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What Forces?• Gravity
Earth’s gravity Gravity between any two objects
• Electrical (Chapter 8)
• Contact forces Billiard balls colliding Guy pushing crate Hulk throwing guy Tires on the road in accelerating your car
Section 4.1
Work - Units
SI System (mks)
W = Fd : newton x meter = N-m = joule (J)
British System (fps)
W = Fd : pound x foot = foot-pound (ft-lb)
Work! The Refrigerator
h = 1.35 m
m = 85 kg
Workers lift a crate with a refrigerator in it onto the backof a truck. How much work is done?
Work! The Refrigerator• Knowns
m, mass h, distance
• Unknowns w, weight, or force of gravity W, work
W = FdW = whW = mgh
W = 85 kg( ) 9.8 m/s2( ) 1.35 m( )W = 1120 J
Work! The Refrigerator
F = 450 N
Ff = 450 N
d = 7.5 m
Workers push the crate from the back of the truckto the front a distance of 7.5 m with a force of 450 N. How much work is done?
Work! The Refrigerator• Knowns
F, force d, distance
• Unknowns W, work
W = FdW = 450 N( ) 7.5 m( )W = 3400 J
Work! The RefrigeratorWhen the workers arrive at their destination, they decideto put the crate on a dolly and role it to the back of thetruck. They lift the crate 15 cm to the dolly and pushwith a force of only 25 N to move the crate to the back.
F = 25 N
Ff = 25 N
d = 7.5 m What total workdid they dolifting and movingthe crate?
h = 15 cm
Work! The Refrigerator• Knowns
F, force against rolling frictiond, distance movedh, height liftedm, mass of crate
• UnknownsWl, work lifting the crateWr, work rolling the crateWtot , Total work
Wl = wh = mgh = 85 kg( ) 9.8 m/s2( ) 0.15 m( ) = 125 J
Wr = Fd = 25 N( ) 7.5 m( ) = 188 J
Wtot = 125 J +188 J = 315 J
Compare this result to the work required to slide the crate
Work! The RefrigeratorUnfortunately, the workers have too much fun pushing the crate and, because of its substantial inertia, it keeps going of the end of the truck and smashes onthe pavement. The crate is damaged.
Ultimately, where did the energy come from to damagethe crate?
A. The speed of the crate as it left the truck.
B. The work the workers did in lifting the crate ontothe truck in the first place.
Potential EnergyPotential Energy - the energy an object has because of its position or location, the energy of position
Most potential energy is due to gravity
Remember that: Work = Force x distance (W = Fd)Weight is a force (w = mg)Substitute h (height) for d
Therefore W = mgh Gravitational potential energy = weight x height
Ep = mgh
Section 4.2
Kinetic Energy: Energy of Motion
Ek is kinetic energym is the moving object’s massv is the moving objects speed
Section 4.2
Ek =12mv2
If an object is already moving:Work = change in kinetic energy
W = ΔEk =12mv2
2 − 12mv1
2
W = ΔEk =12m v2
2 − v12( )
Change in Kinetic Energy – an Example
A 1.0 kg ball is fired from a cannon. What is the change in the ball’s kinetic energy when it accelerates from 4.0 m/s to 8.0 m/s?
GIVEN: m = 1.0 kg; v1 = 4.0 m/s; v2 = 8.0 m/s
ΔΕk = Ek2 – Ek1 = ½mv22 - ½mv12
ΔEk = ½(1.0 kg)(8.0 m/s)2 – ½(1.0 kg)(4.0 m/s)2
ΔEk = 32J – 8.0J = 24J
Section 4.2
Other examples ofPotential Energy would include:
Section 4.2
Springs (compressed or stretched)
Bowstring
Conservation of Energy
Let z be height of pendulumabove height zero. zmax = h
Eh = mgh
E0 =12mv0
2
h
0z
Conservation of Energy
Etot = mgz +12mvz
2
• Energy is not a substance
• Energy is a calculation, an invariant of a system
• Energy has application in all aspects of all physicaland biological science.EcologyEvolutionAll physical sciences
Conservation of Energy
• Energy can neither be created nor destroyed.
• In changing from one form to another, energy is always conserved
• The total energy of an isolated system remains constant
• The total energy does not change with time
Section 4.3