Recent content by e^(i Pi)+1=0

A force normal to the particle's velocity does no work yet would cause a deflection.

Homework Statement Solve 2x''+3x'+40x = 40y+3y' Homework Equations y = 0.05sin(10t) The Attempt at a Solution I used the annihilator method to find the answer of x(t) = Acos(10t)+Bsin(10t)+Ce-0.75tcos(sqrt(311)/4t)+De-0.75tsin(sqrt(311)/4t) where A, B, C and D are constants. The initial...

If they were acting on one another then yes. Initial total momentum of the system would sum to some non-zero number, x, and the final momentum would also sum to x.

What?

v is some velocity and Δv is a change in velocity, but they tend to be used interchangeably. If you define your initial velocity to equal zero, then of course Δv really will equal v, multiply both sides by mass to say impulse = momentum. Or to be more precise, the sum of the impulses equals...

Assuming your frame of reference is centered on the Earth so that it is considered stationary, then yes. It might be a lightbulb moment for you to realize that momentum is merely "stored force." It is the measure of force applied to an object over a time, as opposed to energy which is the force...

Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...

It's an offset vertical cylinder under a hemisphere. I don't follow what else you're saying.

Homework Statement Use polar coordinates to find the volume of the solid inside the hemisphere z=sqrt(16-x^2-y^2) and inside the cylinder x^2+y^2-4x=0 Homework Equations z=sqrt(16-x2-y2) x2+y2-4x=0 x=rcos(Θ) y=rsin(Θ) z=√(16-r2) The Attempt at a Solution ∫∫ r√(16-r2) dr dΘ The problem is...

Thanks. I wasn't sure if I was missing something.

I managed to get it down to 2ab/(4a-3b)-b, but that doesn't seem very simplified to me. I also added and subtracted terms in the numerator to make it factorable, ect but nothings really worked out.

Thanks for the help, I definitely appreciate it. I can make the formula give the correct answer if I choose arcsin(-1) = -pi/2 rather than 3pi/2, but that seems rather arbitrary. How am I supposed to know that the correct answer is the first and not the second?

The cylinder is vertical. The rise of the slope is h, and the run is 2r, so the angle is arctan (h/2r). It's just cut diagonal from the bottom leftmost edge to the top rightmost edge, then discard the bottom portion.

I'm an engineering student, and I'm making a formula for the volume of liquid in a cylinder that is cut in half diagonally. r is the radius, h is the height from the bottom to the top of the sloped flat bottom, and L is the height of the water within the cylinder. So when L = h you would expect...

https://en.wikipedia.org/wiki/Differentiation_under_the_integral_sign I don't understand where the last term comes from, the one that's an integral of a partial derivative. When I solve it using the FTC I get the same answer minus that term. If I differentiate first then integrate I get that...