Buggé: Electrostatics 5
Combining Mechanics and Electrostatics
Problems 1-6 combine mechanics and electrostatics
+
1. Represent and Reason
A positively charged sphere with charge q and mass m hangs at the end of a string.
Another positively charged sphere of a different charge 5q is secured at the top
end of the string to a wooden support. Fill in the table that follows.
+
Both spheres are positive
Hanging sphere is positive, top
sphere is negative
Draw a force diagram
for the hanging sphere
Represent
mathematically using
Newton’s 2nd Law
Draw Newton’s 3rd Law
forces that the spheres
exert on each other.
2. Represent and Reason
The spheres in the illustration below have equal magnitude charge and are very light. They are connected to the
cart and each other by rods made of an insulating material (also very light). The cart rests on a smooth table.
q1
q2
q3
–
+
+
a. Fill in the table that follows. In this instance, consider only electric forces—ignore other types of forces.
Draw a force diagram Draw a force diagram for Draw a force diagram for
Draw a force diagram
for the electric forces
the electric forces
the electric forces exerted
for the electric forces
exerted on the left
exerted on the center
on the right sphere.
exerted on the whole
sphere. Represent the
sphere.
cart (a system with all
object with a dot.
three charged spheres
included).
b. Will the cart accelerate to the left or to the right? Explain your answer.
Buggé: Electrostatics 5
3. Regular Problem An object with a charge of 1.0 C and an object with a charge of 2.0 C are held in place a
distance of 100 m from each other. Where should an object with a –1.0 x 10-3 C charge be located on the line
between the two positively charged objects so that the net electrical force on the third object is zero? Note: In
real life, objects never hold 1 or 2 C of charge. Why might this be?
4. Represent and Reason The application of Newton’s second law for a positively charged object at one instant
of time is shown in the equation that follows. Other charged objects lie along a horizontal line.
(" (2.0 × 10 –4 C)(3.0 × 10 –5 C) % " (9.0 × 10 –4 C)(3.0 × 10 –5 C) % +
(0.15 kg)ax = (9.0 × 10 9 N • m 2 /C2 ) *$ –
2
'& + $# –
'& (2.0
m)
(3.0 m)2
#
)
,
a. Draw a force diagram for the object of interest at the instant the equation applies.
b. Sketch a situation the equation might describe at that particular instant.
c. Write a word problem for which the equation is a solution (it applies at only one time).
d. Determine one change that could be made in the situation so that the net force exerted on the object of interest is
zero.
5. Regular Problem
Three tiny charged spheres lie along the x-axis. The first is located at -0.1 m and has an excess charge of -5 µC.
The second tiny sphere is located at 0.3 m and has an excess charge of +2 µC. A third tiny sphere, with an
excess charge of +3 µC, is placed somewhere along the axis.
a. Determine the net force exerted on the third sphere when it is located at the origin.
b. Determine where the third sphere is located when the net force exerted on the sphere is zero.
c. Qualitatively, where could you place the sphere such that the magnitude of the net force is greatest?
6. Regular problem Two small plastic spheres, which were rubbed with fur, have an excess of negative charge
on them. The two spheres are 20 cm apart from each other; they exert an electrostatic force of 0.5 N on each
other. What is the excess charge on each sphere if the two spheres have the same charge? If one sphere has 6
times more negative charged particles than the other?
Buggé: Electrostatics 5
Problems 7-9 require trigonometry
7. Represent and reason Two equal-mass stationary spheres are attached to the end of two strings. The sphere
on the left has an electric charge of +5Q and the sphere on the right has an electric charge of +Q. Each string
makes an angle less than 45o with respect to the vertical. Fill in the table that follows.
http://paer.rutgers.edu/PT3/movies/Electrostatic7.mov
Draw a force
diagram for the
left sphere.
Draw a force
diagram for the
right sphere.
Decide which
string makes a
bigger angle with
the vertical or if
they make the
same angle.
Apply Newton’s
second law in
component form for
the right sphere.
Based on your analysis, rank order the
forces TS on Q, F5Q on Q, and F E on Q,
listing the largest force first.
Horizontal x-axis:
Explain the ranking:
Vertical y-axis:
8. Regular Problem Two small plastic spheres, each with a mass of 0.30 grams, are suspended by light strings
(L = 15 cm) from a common point. The spheres are given the same electric charge and the spheres repel each
other. Once the system is in equilibrium, each string makes an angle of 8º with the vertical. Determine the
magnitude of the excess charge on each sphere.
9. Regular Problem
Examine the situation below. There are two conducting spheres attached to the wall and there is a cart (mass =
0.75 kg) that has an excess charge of +5.0 µC, located 0.4 m away from the base of the wall. At the base of the
wall, there is a +2.0 µC charged conducting sphere. A +7.0 µC charged conducting sphere lies 0.30 m above the
+2.0 µC sphere. See the picture below.
+
0.3 m
+
+
0.4 m
a. Draw a force diagram for the cart.
b. How is the normal force affected by the charged spheres?
c. Determine the acceleration of the cart at the point shown in the picture. Assume there is no friction.