Hi Nechama!
This questions looks like it is defining position as the "x" component of the piston's position as the wheel spins it around. That x position is described by a simple harmonic motion expression. This is demonstrated by the gif at the top of this page:
https://kaiserscience...

Hi Vans! It looks like this problems is set up as a Young's double-slit experiment (substituting the two point sources for the slits). The clue is that the detection point is much, much farther (1000 times farther) from the sources than the sources are from each other.
NOTE: ...

Hi Achillos!
I will assume these problems are numbered 1 - 5, top to bottom.
1. This problem uses the equilibrium conditions from statics. Using x-y (Cartesian) coordinates, I usually write these as three conditions:
(a) sum of the x-direction...

Hi Sarah!
Assuming the brakes are applying the net force to the car over this situation (which we have to assume, since we are not given information about any other unbalanced force), we can use Newton's 2nd law to determine the force:
Fnet = ma
where
m...

Hi Nechama!
If we treat the salmon as a projectile, we can break the problem down into horizontal and vertical motion, and look at the conditions on each.
HORIZONTAL
---------------
In the horizontal direction, by definition, there is no acceleration for a projectile...

Hi Aryan!
Remember that average speed = [total distance]/[total time]
The total distance is not specified, but we can call it "d".
The total time will be the sum of the two times for each segment of the trip. Those times can be calculated...

If this still will help:
The expression for the electric potential at the surface (referenced to 0 at infinity) is pretty straightforward, since the entire spherically symmetric distribution is contained within that position. Therefore, it presents the same electric potential...

If you still need help with this one, I would suggest setting up Newton's 2nd law in either the horizontal or vertical direction. I would start with the horizontal, since there are fewer force components at work in that direction (since gravity is not present in the horizontal). You...

This can be solved using the definition of Young's modulus, as the ratio of applied stress to compressive or tensile strain. This can be written as:
E = stress/strain = (F/A)/(ΔL/L)
where
F = applied force
A = cross-sectional area of the material...

Hi Zack!
As you may already know, this problem hinges on the Doppler effect, where a shifted frequency f' is observed when a source of absolute frequency f is sounded while the source and observer are in relative motion toward or away from each other:
f' = [(v ± vobs)/(v(-/+)vs)]f
where
v...

Hi Zack!
In addition to Arturo's fine solution, you can also approach this as a conservation of mechanical energy problem (since gravity is the only force doing work in the problem, and gravity is conservative).
Initially, the mechanical energy of this system, meaning...

Hi Pia!
I think the solution in the video you linked to is incorrect. There should be a third imaging considered, because the light physically returns through the lens. The person in the video is treating the system as if it were two lenses, but mirrors and lenses are...

Hi Gustavo!
Gauss' law combined with a symmetry argument can show the electric field at the exact center of a uniform sphere of charge is zero. The same applies in this case, since the off-axis cavities are placed symmetrically around the center.
It can be shown...

Hi Ab!
This problem is a little tricky, because the usual condition about rolling on the ground without slipping does not appear to apply (I will assume, however, that the rope comes off the disk without slipping; otherwise, all bets are off and the problem gets a *lot* more difficult...

Hi Porcia!
You should have a table in whatever textbook or class material you have for something called the "temperature coefficient of resistivity (or resistance)," usually symbolized α. You can also probably find it online. That coefficient is usually...

Hi Arun!
A board swinging about its end is what is called a "physical pendulum." In a simple pendulum, the mass is all concentrated at the end of the support, and the rest of the support is considered to have insignificant mass. In a physical pendulum, though,...

Hi Muhammad!
(a) We are meant to treat this situation as a mass (the climber and equipment) on the end of a spring (the rope). For that, there is a formula for the frequency of oscillation (f).
f = (1/2π)√(k/m)
where
f = frequency...

Hi Arifur!
A singularity is a point with a mass density approaching infinity in the limit. It occurs when all the mass of an object is gravitationally collapsed (under its own weight) to (in the limit) a single point. This happens with some supermassive stars (I think...

Hi Tom!
As long as the cavity is fully inside the metal sphere, it does not matter for this question whether it is off center. Metal being a conductor, it is not allowed to have any standing net electric fields inside of it. Conceptually, this means the electric field...

Hi Ben!
It may be better to ask this as a math question, since you are looking to convert your PDE into an ODE along some characteristic curve that you have to discover. This is, admittedly, not my area of expertise, but I can see what I can find out with a little research....