Exam 1: A: Foundations

A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long.If this solenoid carries a current of 12 A,what is the magnitude of the magnetic field near the center of the solenoid? (μ₀ = 4π × 10^-7 T • m/A)

A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400.00 Hz. The sound he hears reflected back from the wall is at a frequency 408.00 Hz. At what is the speed is the boy riding his bicycle toward the wall? Assume the speed of sound in air is 340 m/s.

An 1100-kg car traveling at 27.0 m/s starts to slow down and comes to a complete stop in 578 m.What is the magnitude of the average braking force acting on the car?

A cubic box with sides of 20.0 cm contains 2.00 × 10²³ molecules of helium with a root-mean-square speed (thermal speed)of 200 m/s.The mass of a helium molecule is 3.40 × 10^-27 kg.What is the average pressure exerted by the molecules on the walls of the container? The Boltzmann constant is 1)38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol • K = 0.0821 L • atm/mol • K.

An 18-mm wide diffraction grating has rulings of 880 lines per mm.Monochromatic light of 590 nm wavelength is incident normally on the grating.What is the largest angle,measured from the central bright spot,at which an intensity maximum is formed?

Two motors in a factory are running at slightly different rates.One runs at 825 rpm and the other at 786 rpm.You hear the sound intensity increase and then decrease periodically due to wave interference.How much time elapses between successive maxima of the sound intensity?

If a 5.0 kg box is pulled simultaneously by a 10.0 N force and a 5.0 N force,then its acceleration must be

A ball drops some distance and gains 30 J of kinetic energy.Do NOT ignore air resistance.How much gravitational potential energy did the ball lose?

A series LRC circuit consists of an ac voltage source of amplitude 75.0 V and variable frequency,a 12.5-µF capacitor,a 5.00-mH inductor,and a 35.0-Ω resistor. (a)To what angular frequency should the ac source be set so that the current amplitude has its largest value? (b)Under the conditions of part (a),what is the maximum current amplitude? (c)Suppose that the voltage source is set to twice the angular frequency needed in part (a).What will be the current amplitude in this case?

The magnitude of the electric field at a point P for a certain electromagnetic wave is 570 N/C.What is the magnitude of the magnetic field for that wave at P? (c = 3.0 × 10⁸ m/s)

As shown in the figure,a rectangular current loop is carrying current I₁ = 3.0 A,in the direction shown,and is located near a long wire carrying a current I_w.The long wire is parallel to the sides of the rectangle.The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire,as shown.We measure that the net force on the rectangular loop is 4.9 × 10^-6 N and is directed towards the wire.(μ₀ = 4π × 10^-7 T • m/A) (a)What is the magnitude of the current I_w? (b)In which direction does I_w flow: from top to bottom or from bottom to top in the sketch?

A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s on a flat road.What is the magnitude of the total resistive force acting on the car (due to friction,air resistance,etc.)? (1 hp = 746 W)

Which of the graphs in the figure illustrates Hooke's Law?

If the electric field is zero everywhere inside a region of space,the potential must also be zero in that region.

A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe,as shown in the figure.The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream.The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s.The density of the air is 1.29 kg/m³,and the density of the paint is 1200 kg/m³.We can treat the air and paint as incompressible ideal fluids.What is the maximum diameter of the constriction that will allow the sprayer to operate?

What is the average power dissipated by a 25-Ω resistor in an LRC series ac circuit for which the power factor is equal to 0.25 and the maximum voltage of the ac source is 8.0 V?

Vector has a magnitude of 5.5 cm and points along the x-axis. Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a)Determine the x and y components of Vector . (b)Determine the x and y components of Vector (c)Determine x and y components of the sum of these two vectors. (d)Determine the magnitude and direction of the sum of these two vectors.

The intensity of sunlight falling on the earth is about 1.4 kW/m² (before any gets absorbed by our atmosphere).At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.)

The figure shows two arcs of a circle on which charges +Q and -Q have been spread uniformly.What is the value of the electric potential at the center of the circle?

One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C exhaust temperature = 430°C 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour,where 1 cal = 4.19 J (a)What is the actual efficiency of this engine? (b)What is the Carnot efficiency of the engine? (c)What is the power output of this engine?