Recent content by Kilgour22

One case that this would hold true is if there's no work done on the system and the system is not moving.

As you get into more complicated questions, make sure to draw your coordinate system indicating which directions are positive! This can save you lots of heartache in the future, especially with problems relating to force.

What does one wavelength look like? A diagram may help shed some light.

Remember what static friction is. The only way that static friction can be overcome is if ##F_{net} > F_s ##. It is as this point where the intermolecular bonds (which is what cause friction in the first place) are unable to keep an object stationary. When this happens, a new type of friction is...

Not a problem. The more you learn and understand physics, the more fascinating and intriguing it becomes. :)

To expand a little bit and perhaps shed some more light about what I'm getting at, remember that momentum is a vector quantity and can therefore be broken into x and y parts. Conservation of momentum tells us something very important relating to this that we can use to solve these types of problems.

What does it mean for a collision to be "perfectly elastic"? Perhaps this tells us something about one of the variables, so we can solve for the other unknown? Also, what does conservation of momentum tell us?

When you push against the table and your chair rolls backwards but not the table, then somewhere there has to be friction. The coefficient of static friction is NEVER less than the coefficient of kinetic friction or rolling friction between two surfaces. As a result, if not enough force is...

For #4, what do we know about the final velocity of the blue car? For #5, which time interval are we missing in order to find the total time, and what do we need to know in order to find that time interval? For #6, think about the formula ##\Delta{x} = v_{0x}\Delta{t} +...

No worries! It just takes practice, and eventually you'll become so familiar with integration that the answer to such problems will be solvable in your head rather easily. :)

Instead of using integration by parts, is there another method we can use, such as letting ## u = 2\pi{x} ##, then getting your integral with respect to ##du## instead of ##dx##? EDIT: Bonus question: Can you spot the flaw with using integration by parts for this integral, and why it will not...

Remember that energy is a scalar quantity, so we want to use the magnitude of the velocity as our ## v_i ## and our ## v_f## instead of ##(v_x)_i##, ##(v_y)_i## ##(v_x)_f## and ##(v_y)_f##. Also, this equation may help you solve this problem: ## \Delta{E} = E_f - E_i = 0J ## What are ##...

In order to get the second answer, you need to take the ln of both sides of the equation, then differentiate implicitly. After rearranging, if done right (presumably the second answer is correct), you should have the same answer.

In general, the integrating factor you multiply the linear ODE by is ## e^\int \frac{M_y - N_x}{N}dx ## or ## e^\int \frac{N_x - M_y}{M}dy ## to make an inexact linear ODE exact, where ## M_y = \frac{\partial M_(x,y)}{\partial y} ## and ## N_x = \frac{\partial N_(x,y)}{\partial x} ##. So if you...

Thank you, that's precisely what I needed to know!