Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855
Exam code: quiz04JuR4



Sections 70854, 70855 results

0- 6 :	** [low = 6]
7-12 :	****
13-18 :	*******
19-24 :	********************** [mean = 21.9 +/- 6.1]
25-30 :	***************** [high = 30]

Physics quiz archive: magnetism, induction

Physics 205B Quiz 6, spring semester 2019
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz06riQ1



Sections 30882, 30883 results

0- 6 :
7-12 :	***** [low = 9]
13-18 :	********
19-24 :	************** [mean = 21.4 +/- 5.5]
25-30 :	*********** [high = 30]

Physics quiz archive: magnetism, induction

Physics 205B Quiz 6, spring semester 2018
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz06Av3g


Sections 30882, 30883 results

0- 6 :	* [low = 6]
7-12 :
13-18 :	************
19-24 :	******************* [mean = 20.1 +/- 4.2]
25-30 :	** [high = 27]

Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz04W3rK



Sections 70854, 70855 results

0- 6 :	* [low = 3]
7-12 :	********
13-18 :	**************
19-24 :	****************** [mean = 19.6 +/- 6.4]
25-30 :	********** [high = 30]

Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz04w33N



Sections 70854, 70855 results

0- 6 :
7-12 :	***** [low = 9]
13-18 :	****************
19-24 :	**************** [mean = 20.8 +/- 5.7]
25-30 :	*********** [high = 30]

Presentation: work and energy

Tarp-lined ramp leading down to a pond? Check. All-terrain vehicle? Check. Pulling a cord attached to a raft and rider? Whee! (Video link: "Human Slingshot Slip and Slide - Vooray.")

In this presentation we will introduce a new connection between forces and motion, in terms of how forces can do work on or against an object in order to speed up or slow down its motion. This is a new approach to connecting forces and motion, compared to the previous discussion in this course of using Newton's laws to relate how forces on an object result in a net force that may or many not change its motion.

First, defining the "amount of motion" of an object in terms of its translational kinetic energy, and then expressing how a force may do work on or against the motion of an object.

Translational kinetic energy KE_tr is the energy of motion. (We'll deal with rotational kinetic energy KE_rot later on.)

Translational kinetic energy KE_tr depends on the mass m and the square of the speed v of the object, and the resulting units of kg·m²/s² are also expressed as joules. A stationary object has no translational kinetic energy, and the faster an object moves, the more translational kinetic energy it has.

Instead of finding out how much translational kinetic energy KE_tr an object has, often we are more concerned with its initial-to-final change ∆KE_tr, which is the final amount of translational kinetic energy minus the initial amount of translational kinetic energy. Notice how the common factors of (1/2) and mass m (which is presumed to be constant) are pulled out, leaving a "difference of squares" for the final and initial speeds in the parenthesis.

In order to change the translational kinetic energy of an object (speeding it up or slowing it down), a force (such as that exerted by the horses) must do a certain amount of work W either on, or against the motion of the object (here the loaded sledge the horses are pulling).

Work is accomplished by exerting a force on an object, but in such a way that the object moves through a displacement s (note the unusual use of "s" for a generic ∆x, ∆y, or other direction displacement!), and the "tail-to-tail" angle θ between the force and displacement vectors (when their "bases" are drawn touching together) is anything besides 90°. The units of work are given in N·m, or yet again, joules, so keep in mind that work can be done on or against any mechanical energy form or forms.

Second, let's now explicitly make the connection between the work done by a force acting on or against the motion of an object, and the resulting changes in translational kinetic energy of the object.

This is an incomplete form of the total energy conservation equation we will utilize later, but this "work-energy theorem" shows how the transfer of energy (as work is done by a force acting on or against the motion of the object) causes a corresponding change in the translational kinetic energy of the object.

If the force does work on the object (by being exerted along the direction of its motion), then the work will have a positive sign, and the translational kinetic energy of the object will increase, making the sign of the ∆KE_tr term positive. Note for this case how the left- and right-hand sides of this equation must have the same positive sign.

