Recent content by americanforest

Right physics, wrong algebra/arithmetic.

B has no horizontal component so you need to find at which angle (other than the one you originally found) the horizontal component of C is exactly opposite to the horizontal component of A. Such an angle is guaranteed to exist (think of the graph of cosine).

What formula do you know that is related to heating and/or transforming material from one physical state to another? Those are the two processes which must occur here.

This looks very well done. My only recommendation is to use numbers more sparingly in your actual work. Use variables and plug in at the very end. It makes it easier to catch mistakes, both for you and for us.

Remember also the rule that if multiple resistors have the same voltage drop associated with them then they are parallel

Firstly, they have different moments of inertia. Secondly, yes, gravity acts at the center of mass which is different for the two systems.

Total relativistic energy is \gamma m c^{2} where \gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^{2}}}. If v=c then this quantity goes to infinity.

Nevermind, I figured it out a way to prove it.

The integral of a complex exponential ( e^(ix) ) over x from 0 to infinity is supposedly such that the value of the definite integral at the upper limit is zero and so it's just -1/i. Why is this? It's just an oscillating function after all.

It depends on initial conditions. If you start the clock when it is at its biggest displacement (as in my example) then use cosine. This is because the cosine of zero is one. Thus, at time zero, the cosine functions is maximum, just like the distance in my example. That's why I used cosine. If I...

Just replace the cosines and sines in the first two equations with the expressions in terms of x and y from the last two equations. Then solve the two first equations for your two unknowns, the Cartesian unit vectors. This will give you the unit vectors as functions of x and y. If you want them...

The rho is the radial unit vector. Centrifugal forces push the mass out; in order for it to stay in a circle there needs to be an equal and opposite force pulling it in. This is what the force in the negative rho direction represents. Mathematically...

To keep it in a circle you need a certain force. To accelerate it tangentially you need another. Superpose them to get the total force. \vec{F}=-\frac{mv^{2}}{R}\hat{\rho}+F_{tan}\hat{\theta} Then use basic kinematic equations with the information given to find the tangential force. Then it's...

Say you have a mass lying on a frictionless table. The mass is attached to a spring which is attached to the wall. The spring is initially unstretched. You stretch it out a certain distance from the initial position. We call that distance d. This is the amplitude of the oscillation. It has units...

Use these facts for conversion from polar to Cartesian and vice versa: \hat{\theta}=-sin(\theta)\hat{x}+cos(\theta)\hat{y} \hat{\rho}=cos(\theta)\hat{x}+sin(\theta)\hat{y} sin(\theta)=\frac{y}{\sqrt{x^{2}+y^{2}}} cos(\theta)=\frac{x}{\sqrt{x^{2}+y^{2}}} Solve this system of equations for...