Electric Forces: Calculating Charge on Two Spheres

[Kris1120]

Homework Statement

Two small metallic spheres, each of mass
0.14 g are suspended as pendulums by light
strings from a common point as shown. The
spheres are given the same electric charge, and
it is found that the two come to equilibrium
when each string is at an angle of 7◦ with the
vertical.
The value of Coulomb’s constant is
8.98755 × 109 N · m2/C2 and the acceleration
of gravity is 9.81 m/s2 .
If each string is 13.7 cm long, find the mag-
nitude of the charge on each sphere.
Answer in units of nC.

Homework Equations

y=Tcos(theta)=mg
x=Tsin(theta)=Fe

The Attempt at a Solution

Tcos(7)=(.14g)(9.81)
T=1.38371

1.38371sin(7)=.168632

q=sqrt((.1683632)(2*(.137sin7)^2))/8.98755x10^9
q=1.44639e-7

 

[LowlyPion]

Homework Statement

Two small metallic spheres, each of mass
0.14 g are suspended as pendulums by light
strings from a common point as shown. The
spheres are given the same electric charge, and
it is found that the two come to equilibrium
when each string is at an angle of 7◦ with the
vertical.
The value of Coulomb’s constant is
8.98755 × 109 N · m2/C2 and the acceleration
of gravity is 9.81 m/s2 .
If each string is 13.7 cm long, find the mag-
nitude of the charge on each sphere.
Answer in units of nC.

Homework Equations

y=Tcos(theta)=mg
x=Tsin(theta)=Fe

The Attempt at a Solution

Tcos(7)=(.14g)(9.81)
T=1.38371
1.38371sin(7)=.168632

q=sqrt((.1683632)(2*(.137sin7)^2))/8.98755x10^9
q=1.44639e-7

Your method looks fine.

I haven't checked the math.
Have you been careful to make sure that the units of grams and cm's is properly matched to the units of g and Coulomb's constant?

Your answer needs to be in nC.

 

[Kris1120]

I changed it no nC and that is 1.44641e2 nC. It's still not right. :(

 

[Kris1120]

sorry i meant *to

 

[LowlyPion]

q=sqrt((.1683632)([2*(.137sin7)]^2))/8.98755x10^9
q=1.44639e-7

You need to square the total distance between the charges.