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Plan for Today (AP Physics I). Notes/Lecture on Potential Energy. One Definition of Energy – the ability to cause change. Example. If I take a brick and put it above a students head a small distance Will it cause a change? Yes What if I raise it farther up? Will it cause more change?
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Plan for Today (AP Physics I) • Notes/Lecture on Potential Energy
Example • If I take a brick and put it above a students head a small distance • Will it cause a change? • Yes • What if I raise it farther up? • Will it cause more change? • Yes • What kind of energy increased? • Potential energy (PEg)
Example • If I pick up a 1 kg brick and move it 1 m, did I do work? • Yes • W = F *x • W = (mg) * h • W = mgh • Is this a form of energy? • How do we know – check the units • PEg = mgh = [kgm/s^2*m) • Yes in joules • Note: h is change in y • Calculation: 1 * 9.8 * 1 = 9.8 J
Gravitational Potential Energy • PEg = mgh
Example • What if I carry a brick across the room? • Is this a change in potential energy? • No? • Still no • What if I stick the brick out the window? • Is this a change in potential energy? • Yes? • But then how is this possible? • I didn’t do any work – so how do I have a change in potential energy?
Same Change in potential energy • Individual values depend on zero point
For the brick outside the window • Could we look at the radius of the earth? • Hi =6,280,006m • Hf=6,280000m • Still have -58.0 J for change in PE
Example • 1 kg brick, 1 m above the ground vs. 6 m above the ground outside • Zero point is the floor • What’s the change in PE from holding it in the classroom to outside the window?
Example • What if we had the same example BUT our zero point was the ground outside? • What’s the change in PE?
So. . . • Change in PE is the same • Just depends on a zero point (to calculate) • We could use from the center of the Earth
Elastic Cord • Could this case a change if I let go? • Yes • So there must be energy • How about now? • More change? • Yes so more energy? • What kind of energy is this? • Elastic potential energy = PEe
Elastic Cord With Data • 1 step – 1 m • 20 N of force • 2 steps – 2 m • 40 N • 3 steps – 3 m • 60 N • 4 steps – 4 m • 80 N
Hmm data • What do we do with this data? • Graph it!
Graph of data • Force on y • Change in length on x • Note: Change in length • Lf – Li!
Looking at the graph • What’s the slope of this line? • Change in y over change in x • So F/x • This is K – a spring constant • What are the units for K? • F/x = Newtons/meters = N/m
Now • What if we double the elastic cord? • Now it’s a different spring • What does that graph look like? • Steeper line • What does this mean?
Summary • Different spring = different k • Stiff spring = big k • Weak spring – small k
Looking at the graph • Force and distance • Work is not F * x, because it varies • If we could use that, the graph would look like this:
Looking at the graph • Force and distance • Work is not F * x, because it varies • If we could use that, the graph would look like this:
Still looking at the graph • So what would work be? • Area under the curve • Area = ½ * b * h • W = ½ x *F • But we need to know in terms of k • Slope = k = F/x • So x * k = F • W = ½ * x * x * k • W = ½ k x^2
Elastic Potential Energy • W = ½ x * x * k • W = ½ k x^2 • Are we sure it’s energy? • How do we know? • Look at the units • N/m *m^2 = Nm = kgm/s^2 * m = kgm^2/s^2 = J
Elastic Potential Energy • PEe = ½ * k * x^2