Exam 1: A: Foundations

Two very large,flat plates are parallel to each other. Plate A,located at y = 1.0 cm,is along the xz-plane and carries a uniform surface charge density -1.00 μC/m². Plate B is located at y = -1.0 cm and carries a uniform surface charge density +2.00 μC/m².What is the electric field vector at the point having x,y,z coordinates (-0.50 cm,0.00 cm,0.00 cm)? (ε₀ = 8.85 × 10^-12 C²/N • m²)

A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 500 N/m.The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.When the displacement is x = -0.052 m,find the acceleration of the block.

A block is given a very brief push up a 20.0° frictionless incline to give it an initial speed of 12.0 m/s. (a) How far along the surface of the plane does the block slide before coming to rest? (b) How much time does it take to return to its starting position?

A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal.How fast is it moving after it has rolled 2.2 m down the plane?

A force = 3.00 N - 2)00 N Acts at a location = 1)00 m + 2)00 m On an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

The capacitance per unit length of a very long coaxial cable,made of two concentric cylinders,is 50 pF/m.What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Three particles travel through a region of space where the magnetic field is out of the page,as shown in the figure.The electric charge of each of the three particles is,respectively,

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1370 Hz.You are relieved that he is in pursuit of a different speeder when he continues past you,but now you perceive the frequency as 1330 Hz.What is the speed of the police car? The speed of sound in air is 343 m/s.

A 150-N box is being pulled horizontally in a wagon accelerating uniformly at 3.00 m/s². The box does not move relative to the wagon,the coefficient of static friction between the box and the wagon's surface is 0.600,and the coefficient of kinetic friction is 0.400. The friction force on this box is closest to

Three identical very small 50-kg masses are held at the corners of an equilateral triangle,0.30 m on each side.If one of the masses is released,what is its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10^-11 N • m²/kg²)

The figure shows a graph of the acceleration of a 125-g object as a function of the net force acting on it.What is the acceleration at points A and B?

Which one of the following free-body diagrams best represents the free-body diagram,with correct relative force magnitudes,of a person in an elevator that is traveling upward with an unchanging velocity? _f is the force of the floor on the person and _g is the force of gravity on the person.

At most,how many bright fringes can be formed on each side of the central bright fringe (not counting the central bright fringe)when light of 625 nm falls on a double slit whose spacing is 1)97 × 10^-6 m?

A series LRC circuit consists of a 5.00-pF capacitor,a 7.25-mH inductor,a 75.0-Ω resistor,and a 50.0-V ac power source of variable frequency.At what frequency will the impedance of this circuit be equal to 75.0 Ω?

A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine.Both liquids are clear and do not intermix.Point O is at the bottom of the tank,on a vertical axis.The indices of refraction of the oil and the brine are 1.40 and 1.52,respectively.A ray originating at O crosses the brine-oil interface at a point 0.60 m from the axis.The ray continues and emerges into the air above the oil.What is the angle that the ray in the air makes with the vertical?

As shown in the figure,a square insulating slab 5.0 mm thick measuring 2.0 m × 2.0 m has a charge of 8.0 × 10^-11 C distributed uniformly throughout its volume.Use Gauss's law to determine the electric field at point P,which is located within the slab beneath its center,1.0 mm from one of the faces. (ε₀ = 8.85 × 10^-12 C²/N • m²)

A nonuniform,80.0-g,meterstick balances when the support is placed at the 51.0-cm mark.At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s.What is its speed when the displacement is 1.75 cm?

Two unknown resistors are connected together.When they are connected in series their equivalent resistance is 15 Ω.When they are connected in parallel,their equivalent resistance is 3.3 Ω.What are the resistances of these resistors?

Treat each of your eyes as a circular aperture of diameter 3.5 mm.Light of wavelength 500 nm is used to view two point sources that are 894 m distant from you.How far apart must these two point sources be if they are to be just resolved by your eye? Assume that the resolution is diffraction limited and use Rayleigh's criterion.