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Oh, that makes sense now. So setting the limits from a larger to smaller distance by itself establishes that the electric force is in the opposite direction of the displacement, meaning that the negative from the dot product is redundant.

Wait i thought the direction of ds was the direction of the path taken. Thats why I thought ds and the electric field pointed in opposite direction so the dot product was negative. If that's not the case, what determines the direction of ds?

Oh, I thought I took care of the negative outside the integral though.

well, I know that if an external agent is doing positive work, then the potential energy change is positive, and the potential energy change is negative if the external agent is doing negative work. In my example of moving q2 closer to q1, the work from the external agent should be positive and...

i'm not sure what the problem is with the integration. ∫ Kq1q2/r^2 dr from b to c is kq1 q2 ∫ dr/r^2 from b to c = kq1q2 (-1/r) from b to c = kq1q2(-1/c - (-1/b)) = kq1q2(-1/c + 1/b). Should i have done the integral from c to b? if so, why?

I am confused about the signs in calculating the potential energy change from the electrostatic force. Suppose there was a point charge +q1 and I moved a second point charge +q2 from a distance of b from q1 to a distance of c from q1. c is smaller than b. So the potential energy change is - ∫...

I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The...

Homework Statement Given a semi-infinite stick (that is, one that goes off to infinity in one direction), determine how its density should depend on position so that it has the following property: If the stick is cut at an arbitrary location, the remaining semi-infinite piece will balance on a...

Ok I see that the direction should be flipped since theta is negative. That would give me T(theta) >= T(0) e^(u*theta). So is this the lower bound for T(theta) and the solution's T(theta) is the upper bound?

Homework Statement A disk of mass M and radius R is help up by a massless string. Let there now be friction between the disk and the string, with coefficient u. What is the smallest possible tension in the string at its lowest point? The problem is problem 8 from here...

You prepare 0.5 liters of a solution by adding 0.75 moles of a weak acid HA to water. For HA, Ka = 10^-1 Finally you dilute this solution to a final volume of 2.0 liters. What is the pH of the diluted solution? My solution is this. [HA] = .75 mol /.5 L = 1.5 M. HA + H2O -> H3O+ + A-. If x...

OH. That makes so much sense. If R2 has E voltage and the emf is E, there can initially be no current from the emf. But as the capacitor discharges, the current from the emf increases so the circuit eventually reaches a "uniform" current.

If the capacitor's initial voltage is E and it discharges, does R2 get the same voltage at that instant?

Then why does the capacitor have current immediately after the switch is closed while the battery has not produced current in R1?

Oh, Ok. That makes sense. I see that there is current through the capacitor, but how does this lead to I1 = 0?

I am confused. At t = 0, the capacitor will not have discharged yet to Ic = 0 so I1 = I2, which is incorrect.

I think I understand what happens before new t = 0. My only question is why immediately after new t = 0 the battery doesn't produce a current through R1. The current in R1 immediately after new t = 0 is 0, but can't the battery produce a current through R1 now that a safe path around the...

Why is there no current immediately after t = 0? Doesn't the emf source also drive a current through R2?

Homework Statement The circuit in the link below contains a capacitor of capacitance C, a power supply of emf E, two resistors of resistances R1 and R2, and two switches S1 and S2. After switch S1 has been closed for a long time, switch S2 gets closed at a time t = 0. Sketch graphs of the...

Suppose there is a circuit consisting of a battery, a resistor, and an inductor, and that there is initially no current. As current is increasing, the inductor creates an induced current in the opposite direction. I am confused as to which end of the inductor is at a higher voltage. Since the...

Homework Statement A positive point charge q is located inside a neutral hollow spherical conducting shell. The shell has inner radius a and outer radius b; b − a is not negligible. The shell is centered on the origin. Assume that the point charge q is located at the origin in the very center...

If you draw a free body diagram of the person, the vector sum of the normal and friction forces should be parallel to the person's body so the two vectors form a right triangle with one of the angles being a. And torque is taken about the point of contact. I think my mistake was saying that...

Suppose that a bicyclist is moving in a circle of radius R, leaning inwards at an angle a from the verticle, and that the height of the person (h) is less than R but not negligible. I am trying to find the angular velocity the bicyclist must move at. I tried doing this in two ways: using...

Homework Statement The problem is #12 found here: https://www.aapt.org/physicsteam/2013/upload/exam1-2012-unlocked-solutions.pdf. A uniform cylinder of radius a originally has a weight of 80 N. After an off-axis cylinder hole at 2a/5 was drilled through it, it weighs 65 N. The axes of the two...

My book says that for uniform rotational flow, the velocity at any point is proportional to r (v = wr.) In vortex flow, the velocity at any point is proportional to 1/r (angular momentum is conserved.) However, in uniform rotational flow, isn't angular momentum also conserved so the same logic...

Hm, Ok. I have another question. Since the force of gravitation is in the same direction as the particle's path as it is moved from infinity to a distance b away from another particle, the work done by gravity should be positive. However, the math shows that the work done by gravity is...

I understand that GPE is negative, but it does not come out this way when i try to derive it. I took the change in potential energy in bringing a particle from an infinite distance to a distance of b from another particle. ## \Delta U = - \int \vec F \cdot d \vec r ##. Since the...

I don't think I made myself clear. An identical problem is here: http://physics.bu.edu/~duffy/semester1/c14_atwood2.html. My question is how we can assume the string is massless because it is clear that the tension of the two sides of the string is different (the pulley would not rotate if the...

Suppose there is a pulley (a disc) of mass m1 and a string passes over the pulley with masses m2 and m3 hanging on both ends of the string with m3 > m2. I know that the acceleration should be (m3 - m2)g/(1/2m1 + m2 + m3) and I know how to get there. However, since the pulley rotates and has...

They would be mg/2. In the problem, why do the tensions in the vertical lengths have to be equal? The tension in the string increases opposite the direction of friction so from this argument, I see that the vertical lengths have different tensions. What am I missing?

A disk of mass M and radius R is held up by a massless string. (The two ends of the string are connected to a ceiling and the disk rests on the bottom of the string.) The coefficient of friction between the disk is μ. What is the smallest possible tension in the string at its lowest point...

A rope is wrapped around a pole with one end attached to a large object and the other end pulled with a tension T. The rope does not slip. I am confused why the tension varies within the rope. How would I know that the static friction force is non-zero?

Wait so this is asking for the maximum sustained speed. Therefore, the net force must be 0 so f_static + Mg sin theta = F_engine. The correct answer for the max speed requires Mg sin theta = F_engine so f_static = 0. Why can we let the value of static friction go to 0? The problem states...

Ok, that part makes sense to me now. However, how would I know to consider the axis of rotation to be at the point of contact instead of the center of mass in this question? I think that these two setups would lead to two different answers because rotation about the center of mass involves...

Homework Statement The maximum torque output from the engine of a new experimental car of mass m is τ . The maximum rotational speed of the engine is ω. The engine is designed to provide a constant power output P. The engine is connected to the wheels via a perfect transmission that can...

Homework Statement A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which...

Homework Statement A cubical box of mass 10 kg with edge length 5 m is free to move on a frictionless horizontal surface. Inside is a small block of mass 2 kg, which moves without friction inside the box. At time t = 0, the block is moving with velocity 5 m/s directly towards one of the...

say that a particle collides elastically with a wall 60 degrees from the wall's normal. the force from the wall is along the wall's normal. My questions is why there is no parallel component to the force from the wall since the particles velocity had a parallel component.