If the force does work against the object (by being exerted opposite to the direction of its motion), then the work will have a negative sign, and the translational kinetic energy of the object will decrease, making the sign of the ∆KE_tr term negative. Note for this case how the left- and right-hand sides of this equation must have the same negative sign.

Squirrel. Catapult! Squirrel catapult! (Note the person behind the sliding glass door, cutting the release cord with a scissors to launch the squirrel.) (Video link: "squirrelcatapult.gif.")

To keep things simple, let's consider a strictly horizontal version of this contraption, which would make the work done by any vertical forces (such as the weight force of Earth on the squirrel) zero, as the angle between these vertical forces and the horizontal direction of motion is 90°.

The bungee cord (and basket) exerts a force on the squirrel directed to the right, along the direction of motion, so the bungee cord does work on the squirrel. As a result, the squirrel picks up speed (starting from rest), and since translational kinetic energy depends on the square of the speed, since speed increases, then the squirrel's translational kinetic energy increases.)

In the work-energy theorem equation:

W = ∆KE_tr,

the work will have a positive sign (as work was done on the squirrel by the bungee cords), causing the squirrel's translational kinetic energy to increase (and also have a positive sign), so the +/– signs of both the left-hand side and the right-hand side of the equation are consistent with each other:

(+) = (+).

(If you were to calculate the numerical values for the work done (in J) and the resulting numerical value for the increase in translational kinetic energy (in J), then they would have to be equal to each other (along with having the same sign).

For the catapulted squirrel, the bungee cord force does work __________ the squirrel, which __________ the squirrel's translational kinetic energy.)
(A) on; increases.
(B) against; decreases.
(C) (Unsure/lost/guessing/help!)

Note as this car stops, the brakes glow from the heat generated! (Video link: "McLaren SLR review - Top Gear - BBC.")

For the braking car, the brakes do work __________ the car, which __________ the car's translational kinetic energy.
(A) on; increases.
(B) against; decreases.
(C) (Unsure/lost/guessing/help!)

Don't blink, or you'll miss Mrs. P-dog in action! (Video link: "110530-1230869-excerpt.")

For Mrs. P-dog being catapulted upwards, the bungee cords do work __________ Mrs. P-dog, while the weight force does work __________ Mrs. P-dog.
(A) on; on.
(B) on; against.
(C) against; on.
(D) against; against.
(E) (Unsure/lost/guessing/help!)

For Mrs. P-dog's translational kinetic energy to be increased while being catapulted upwards, the amount of work from the bungee cords must be __________ the amount of work from the weight force.
(A) less than.
(B) the same as.
(C) greater than.
(D) (Not enough information is given.)
(E) (Unsure/lost/guessing/help!)

Physics quiz archive: magnetism, induction

Physics 205B Quiz 6, spring semester 2017
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz06LnDr


Sections 30882, 30883 results

0- 6 :
7-12 :
13-18 :	******** [low = 15]
19-24 :	************** [mean = 21.8 +/- 4.1]
25-30 :	******* [high = 30]

Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2016
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz04th1R



Sections 70854, 70855, 73320 results

0- 6 :
7-12 :	**** [low = 9]
13-18 :	****************
19-24 :	*********************** [mean = 20.5 +/- 4.8]
25-30 :	******** [high = 27]

Physics quiz archive: magnetism, induction

Physics 205B Quiz 6, spring semester 2016
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz06eL3k



Sections 30882, 30883 results

0- 6 :	*   [low = 6]
7-12 :	*****
13-18 :	*********************   [mean = 17.0 +/- 5.1]
19-24 :	**********
25-30 :	*   [high = 27]

Presentation: electric potential energy

Look at all these batteries. Just look at them. While we might think of them as "containing" electrical potential energy, or even as voltage "sources," we'll see that just two charges can "contain" electric potential energy, and that just a single charge can be thought of as a voltage "source." In subsequent presentations we'll explore more complex voltage "sources" that "contain" electric potential energy: capacitors, batteries, and household electric outlets.

