Exam 1: A: Foundations

System S' has a velocity u = +0.45c relative to system S,as shown in the figure.The clocks of S and S'are synchronized at t = t' = 0 when the origins O and O' coincide.An event is observed in both systems.The event takes place at x = 600 m and at time t = 1.9 μs,as measured by an observer in S.What is the x'-coordinate of the event,measured by an observer in S'?

Two men,Joel and Jerry,push against a wall.Jerry stops after 10 min,while Joel is able to push for 5.0 min longer.Compare the work they do.

When two point charges are 2.0 cm apart,each one experiences a 1.0-N electric force due to the other charge. If they are moved to a new separation of 8.0 cm,the electric force on each of them is closest to

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume.At a certain distance r₁ (r₁ < R)from the center of the sphere,the electric field has magnitude E.If the same charge Q were distributed uniformly throughout a sphere of radius 2R,the magnitude of the electric field at the same distance r₁ from the center would be equal to

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long.You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest.What is your sister's mass,assuming negligible friction?

Is it possible to transfer heat from a cold reservoir to a hot reservoir?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2)40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

When monochromatic light illuminates a grating with 7000 lines per centimeter,its second order maximum is at 62.4°. What is the wavelength of the light?

Two radio antennas are 120 m apart on a north-south line,and they radiate in phase at a frequency of 3.4 MHz.All radio measurements are made far from the antennas.If the east-west reference line passes midway between the two antennas,what is the smallest angle from the antennas,measured north of east,at which constructive interference of two radio waves occurs? (c = 3.00 × 10⁸ m/s)

The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact.The magnitude of the current is the same in all the wires,and the directions of current flow are as indicated.For which (if any)configuration will the magnetic field at the center of the square formed by the wires be equal to zero?

When a fixed amount of ideal gas goes through an isothermal expansion

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth.If the satellite instead had mass 4m,its orbital period would be

When you ride a bicycle,in what direction is the angular velocity of the wheels?

A He-Ne laser,which produces light of wavelength 632.8 nm,is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5° from the central spot,what is the distance between the slits of the grating?

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of 411 nm.The entire central band of the diffraction pattern is observed at ±90°.The illumination is now replaced by a nonrelativistic beam of electrons,each having a kinetic energy of 980 eV.When this beam hits the slit at normal incidence,at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-34 J • s,m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19 J)

A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m³. (a)What is the mass of the sphere? (b)What is the average density of this sphere?

What is the average translational kinetic energy per molecule of an ideal gas at a temperature of 300 K? The Boltzmann constant is 1.38 × 10^-23 J/K.

Express (4.3 × 10⁶)^-1/2 in scientific notation.

A proton is first accelerated from rest through a potential difference V and then enters a uniform 0.750-T magnetic field oriented perpendicular to its path.In this field,the proton follows a circular arc having a radius of curvature of 1.84 cm.What was the potential difference V? (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19C)

A rock is thrown directly upward from the edge of the roof of a building that is 66.2 meters tall.The rock misses the building on its way down,and is observed to strike the ground 4.00 seconds after being thrown.Neglect any effects of air resistance.With what speed was the rock thrown?