Exam 1: A: Foundations

A 25.0-mH inductor,a 2.00-μF capacitor,and a certain resistor are connected in series across an ac voltage source at 1000 Hz.If the impedance of this circuit is 200 Ω,what is the resistance of the resistor?

A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 10⁶ kg of coal each day. The heat produced by the combustion of coal is 3.3 × 10⁷ J/kg. The steam that drives the turbines is at a temperature of 300°C,and the exhaust water is at 37°C. (a)What is the overall efficiency of the plant for generating electric power? (b)What is the maximum efficiency that this plant could possibly have using the same temperature extremes that it presently uses? (c)How much thermal energy is exhausted each day by this plant?

A proton,with mass 1.67 × 10^-27 kg and charge +1.6 × 10^-19 C,is sent with velocity 7.1 × 10⁴ m/s in the +x direction into a region where there is a uniform electric field of magnitude 730 V/m in the +y direction.What are the magnitude and direction of the uniform magnetic field in the region,if the proton is to pass through undeflected? Assume that the magnetic field has no x-component and neglect gravitational effects.

A researcher is investigating a cubic crystal with x-rays.He is looking at Bragg reflection from the planes parallel to the cube faces.He finds that when using x-rays of 0.165 nm a strong first maximum occurs when the beam makes an angle of 23.5° with the planes.What is the spacing of adjacent atoms in the crystal?

Two optically flat glass plates,16.0 cm long,are in contact at one end and separated by 0.0200 mm at the other end.The space between the plates is occupied by oil with index of refraction 1.45.The index of refraction of the glass plates is 1.55.The plates are illuminated at normal incidence with monochromatic light,and fringes are observed.If the dark fringes are spaced 2.00 mm apart,what is the wavelength of the monochromatic light?

A uniform 300-kg beam,6.00 m long,is freely pivoted at P,as shown in the figure.The beam is supported in a horizontal position by a light strut,5.00 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 23,000 N in the strut is permitted,due to safety.The maximum mass M of the load is closest to

If you double the pressure on the surface of a can of water,the buoyant force on a stone placed in that water will

For the circuit shown in the figure,all quantities are accurate to 2 significant figures.What is the value of the current I₁?

A tiny vibrating source sends waves uniformly in all directions.An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s. (a)What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source? (b)At what rate is energy leaving the vibrating source of the waves?

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume.At a radial distance r₁ = R/4 from the center,the electric field has a magnitude E₀. What is the magnitude of the electric field at a radial distance r₂ = 2R?

An LRC series circuit consists of an 85.0-Ω resistor,a 14.0-μF capacitor,a 1.50-mH inductor,and a variable frequency ac source of voltage amplitude 13.25 V.At what angular frequency will the inductive reactance be 4.00 times as large as the capacitive reactance?

A stationary siren emits sound of frequency 1000 Hz and wavelength 0.343 m.An observer who is moving toward the siren will measure a frequency f and wavelength λ for this sound such that

What is the maximum distance we can shoot a dart,from ground level,provided our toy dart gun gives a maximum initial velocity of 2.78 m/s and air resistance is negligible?

If an electron is accelerated from rest through a potential difference of 9.9 kV,what is its resulting speed? (e = 1.60 × 10^-19 C,k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C², ^m_el = 9.11 × 10^-31 kg)

A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod?

The entropy of an isolated system must be conserved,so it never changes.

A block slides down a frictionless inclined ramp.If the ramp angle is 17.0° and its length is 30.0 m,find the speed of the block as it reaches the bottom of the ramp,assuming it started sliding from rest at the top.

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years.Saturn circles the Sun at a distance of 1.43 × 10¹² m.What is the orbital period of Saturn?

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board (a)by pillar A. (b)by pillar B.

You have available lenses of focal lengths 2.0 cm,4.0 cm,8.0 cm,and 16.0 cm. (a)If you were to use any two of these lenses to build a telescope,what is the maximum magnification you could achieve? (b)If you were to use any two of these lenses to build a telescope,what is the lens separation for the maximum magnification telescope?