In this presentation we will consider different approaches to analyze electric potential energy.

First, a direct approach to electric potential energy.

Recall that in the direct approach to electric forces, a source charge q₁ can be said to exert a force F on a separate test charge q₂.

Similarly, a direct approach to electric potential energy is that a source charge q₁ can be said to store electric potential energy EPE on with a separate test charge charge q₂.

∆EPE changes in this electric potential energy are caused by moving the source charge and test charge closer together, or moving them farther apart. EPE can be increased (thus making ∆EPE positive) by pushing together like-sign charges (positive-positive, or negative-negative), or pulling apart opposite-sign charges (positive-negative, or negative-postive). This is because it takes work to push together like-sign charges (which repel, and don't want to be pushed together); or takes work to pull apart opposite-sign charges (which attract, and don't want to be pulled apart).

On the other hand, work is done by charges that are allowed to do what they want to, thus decreasing EPE (and making ∆EPE negative), by letting like-sign charges (positive-positive, or negative-negative) move farther apart from each other (because these charges repel); or letting opposite-sign charges (positive-negative, or negative-positive) move closer to each other (because these charges attract).

The value of the electric potential energy of a source charge q₁ and test charge q₂ at a certain distance r from each other can be calculated by an equation that looks similar to the magnitude of the electric force (but note the r^–1 dependence for electric potential energy, as opposed to the r^-2 dependence of electric forces). With the constant k, units of coulombs² and meters cancel, leaving units of N·m, which is what we have seen last semester as joules.

(Note that this equation calculates the value of electric potential energy EPE of two charges at a fixed separation distance from each other. In order to find the ∆EPE change in electric potential energy, you would need to calculate the initial EPE_i and final EPE_f electric potential energies of the two charges at their initial r_i and final r_f separation distances.)

Second, the two-step approach to electric potential energy.

Recall that in the two-step approach to electric forces, a source charge Q can be said to create an electric field E everywhere around itself, and then this electric field exerts a force F on a separate test charge q.

Similarly, a two-step approach to electric potential energy is that a source charge Q can be said to create a potential V everywhere around itself, and this potential stores electric potential energy EPE with a separate test charge charge q.

Let's focus on the first step of this two-step model. The source charge Q creates a potential V everywhere around it. The magnitude of this potential can be calculated for a location at a distance r from the source charge, and has units of joules per coulomb (J/C), which is often re-expressed as volts (V). The sign of the potential depends on the sign of the source charge Q: if the source charge is positive, then the values of the potential everywhere around it are positive; if the source charge is negative, then the values of the potential everywhere around it are negative.

Recall that electric fields surrounding a single source charge are visualized as lines emanating outwards from, or pointing in towards the source charge. In contrast, the potentials surrounding a single source charge are visualized (here, in two-dimensions) as circles, as every location at the same distance r from the source charge must have the same value of potential, such that these circles are often referred to as equipotentials.

Note that the direction of electric field lines is indicative of the relative values of the equipotentials: for the positive source charge, each subsequent outer equipotential corresponds to smaller and smaller positive values of potential (due to the r^–1 dependence); for the negative source charge, each subsequent inner potential equipotential corresponds to larger and larger negative values of potential. So in either case, electric field lines point towards decreasing electric potential values.

A nice visualization is to imagine that a positive source charge creates a "peak" of potential around it--as you get closer in towards this positive source charge, the values of potential become bigger and bigger positive numbers, corresponding to a increase in elevation. In contrast, a negative source charge creates a "well" of potential around it--as you get closer in towards this negative source charge, the values of potential become bigger and bigger negative numbers, corresponding to a decrease in elevation.

So where does "voltage" come in? The amount of potential (which is measured in volts) at a location in space is often called the "voltage." So "potential" and "voltage" really mean the same thing (and just to confuse things even further, "electrical tension" is an equivalent archaic term). Get used to these terms, as we will be referring to them interchangeably through the remainder of this semester. Nobody ever thinks this is a big deal, so deal with it. (But yes, it is a big deal.)

