Starting with a suitable relativistic lagrangian for single particle: l = -mc2 (1-b2)1/2 - v
derive the equation of motion.

Molten iron fills a mould, which has a volume of 200 cm cubed. calculate the volume when the iron cools and solidifies. molten iron has a density of 7.0g/cm cubed. in its solid state, iron has a density of 8.0g/cm cubed.

It's a snowy day and you're pulling a friend along a level road on a sled. you've both been taking physics, so she asks what you think the coefficient of friction between the sled and the snow is. you've been walking at a steady 1.5m/s, and the rope pulls up on the sled at a 32 ∘ angle. you estimate that the mass of the sled, with your friend on it, is 65 kg and that you're pulling with a force of 80 n .

Two charged particles, q1 and q2, are located on the x-axis, with q1 at the origin and q2 initially at x1 = 12.2 mm. in this configuration, q1 exerts a repulsive force of 2.62 µn on q2. particle q2 is then moved to x2 = 18.0 mm. what is the force (magnitude and direction) that q2 exerts on q1 at this new location? (give the magnitude in µn.)