EnergyEnergy

The ability to do workThe ability to do work

Kinetic Energy (KE)Kinetic Energy (KE)

The energy that an object has due to its motion. The energy that an object has due to its motion.

KE = ½ KE = ½ mm vv22

– KE KE mm andand KE KE v v22 – Kinetic energy is a scalar quantity.Kinetic energy is a scalar quantity. – Energy units are the same as work units Energy units are the same as work units

(kg*m(kg*m22/s/s22) = N*m = J) = N*m = J

F

dvi = 0

Ex: Ex: A 7.00 kgA 7.00 kg bowling ball is moving at a bowling ball is moving at a speed of 3.00 m/s. How much kinetic energy speed of 3.00 m/s. How much kinetic energy

does it have?does it have? Given:Given: m = 7.00 kg m = 7.00 kg

v = 3.00 m/s v = 3.00 m/s

Find:Find: KE = ? KE = ?

KE = ½ mvKE = ½ mv22

= ½ (7.00 kg)(3.00 m/s)= ½ (7.00 kg)(3.00 m/s)22

= 31.5 J= 31.5 J

Ex. 2:Ex. 2: What speed would a 2.45 g ping-pong What speed would a 2.45 g ping-pong ball need in order to have the same kinetic ball need in order to have the same kinetic

energy as the bowling ballenergy as the bowling ball??

Given:Given: m = 0.00245 kg m = 0.00245 kg

KE = 31.5 J KE = 31.5 J

Find:Find: v = ? v = ?

KE = ½ mvKE = ½ mv22

[(2 KE) / m] = v [(2 KE) / m] = v

[2(31.5J) / 0.00245 kg] [2(31.5J) / 0.00245 kg] =v=v

1.60 x 10 1.60 x 10 22 m/s = v m/s = v

Gravitational Potential Energy Gravitational Potential Energy (PE(PEgg))

Energy that is stored Energy that is stored in an object due to its in an object due to its position above a position above a surface.surface.

PEPEgg = work done to = work done to

raise mass raise mass mm a a distance distance hh

PEPEgg = mg = mg hh

Units = JoulesUnits = Joules

Δh

Gravitational Potential Energy Gravitational Potential Energy (PE(PEgg))

A reference level for determining A reference level for determining h must h must be determined (level where be determined (level where h = 0).h = 0).

The exact path taken while changing The exact path taken while changing h is h is not important.not important.

If If h is positive, then PEh is positive, then PEgg is positive. If is positive. If h h

is negative, then PEis negative, then PEgg is negative. is negative.

Ex:Ex: A 50 kg girl climbs a staircase of 15 A 50 kg girl climbs a staircase of 15 steps, each step 20 cm high. How much steps, each step 20 cm high. How much gravitational potential energy did the girl gravitational potential energy did the girl gain?gain?

Given: Given: m = 50 kg m = 50 kg

h = 0.20 m (15 steps) h = 0.20 m (15 steps)

= 3.0 m = 3.0 m

Find:Find: PE PEgg = ? = ?

PEPEgg = mg = mg h h

= (50 kg)(9.81 m/s= (50 kg)(9.81 m/s22)(3.0 m))(3.0 m)

= 1.5 x 10= 1.5 x 1033 J J

Elastic Potential Energy (PEElastic Potential Energy (PEee))

Energy stored in an elastic object (usually Energy stored in an elastic object (usually a spring) by deforming it (doing work on it). a spring) by deforming it (doing work on it).

PEPEee = ½ kx = ½ kx22

x = x = distance spring is deformed (stretched distance spring is deformed (stretched or compressed)or compressed)k = k = spring constantspring constant: : How resistant an How resistant an elastic object is to being stretched or elastic object is to being stretched or compressed compressed (stiffness). Units = N/m(stiffness). Units = N/mUnits = Units = N/m (mN/m (m22) = N*m =) = N*m = Joules Joules

Ex:Ex: A spring with a spring constant of A spring with a spring constant of 160 N/m is normally 14.0 cm long. How 160 N/m is normally 14.0 cm long. How much energy is stored in it when it is much energy is stored in it when it is compressed to 6.0 cm?compressed to 6.0 cm?

Given:Given: k = 160 N/m k = 160 N/m x xii = =

0.140 m0.140 m x xff

= 0.060 m= 0.060 m

Find:Find: PE PEee = ? = ?

PEPEee = ½ kx = ½ kx22

= ½ (160 N/m)(0.140 m -= ½ (160 N/m)(0.140 m -0.060 m)0.060 m)22

PEPEee = 0.51 J = 0.51 J

Mechanical EnergyMechanical Energy (E) (E): :

The energy of an object due to its position The energy of an object due to its position or its motion.or its motion.– Sum of kinetic energy, gravitational potential Sum of kinetic energy, gravitational potential

energy, and elastic potential energy. energy, and elastic potential energy.

E = KE + PE = KE + PEE = KE + PE = KE + PEgg + PE + PEee

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

In the absence of friction, the total In the absence of friction, the total mechanical energy remains the same.mechanical energy remains the same.

EEii = E = Eff

oror

KEKEii + PE + PEg,ig,i + PE + PEe,ie,i = KE = KEff + PE + PEg,fg,f + PE + PEe,fe,f

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

Mechanical energy is Mechanical energy is not conservednot conserved if if friction is present. friction is present. – Friction converts mechanical energy into other Friction converts mechanical energy into other

forms of energy (heat, etc.). forms of energy (heat, etc.). – Total energyTotal energy is always conserved. is always conserved.

Ex: A bird is flying horizontally 5.0 m above Ex: A bird is flying horizontally 5.0 m above the water at a speed of 18 m/s when it drops the water at a speed of 18 m/s when it drops a fish. How fast is the fish moving when it a fish. How fast is the fish moving when it hits the water?hits the water?

Given:Given: v vii = 18 m/s = 18 m/s

ΔΔh = 5.0 mh = 5.0 m

Find:Find: v vff = ? = ?

EEii = E = Eff

PEPEg,Ig,I + KE + KEii = KE = KEff

mg mg ΔΔh + ½ mvh + ½ mvii22 = ½ mv = ½ mvff

22

2g 2g ΔΔh + vh + vii22 = v = vff

22

√√[(2g [(2g ΔΔh) + vh) + vii22] = v] = vff

√√[(2*9.81 m/s[(2*9.81 m/s22)(5.0 m)+(18 m/s)(5.0 m)+(18 m/s)2)2] ] = v= vff

vvf f = 20.m/s= 20.m/s