CalculatingEnergyContents:

•Gravitational Potential•Whiteboards

•Kinetic•Whiteboards

Gravitational Potential Energy

TOC

Lifting a box of mass m:W = Fs = energy givenF = mg, s = hW = Fs = mgh

m

h

Ep = mghEp - gravitational potential energyh - Change in heightm - Massg - 9.81 N/kg on Earth

There are two waysto lift the object...

Whiteboards: Gravitational Potential Energy

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TOC

6.0 J W

Ep = mgh, h = .135 mEp = (4.5 kg)(9.81 N/kg)(.135 m) = 5.959575 (6.0 J)

What is the potential energy of a 4.5 kg bowling ball, 13.5 cm above the ground?

2.14 m W

Ep = mghh = Ep/(mg) = (1573 J)/(75 kg)/(9.81 N/kg) = 2.13795…

Toby Continued lifts a 75.0 kg box doing 1573 J of work. What is the change in height of the box?

65 kg W

Ep = mghm = Ep/(gh) = (9555 J)/(9.81 N/kg)/(15 m)= 64.9337…

Colin Host lifts himself up 15 m doing 9555 J of work. What is his mass?

Kinetic Energy

TOC

Speeding up a box of mass m with force F W = Fs = energy givenF = ma, s = dW = (ma)dv2 = u2 + 2as, d = v2/(2a) (if u = 0)

W = (ma)(v2/(2a)) = mv2/2 = 1/2mv2

Ek = 1/2mv2

m

There are two ways to speed up the mass...

d Fv

Ek = 1/2mv2

Ek - Kinetic energy

v- velocity

m - mass

Whiteboards: Kinetic Energy

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TOC

1960 J W

Ek = 1/2mv2 = 1/2(.0042 kg)(965 m/s)2 = 1955.5725(1960 J)

What is the kinetic energy of a 4.20 g bullet going 965 m/s?

20.30 g

Ek = 1/2mv2

m = 2 Ek/v2 = 2(2.055 J)/(14.23 m/s)2 = .020297…(20.29 g)

A European swallow has 2.055 J of kinetic energy when it is flying at 14.23 m/s. What is its mass in grams?

W

11 m/s

Ek = 1/2mv2

v = (2 Ek/m) = (2(34 J)/(.563 kg)) = 11 m/s

What speed must a .563 kg hammer move to store 34 J of energy?

W

90. J

initial: Ek = 1/2mv2 = 1/2(4.0 kg)(6.0 m/s)2 = 72 J final: Ek = 1/2mv2 = 1/2(4.0 kg)(9.0 m/s)2 = 162 JSo the increase is 162 – 72 = 90. J increase

A 4.0 kg shot is sped up from 6.0 m/s to 9.0 m/s. What is the change in kinetic energy?

W