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A simple harmonic oscillator takes 12 s to undergo 5 complete vibrations. Find (a) the period of its motion, (b) the frequency in hertz and (c) the angular frequency in radians per second.
A ball is dropped from a height of 4 m and makes an elastic collision with the ground. Assume that no mechanical energy is lost to air resistance. (a) Show that the ensuing motion is periodic. (b) Determine the period of the motion. (c) Is the motion..
A simple pendulum has a period of 2.5 s. (a) What is its period if its length is made four times larger? (b) What is its period if the mass of the suspended bob is made two times larger?
Suppose that a binary star system consists of two stars of equal mass. They are observed to be separated by 400 million kilometers and to take 3.0 Earth years to orbit about a point midway between them. What is the mass of each?
When the Sun evolves to the red giant stage its radius may increase to as high as 100 solar radii. Using the expression density = Mass/volume, and assuming the mass doesn’t change, by what factor does the Sun’s density change when it expands to the r..
Using the mass-luminosity relationship if a main sequence star has a luminosity of 3000 times the luminosity of the Sun, what is its mass in relation to the Sun?
The current density inside a long, solid, cylindrical wire of radius a is in the direction of the central axis and its magnitude varies with radial distance r from the axis according to J = br2, where b is a positive constant.
Now adapt the ideas of the energy and entropy of mixing to gasses in different cylinder. The temperature is fixed (there is a thermal reservoir so that all changes are done isothermally). A system starts with n(He)=10 moles of helium in a cylinder..
The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius rh = 0.474 m and mass 5.46 kg, and two thin crossed rods of mass 7.80 kg each. You would like to replace the wheels with uniform disks that are 5.25 cm th..
A 109-kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical axis through its center. A 69.9-kg person stands on the platform at a distance of 1.07 m from the center and a 29.9-kg dog sits on the platform near the..
A uniform thin rod of mass 4.55 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass 0.577 kg, are attached to the ends of the rod. What must the length of the rod be so that the moment of inertia..
A lithium-5 nucleus is moving at 1.6 Mm/s when it decays into a proton and an alpha particle. What are the magnitude and direction of the proton's velocity
A convex mirror has a focal length of -48.0 cm. A 12.0-cm-tall object is located 36.0 cm in front of this mirror. Using a ray diagram drawn to scale, determine the location of the image. Note that the mirror must be drawn to scale
The electric field has been measured to be vertically upward everywhere on the surface of a box 20 cm long, 4 cm high, and 3 cm deep, What is the amount of charge enclosed by the box
Juan and Pablo carry a load weighing 720 N on a pole between them. If the weight of the 120-N pole is considered, what force does each person support
A Young's double-slit interference experiment is performed with blue-green argon laser light. What is the wavelength of argon laser light
A current with sinusoidal time-dependence, whose peak value is 3.55 A and frequency is 775 cycles per second, Calculate the average power dissipated by the loop
A long straight horizontal wire located on the equator carries a current. What direction should current be
suppose that .12 mol of nitrogen gas in contact with a thermal reservoir that holds the temperature fixed at T0=9.8C has an initial volume of 1.3L and does 14J of work
Prove that, given two angular momenta, L and S, their sum J = L+ S satisfies the commutation relations of the angular momentum (and therefore has the all the general properties of an angular momentum, e.g., the ladder structure, etc.).
With its double helix structure, DNA is coiled like a spring. A biophysicist grabs the end of a DNA strand with optical tweezers, What's the DNA spring constant
A 7.0 k resistor is in series with a 26.0-mH inductor, Calculate the impedance of the circuit for the following source frequencies
Find the speed of a satellite moving in a circular orbit just above the surface of Mars. Mars has a radius of 3.40 106 m and a mass of 6.42 1023 kg
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