PhyzSpringboard:
A Slippery Affair
Felix
1-4: Series Slides
Develop equations for the characteristics of each slide in terms of the elevation E and run
length R of slide 1.Then compare the expressions for the individual inclines (I1, I2, etc.) and total
incline of each slide to the original incline I0 by means of a product (ex: 2I0) or quotient (ex:
I0/3).Repeat comparisons for power.
1.Yer Basic Slide
V0 = ε
I0 = ε/R
V0
E
P0 = ε2/R
R
2.Double-Length (R1 = R2 = R)
VTOT =
ε
ITOT =
ε/2R = I0/2
PTOT =
ε2/2R = P0/2
V1
E
V2
R1
V1 =
ε/2
R2
V2 =
ε/2
I1 =
ε/2R = I0/2
I2 =
ε/2R = I0/2
P1 =
ε2/4R = P0/4
P2 =
ε2/4R = P0/4
The Book of Phyz © Dean Baird. All rights reserved.
REQ = 2R
1/21/08
db
3.Thrice-as-Nice (R1 = R2 = R3 = R) (this time, you draw in the V’s and I’s)
ε
R1
R2
R3
VTOT =
ε
V1 = ε/3
V2 = ε/3
V3 = ε/3
ITOT = ε/3R = I0/3
I1 = ε/3R = I0/3
I2 = ε/3R = I0/3
I3 = ε/3R = I0/3
PTOT =
P1 = ε2/9R = P0/9
P2 = ε2/9R = P0/9
P3 = ε2/9R = P0/9
REQ = 3R
ε2/3R = P0/3
4. Unequal Runs (R2 = 3R1; R1 = R) (this time, you draw in the V’s and I’s)
ε
R1
R2
V1 = ε/4
V2 = 3ε/4
I1 = ε/4R = I0/4
I2 = ε/4R = I0/4
ITOT =
ε/4R = I0/4
P2 = 3ε2/16R =
PTOT =
ε2/4R = P0/4
P1 =
ε2/16R = P0/16
VTOT =
ε
3P0/16
REQ = 4R
The Book of Phyz © Dean Baird. All rights reserved.
1/21/08
db