Differences

This shows you the differences between two versions of the page.

--- 184_notes:examples:week3_balloon_wall [2018/01/24 21:41] – [Solution] tallpaul
+++ 184_notes:examples:week3_balloon_wall [2021/01/26 21:21] (current) – [Solution] bartonmo
@@ Line 1: / Line 1: @@
-=====Balloon Stuck to a Wall=====
+[[184_notes:pc_force|Return to Electric Force]]
+=====Example: Balloon Stuck to a Wall=====
 When you rub part of a rubber balloon against wool (or your hair), electrons will leave the wool, which is slightly conductive, and go onto the balloon. The rubber on the balloon is much less conductive (rubber is more of an insulator than wool), and the electrons will not readily leave the balloon. As a result, the balloon becomes negatively charged. Imagine you bring the negatively charged balloon up to a wall, and it sticks (This is possible! A quick internet search will yield many explanations and demonstrations. You can also try it yourself). Why would the balloon stay in one place on the wall? Draw a free body diagram for the balloon to help your explanation.
@@ Line 14: / Line 16: @@
   * The wall is perfectly vertical (parallel to the gravitational force).
 </WRAP>
-{{ 184_notes:3_balloon_picture_bare.png?200 }}
+[{{ 184_notes:3_balloon_picture_bare.png?200|Balloon stuck to wall }}]
 ===Goal===
@@ Line 27: / Line 29: @@
 </WRAP>
-The only other force we could have is the electric force between the balloon and the wall. Since the net force on our balloon is zero, the free body diagram looks something the following representation:
+We know the balloon is motionless, so air resistance is not a factor here, as it often is with balloons. The only other force we could have is the electric force between the balloon and the wall. Since the net force on our balloon is zero, the free body diagram looks something the following representation:
-{{ 184_notes:3_balloon_diagram.png?200 |Balloon Force Diagram}}
+[{{ 184_notes:3_balloon_diagram.png?200 |Balloon Force Diagram}}]
 In order to describe how we might get this diagonal electric force, we'll make a few more assumptions.
@@ Line 41: / Line 43: @@
 </WRAP>
-===Approximations & Assumptions===
+With these assumptions in mind, it's reasonable to say that the interaction between the wall and the extra negative charges on the balloon is much stronger than the interaction between the wall and any polarized atoms in the balloon. For this reason, we can ignore polarized atoms in the balloon. This seems reasonable, since a balloon will not stick to a wall without having rubbed the balloon with something that will transfer some of its electrons to the balloon.
-  * The balloon is not very conductive, so the electrons from the wool are stuck where they are. We'll say they are distributed near the part of the balloon close to the wall.
-  * The wall is a perfect insulator, and is neutral.
+We can use the following representation, in which the balloon is motionless, to show how we are thinking of the balloon and the wall at this point:
-  * The interaction between the wall and the extra negative charges on the balloon is much stronger than the interaction between the wall and any polarized atoms in the balloon. For this reason, we choose to ignore polarized atoms in the balloon. This seems reasonable, since a balloon will not stick to a wall without having rubbed the balloon with something that will transfer some of its electrons to the balloon.
+[{{ 184_notes:3_balloon_picture.png?200 | Balloon Stuck to Wall (with charges shown)}}]
-Based on our Approximations and Assumptions, we can draw the following diagram of the (motionless) situation:
+We know that the balloon is negatively charged from rubbing it on wool/hair. When we bring the charged balloon close to the wall, the atoms in the wall near to the balloon become polarized with the electron clouds being pushed away from the negative balloon. See the notes on [[184_notes:charge_and_matter|Charges and Matter]] for more information on polarization. This means that the negative balloon is now //attracted// to the positive nuclei in the polarized wall. (The balloon is also repelled from the negative electron clouds, but since the nuclei are closer to the balloon, the attractive force is more powerful).
-{{ 184_notes:3_balloon_picture.png?200 |Balloon Stuck to Wall}}
-We know that the balloon is negatively charged from rubbing it on wool/hair. When we bring the charged balloon close to the wall, the atoms in the wall near to the balloon become polarized with the electron clouds being pushed away from the negative balloon. See the notes on [[184_notes:charge_and_matter|Charges and Matter]] for more information on polarization. This means that negative balloon is now //attracted// to the positive nuclei in the polarized wall.
-We know the balloon is motionless, so air resistance is not a factor here, as it often is with balloons. Also, because the balloon is motionless, the net force is zero so all of our forces must cancel out. We know we have a gravitational force from the earth, a normal force from the wall, and an attractive electric force from the wall. That is all! Notice that the electric force needs to point both to the left and upward in order for the net force to be zero. If you were to try this experiment out yourself, you may notice the balloon rolling slightly up and down (oscillating) before settling to a motionless state. As the balloon rolls, the charge distribution on the balloon moves with respect to the wall, which changes the direction of the electric force on the balloon from the wall. When the balloon settles, we know it has come to a place where the direction and magnitude of the electric force results in a net force of zero. A force diagram on the motionless balloon is shown below.
+Notice that the electric force needs to point both to the left and upward in order for the net force to be zero. If you were to try this experiment out yourself, you may notice the balloon rolling slightly up and down (oscillating) before settling to a motionless state. As the balloon rolls, the charge distribution on the balloon moves in the same way that the balloon does, which changes the direction of the electric force on the balloon from the wall. When the balloon settles, we know it has come to a place where the direction and magnitude of the electric force results in a net force of zero.
-{{ 184_notes:3_balloon_diagram.png?200 |Balloon Force Diagram}}
-Note on friction: We do not include friction in the force diagram. We assume the electric force has enough of an upwards component that friction contributes nothing. However, depending on assumptions that you make, you may have friction in your force diagram. In reality, there is probably both friction and a slightly upwards electric force component at play here.
+//Another note on our assumption about friction//: We do not include friction in the force diagram. We assume the electric force has enough of an upwards component that friction contributes nothing. However, depending on assumptions that you make, you may have friction in your force diagram. In reality, there is probably both friction and a slightly upwards electric force component at play here.