Static Electricity Legacy Problem #3 Guided Solution
Problem*
Two ping pong balls have been painted with metallic paint and charged by contact with a Van de Graaff generator. The charges on the balls are -3.1x10-7 C and -3.7x10-7 C. Determine the force of electrical repulsion when held a distance of 42 cm apart.
Audio Guided Solution
In physics, we understand that objects which become charged can interact with one another, exerting attractive and repulsive forces upon each other. Objects which are like-charged will exert repulsive forces upon each other, and objects which are oppositely charged will exert attractive forces upon each other. The cool thing about physics is that we can use Coulomb's law in order to calculate the amount of force of attraction or repulsion. Well Coulomb's law equation states that the force of attraction or repulsion is equal to k, proportionality constant, times q1 times q2, the quantities of charges upon the two objects, divided by the distance squared, which separates their centers from one another. Here in this problem, we're given the values of q1 and q2 in units of Coulomb's, as is usually the case, and we're given the distance of separation between the two objects' centers. Now you'll notice that the distance separating these two objects is stated in centimeters. The value of k actually has units of meters squared. So as we begin to approach this problem and begin to substitute into the equation to solve for the force, we need to give consideration to units. The value of k is 8.99 times 10 to the positive ninth, with units of Newtons times meters squared per Coulomb squared. So in order to use this Coulomb's law constant appropriately, we always need to substitute in values of q1 and q2 in units of Coulomb's, and values of d in units of meters. So before I actually begin my substitution, I need to take the 42 centimeters and move the decimal place twice in order to get it to units of meters. That would be .42 meters. Then I need to substitute all values into my equation and solve for the value of force.
Solution
5.8x10-3 N
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities; record them in an organized manner. A diagram is a great place to record such information. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(Q_1 = 2.4 \unit{\micro\coulomb}\); \(Q_2 = 3.8 \unit{\micro\coulomb}\); \(d = 1.8 \unit{m}\); \(F_\text{elect} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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