kx 2= (1/2)(71.8)(29.0)2 = 30,200J
 PE total = PEg + PE (elastic)
 PE = 34, 300 J
CONSERVATION OF ENERGY

Mechanical Energy-the sum of kinetic energy and
all forms of potential energy
 ME
= KE + PE
In the absence of friction, ME remains constant;
CONSERVATION of MECHANICAL ENERGY
 MEi = MEf (no friction)

 1.
If only force is gravity:
 1/2mvi2
 2.
+ mghi = 1/2mvf2 + mghf
What if you had gravity and a spring?
SAMPLE PROBLEM
AIR HOCKEY PUCK ON INCLINE, NO FRICTION. WHAT VELOCITY
DOES IT SLIDE WITH AT THE BOTTOM?





PE = mgh
hi = 1.1 m
hf = 0 m
m= 2.0Kg
g = 9.81 m/s2



KE = ½ mv2
Vf= ?
Vi = 0
SAMPLE PROBLEM (CONT.)
PEgi + KEi = PEgf +KEf
 mghi + (1/2)mv2 = mghf + (1/2)mvf2
 (2.0)(9.81)(1.1) + 0 = 0 + (1/2)(2.0)(Vf)2

Vf = √(21.56)
 Vf = 4.7 m/s