Now what? If there is another charge anywhere in the presence of a potential, this potential will store electrical potential energy with the test charge q. In this equation, the electrical potential energy EPE stored by the test charge q is the test charge q multiplied by the potential V at the test charge's location. Since the test charge q could be positive or negative, and the potential V could have positive or negative values, then the electrical potential energy stored would have the correct sign depending the the product of these two signs.

(Notice that coulombs (C) multiplied by volts (V, or J/C) results in units of joules (J). In this sense potential or "voltage" can be said to be "potential" potential energy, that is, a location in space will only have a value for potential (measured in volts, or joules per coulomb), but any test charge q placed at this location in space will then have a value for electric potential energy (measured in joules) given by the product of the potential and amount of charge placed there.)

Here, from before, we show the electrical fields and potentials filling in all space surrounding a positive or a negative source charge. Putting a positive test charge in the presence of these electrical fields and potentials will cause an electrical force to be exerted along a field line, which would also point in the direction of decreasing potential and decreasing potential energy; while putting a negative test charge in the presence of these electrical fields and potentials will cause an electrical force to be exerted in the opposite direction of a field line, which would point in the direction of increasing potential, but decreasing potential energy.

In any case, as a check the direction of the force on any source charge q should be attractive or repulsive depending on whether it has the opposite or same sign as the source charge Q, and also check that the source charge q moves in the direction that would decrease its electric potential energy. However, positive test charges move in the direction of decreasing potential, while negative test charges move in the direction of increasing potential! (If all this sounds confusing, at least be assured that these rules are consistent.)

As previously above, we visualized a positive source charge +Q as a "peak." Here we have a positive test charge +q as a hapless snowmobiler on this "peak." Initially as the snowmobiler rides up the "peak," increasing his potential and increasing his potential energy, work is required to push it "uphill" (provided by an external source, here the snowmobile engine). Left alone, the snowmobile and snowmobiler will slide "downhill," in the direction of decreasing potential and decreasing potential energy (as we have seen before, for two positive charges separating from each other). What would happen if the snowmobiler were a negative test charge –q? Then we would observe the very odd behavior of this negative snowmobiler sliding "uphill," in the direction in increasing potential--but this would be the direction of decreasing potential energy, as we have seen before, for a negative charge and a positive charge getting closer to each other.

What would happen if there was a negative source charge –Q creating a "well?" Then a positive test charge +q snowmobiler, left alone, would slide "downhill," in the direction of decreasing potential and decreasing potential energy (as we have seen before, for a negative charge and positive charge getting closer to each other). Then consider the very odd case of a negative test charge –q snowmobiler sliding on this "well"--we would observe the very odd behavior of this negative snowmobiler sliding "uphill," in the direction in increasing potential--but this would be the direction of decreasing potential energy, as we have seen before, for two negative charges separating from each other. (Video source: "Grazy hill climb crash with go pro cam.")

Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2015
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz04w04K



Sections 70854, 70855, 73320 results

0- 6 :	** [low = 6]
7-12 :	*******************
13-18 :	************************
19-24 :	****************************** [mean = 18.1 +/- 5.6]
25-30 :	*** [high = 30]

Physics quiz archive: magnetism, induction

Physics 205B Quiz 6, spring semester 2015
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz06t3SL



Sections 30882, 30883 results

0- 6 :	**   [low = 3]
7-12 :	*********
13-18 :	***************   [mean = 17.8 +/- 6.2]
19-24 :	****************
25-30 :	****   [high = 30]

Physics quiz archive: energy conservation, momentum conservation

Physics 205A Quiz 4, fall semester 2014
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz04w3Rc



Sections 70854, 70855, 73320 results

0- 6 :	**** [low = 3]
7-12 :	********
13-18 :	******************
19-24 :	************************ [mean = 19.5 +/- 6.6]
25-30 :	*********** [high = 30]