Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
Worksheet #14
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Wesley
PHYS 221
Canfield
10/08/2013
1. (Conservation of Energy with Springs) The brothers of Iota Eta Pi fraternity build a
platform, supported at all four corners by vertical springs, in the basement of their frat
house. A brave fraternity brother wearing a football helmet stands on the middle of the
platform; his weight compresses the springs by a value of δ. Then 4 of his fraternity
brothers, pushing down at the corners of the platform, compress the springs by another
distance of x until the top of the brave brother’s helmet is a distance d from the basement
ceiling. They then release the platform simultaneously. Ignore the masses of the springs
and the platform.
a. When the dust clears, the fraternity asks you to calculate their fraternity brother’s
speed just before his helmet hit the flimsy ceiling.
b. Without the ceiling, how high would he have flown?
c. In discussing their probation, the dean of students suggests that the next time they
try this, they do it outdoors on another planet. Would the answer to part (b) be the
same if this stunt were performed on a planet with a different value of g? Assume
the brothers depress the platform the same distance x.
x = 0.53 m
d = 0.90 m
δ =0.18 m
a. v = 3.6 m/s
b. h = 1.56 m
c. yes, it would be the same; part b is independent of g.
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Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
2. (Potential Energy Functions/Diagrams) The potential energy of two atoms in a diatomic
molecule is approximated by:
𝐴
𝐵
𝑈(𝑥) = 12 − 6
𝑥
𝑥
Where x is the distance between the two atoms and A and B are positive constants.
a. Find the force F(x) on one atom as a function of r.
b. Find the equilibrium distance between the two atoms. Is this stable equilibrium?
c. Suppose the distance between the two atoms is equal to the equilibrium distance
found in part (b). What minimum energy must be added to the molecule to
dissociated it – to separate the two atoms to an infinite distance apart?
d. For CO, the equilibrium distance between the carbon and oxygen atoms is d, and
the energy needed for dissociation is E per molecule. Find the values of A and B.
d = 1.13 X 10-10 m
E = 1.54 X 10-18 J
a. 𝐹(𝑥) = 12𝐴𝑥 −13 − 6𝐵𝑥 −7
2𝐴
1⁄
6
b. 𝑥 = ( 𝐵 )
𝐵2
c. 𝐸 = 4𝐴
d. 𝐵 = 6.41 ∗ 10−78
𝐴 = 6.68 ∗ 10−138