The spring is now compressed so that unconstrained end moves from x = 0 to x = L.
Using the work integral W = ∫ x f(xᵢ) F(x)⋅dx, find the work done by the spring as it is compressed. Express the work done by the spring in terms of k and L.

Agas is contained in a vertical, frictionless piston–cylinder device. the piston has a mass of 3.2 kg and a cross-sectional area of 35 cm2. a compressed spring above the piston exerts a force of 190 n on the piston. if the atmospheric pressure is 95 kpa, determine the pressure inside the cylinder.

An alpha particle with kinetic energy 12.5 mev makes a collision with lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude l = p0 b, where p0 is the magnitude of the initial momentum of the alpha particle and b=1.40×10−12 m. (assume that the lead nucleus remains stationary and that it may be treated as a point charge. the atomic number of lead is 82. the alpha particle is a helium nucleus, with atomic number 2.) what is the distance of closest approach?

By examining a wave’s pattern after it interacts with a barrier or gap, measurements can be made to better understand certain wave phenomena. what is a broad question you can answer by doing this experiment?