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Unformatted text preview: Physics 217: Problem Set 1 Solutions
by Jolyon Bloomﬁeld
Due Friday, Jan 23rd, 2009 1 Purcell 1.1 The attractive gravitational force is
FG = Gm2
p
r2 and the repulsive electrostatic force is
FE =
The ratio of these two is e2
.
4π 0 r2 4π 0 Gm2
FG
p
= 7.4 × 10−37 .
=
FE
e2 The electrostatic repulsion, using r = 10−13 cm, is 23 N. 2 Purcell 1.2 Balancing the Coulomb and gravitational forces, if e2 /4π 0 r2 = mg , then
r= e2
.
4π 0 mg Substituting in numbers, we ﬁnd r = 4.80 m. 3 Purcell 1.3 Look at a single volleyball. There are three forces acting on it  gravitational, electrostatic, and tension.
From the Coulomb force law, we can rearrange to obtain
q=r 4π 0 F where F is the force.
To ﬁnd out what the force should be, we need to calculate what the horizontal tension force is which
opposes the electrostatic repulsion. Deﬁning θ to be the angle between the horizontal and the string from
a volleyball, we ﬁnd the horizontal component of the force is T cos θ, and the vertical component is T sin θ.
As the vertical component has to balance with gravity, we ﬁnd
M g = T sin θ. 1 This solves for T . The horizontal component of the force from the tension is then
F = Mg cos θ
Mg
=
.
sin θ
tan θ We have tan θ = 10 from the geometry. Substituting this in to ﬁnd the charge, we have
q=r 4π 0 Inserting numbers obtains q = 2.86 × 10−6 C. 2 × 0.1M g. ...
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This note was uploaded on 06/10/2011 for the course PHYS 2217 taught by Professor Leclair, a during the Spring '06 term at Cornell.
 Spring '06
 LECLAIR, A
 Force

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