Exam 1: A: Foundations

A large cylindrical water tank is mounted on a platform with its central axis vertical.The water level is 3.75 m above the base of the tank,and base is 6.50 m above the ground.A small hole,2.22 mm in diameter,has formed in the base of the tank.Both the hole and the top of the tank are open to the air.We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m³. (a)How many cubic meters of water per second is this tank losing? (b)How fast is the water from the hole moving just as it reaches the ground?

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s.At what rate is water flowing in this channel?

A horizontal tube consists of a 7.0-cm diameter pipe that narrows to a 2.0-cm-diameter throat.In the pipe,the water pressure is twice atmospheric pressure and the water flows with a speed of 0.40 m/s.What is the pressure in the throat,assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m³,and atmospheric pressure is 1.01 × 10⁵ Pa.

A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north.What is the direction of the magnetic force on this current due to the field?

If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm,what is the average current density in this wire?

A projectile is fired from point 0 at the edge of a cliff,with initial velocity components of v_0x = 60.0 m/s and v_0y = 175 m/s,as shown in the figure.The projectile rises and then falls into the sea at point P.The time of flight of the projectile is 40.0 s,and it experiences no appreciable air resistance in flight.What is the height of the cliff?

A wind farm generator uses a two-bladed propeller (see figure)mounted on a pylon at a height of 20 m.The length of each propeller blade is 12 m.A small piece from the tip of the propeller breaks off when the propeller is vertical.At that instant,the period of the motion of the propeller is 1.2 s.The fragment flies off horizontally,falls with negligible air resistance,and strikes the ground at P. (a) How far is point P from the base of the pylon? (b) At what angle with respect to the vertical is the fragment moving just as it strikes the ground at P?

How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s)

If the electric potential in a region is given by V(x)= 6/x²,the x component of the electric field in that region is

An uncharged conductor has a hollow cavity inside of it.Within this cavity there is a charge of +10 µC that does not touch the conductor.There are no other charges in the vicinity.Which statement about this conductor is true? (There may be more than one correct choice.)

A particle with charge -5.00 C initially moves at = (1.00 + 7)00 )m/s. If it encounters a magnetic field Find the magnetic force vector on the particle.

Certain planes of a crystal of halite have a spacing of 0.399 nm.The crystal is irradiated by a beam of x-rays.First order constructive interference occurs when the beam makes an angle of 20° with the planes.What is the wavelength of the x-rays?

A beam of light of two different wavelengths enters a pane of glass 3.00 mm thick at an angle of incidence of 56°. The indices of refraction for the two different colors are 1.514 and 1.528.Because of dispersion,the colored beams,although parallel,are separated by a small distance.How far apart are they?

An object has a position given by = [2.0 m + (5.00 m/s)t] + [3.0 m - (2.00 m/s²)t²] ,where quantities are in SI units.What is the speed of the object at time t = 2.00 s?

Light of frequency 6.00 × 10¹⁴ Hz illuminates a soap film (n = 1.33)having air on both sides of it. When viewing the film by reflected light,what is the minimum thickness of the film that will give an interference maximum when the light is incident normally on it? (c = 3.00 × 10⁸ m/s)

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power.How much power is it discharging to the outdoors?

A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min,what is the average power generated by the child?

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m²? (μ₀ = 4π × 10^-7 T • m/A)

During an adiabatic process,an ideal gas does 25 J of work. What is the change in the internal (thermal)energy of the gas during this process?

For a long ideal solenoid having a circular cross-section,the magnetic field strength within the solenoid is given by the equation B(t)= 5.0t T,where t is time in seconds.If the induced electric field outside the solenoid is 1.1 V/m at a distance of 2.0 m from the axis of the solenoid,find the radius of the solenoid.