A small marble is rolling on the inside of a parabolic bowl whose surface is given by z = ®r2 in cylindrical polar coordinates. There is no friction, but the gravity is pulling down (in the negative-z direction). Consider the most general case where the marble is free to move in any direction on the surface. (a) Identify all
A block of mass M= 2.5 kg is suspended in equilibrium by a long cord. A bullet of mass m= 0.055 kg, moving vertically upward with an unknown velocity v, hits the block from below. The block with embedded bullet then rises a total distance H= 1.2 meters above its initial position. Find v, the velocity of the bullet before impact.
A particle of mass m moves in one dimension along the positive x axis. It is acted on by a constant force directed toward the origin with magnitude B, and an inverse square law repulsive force with magnitude A/x^2. a) Find the potential energy function U(x) b) Sketch the energy diagram for the system when the maximum kineti
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?
A box sits at rest at the top of a frictionless hill, at a height of 40.50 m above the ground. The box slides down the hill, and then continues across rough ground (with coefficient of kinetic friction 0.36) until it stops. What distance will the box slide along the ground before coming to a stop?
A block of mass M slides along a horizontal table with speed Vo. At x=0 it hits a spring constant k and begins to experience a frictional force. The coefficient of friction is a variable and is given by u=bx, where b is a constant. Find the loss in mechanical energy when the block has come momentarily to rest.
Two point particles, each with charge Q, are placed at positions +- a x. A) What is the elctric potential anywhere along the y axis? B) How much energy does it take to move a thrid particle, charge Q, from infinity to a position in order to make an equilateral triangle among the charges? (ie. all edges have length 2a)
Two particles, of mass 1 kg and 3 kg, are traveling towards each other with velocities of 100 m/s and -40 m/s respectively. Using the laws of physics (e.g. conservation of energy & momentum) calculate the following: a) What are the initial energies of the particles? b) What are the final velocities of the particles? c) Wh
Draw a simple pendulum and label the locations of the maximum and minimum of (a) speed (b) acceleration (c) kinetic energy (d) potential energy
A sample of an ideal crosslinked rubber has a number average molecular weight between crosslinks of 5000 and a density of 900kg/m3. A block of this rubber, a cube of sides 100mm, is tested at a temperature of 300K. a). What is its tensile modulus? b). What is its shear modulus? Axes X, Y, and Z are chosen parallel to th
The lowest lying excited state of sodium is 2.104 eV above the ground state. Given that Planck's constant is 4.135x10 (to the negative 15 pwr.) eV/Hz, what color of light do you expect sodium atoms to give off? Table salt is the crystal sodium-chloride NaCl. If you have a gas burner in your kitchen, take some salt and throw it
Solar energy reaches the earth at a rate of about 1400 W/m^2 of surface perpendicular to the direction to the sun. By how much does the mass of sun decrease in each second?
An ideal, massless spring, pointing upwards from a surface has a mass of 3.0 kg placed on it, compressing it by 25 cm. The 3.0 kg mass is replaced by a 5.0 kg mass. The spring is then compressed by hand so that the end of the spring is 67 cm lower than the position of the spring when no mass is attached. The spring is then relea
Conservation of energy problem dealing with a frictionless pulley and two masses. Solution in MS Word.
A system containing a frictionless pulley is described in the diagram (see question attachment). If this system is released, at what speed does the 12.0 kg object hit the floor? HINT: Does the 12.0 kg object undergo free fall? Why or why not?