Calculating the reading on a scale.

A chain of mass M and length l is suspended vertically with its lowest end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of chain, x, has fallen? (Neglect the size of individual links)

Using Hooke's Law and velocity to calculate compression.

A 2100.00 kg car moving at 27.50 m/s hits an initially uncompressed horizontal spring with spring constant of 1.60à—10^6 N/m. What is the maximum compression of the spring? (Neglect the mass of the spring)

Energy conservation using centripetal motion.

A roller coaster has an initial speed of 9.50 m/s at the top of the first hill, which is 44.00 m above the ground. Neglecting friction, what will be the speed of the roller coaster at the top of the next hill, which is 26.00 m above the ground?

Interaction between two atoms

A commonly used potential energy function to describe the interaction between two atoms is the Lennard-Jones potential U=e((Ro/R)^12-2(Ro/R)^6) a) Show that the radius at the potential minimum is Ro, and that the depth of the potential well is e. b) Find the frequency of small oscillations about equilibrium for 2 identical atoms of mass m bound to each other by the Lennard-Jones interaction. Ans: w=12 sqr(e/Ro^2m)

Calculating the gravitational energy of a beat and its velocity.

A bead of mass, m, slides without friction on a smooth rod along the x-axis. The rod is equidistant between two spheres of mass M. The spheres are located at x=0, y= +a and x=0, y=-a, and attract the bead gravitationally. a) Find the potential energy of the bead. b) The bead is released from at x=3a with velocity Vo toward the origin. Find the speed as it passes the origin.