Exam 1: A: Foundations

In a certain region,the electric potential due to a charge distribution is given by the equation V(x,y,z)= 3x^2y2 + yz³ - 2z^3x,where x,y,and z are measured in meters and V is in volts.Calculate the magnitude of the electric field vector at the position (x,y,z)= (1.0,1.0,1.0).

A pool player is attempting a fancy shot.He hits the cue ball giving it a speed of 5.57 m/s and directs its center on a path tangent to the surface of the target ball having the same mass as the cue ball.After the collision (on a frictionless table)the initially-stationary ball moves with a speed of 4.82 m/s.After the collision,the new speed of the cue ball and the relative direction of the balls are closest to

A ball is projected upward at time t = 0.00 s,from a point on a roof 70 m above the ground and experiences negligible air resistance.The ball rises,then falls and strikes the ground.The initial velocity of the ball is 28.5 m/s.Consider all quantities as positive in the upward direction.The velocity of the ball when it is 39 m above the ground is closest to

In the figure,two solenoids are approaching each other with speed v as shown.The induced current through the resistor R is

A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm.If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT,what is the value of N? (μ₀ = 4π × 10^-7 T • m/A)

A 60.0-kg person rides in an elevator while standing on a scale. The scale reads 400 N. The acceleration of the elevator is closest to

Is it possible for a system to have negative potential energy?

A car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg. Spring mounted bumpers ensure that the collision is essentially elastic.If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity)after the collision,what was the initial speed of the car?

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a)What is the maximum speed of the needle? (b)What is the maximum acceleration of the needle?

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s.The cars stick together.Assume that any other unbalanced forces are negligible. (a)What is the speed of the wreckage just after the collision? (b)In what direction does the wreckage move just after the collision?

As a tile falls from the roof of a building to the ground its momentum is conserved.

Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²) (a)What is the potential at point A (relative to infinity)due to these charges? (b)What is the potential at point B (relative to infinity)due to these charges?

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value.If the speed of the water in the larger section of the pipe was 36 m/s,what is its speed in this smaller section?

An electron moving with a velocity = 5.0 × 10⁷ m/s Enters a region of space where perpendicular electric and a magnetic fields are present.The electric field is = )What magnetic field will allow the electron to go through the region without being deflected?

A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure.A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor. (a)What is the tension in the rope? (b)What is the magnitude of the force that the floor exerts on the plank?

A metallic sheet has a large number of slits,5.0 mm wide and 20 cm apart,and is used as a diffraction grating for microwaves.A wide parallel beam of microwaves is incident normally on the sheet.What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 10⁸ m/s)

A gas of helium atoms (each of mass 6.65 × 10^-27 kg)are at room temperature of 20.0°C.What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J • s,the Boltzmann constant is 1.38 × 10^-23 J/K)

An airplane is flying at a speed of 2.00 × 10² m/s in level flight at an altitude of 8.00 × 10² m. A package is to be dropped from the airplane to land on a target on the ground.Ignore air resistance. (a) At what horizontal distance away from the target should the package be released so that it lands on the target? (b) In what direction relative to the horizontal will the package be traveling when it hits the ground?

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400,how much work did she do?

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.Under maximum load,find the magnitude of the x component of the force exerted on the beam by the pivot at P.