# Search results

1. ### Kinetic energy of inelastic collision problem

Homework Statement A particle of mass m1 and velocity u1 collides with a particle of mass m2 at rest. The two particles stick together. What fraction of the original kinetic energy is lost in the collision? Homework Equations Conservation of momentum law The Attempt at a Solution...
2. ### Conservation Laws and Projectile Motion

Homework Statement A cannon in a fort overlooking the ocean fires a shell of mass M at an elevation angle, theta and muzzle velocity, v0. At the highest point, the shell explodes into two fragments (masses m1 + m2 = M), with an additional energy E, traveling in the original horizontal...
3. ### Find the Fourier Series

Homework Statement Consider F(t) = sin(wt) when 0 < t < pi/w and 0 when pi/w < t < 2pi/w. Where w is the frequency and t is the time. Find the Fourier Series Homework Equations F(t) = sum of (ck e^ikt) See attached doc with math type; its a lot more readable. The Attempt...
4. ### Finding frequency of a pendulum with a cycloidal path

Homework Statement A pendulum is suspended from the cusp of a cycloid cut in a rigid support. The path described by the pendulum bob is cycloidal and given by x = a(phi – sin(phi)) y = a(cos(phi) – 1) where the length of the pendulum is l = 4a, and where phi is the angle of rotation...
5. ### Showing position vector follows parabolic path

Homework Statement Hi, got my HW back from prof. There were a few problems... I want to understand these before the test. Show that r(t) = (at^2)/2 + vt + r lies in a plane and that if a and v are not parallel, then r(t) traces out a parabola. Note a, v, and r are constant vectors here...