Exam 1: A: Foundations

In the figure,a slit 0.30 mm wide is illuminated by light of wavelength 426 nm.A diffraction pattern is seen on a screen 2.8 m from the slit.What is the linear distance on the screen between the first diffraction minima on either side of the central diffraction maximum?

Sputnik I was launched into orbit around Earth in 1957.It had a perigee (the closest approach to Earth,measured from Earth's center)of 6.81 × 10⁶ m and an apogee (the furthest point from Earth's center)of 7.53 × 10⁶ m.What was its speed when it was at its perigee? The mass of Earth is 5.97 × 10²⁴ kg and G = 6.67 × 10^-11 N • m²/kg².

A 20.0-N box rests on a 50.0-N box on a perfectly smooth horizontal floor.When a horizontal 15.0-N pull to the right is exerted on the lower box (see figure),both boxes move together.Find the magnitude and direction of the net external force on the upper box.

An object 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror.The radius of curvature of the mirror has a magnitude of 52 cm. (a)How far is the image from the vertex of the mirror? (b)What is the height of the image?

The point charge at the bottom of the figure is Q = +17 nC,and the curve is a circular arc.What is the magnitude of the force on the charge Q due to the other point charges shown? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

A toroidal solenoid has a central radius of 0.50 m and a cross-sectional diameter of 10 cm.When a current passes through the coil of the solenoid,the magnetic field inside the solenoid at its CENTER has a magnitude of 2.0 μT.What is the largest value of the magnetic field inside the solenoid when this current is flowing? (μ₀ = 4π × 10^-7 T • m/A)

A factory siren indicating the end of a shift has a frequency of 90.0 Hz.The speed of sound is 343 m/s. (a)What frequency is perceived by the occupant of a car traveling towards the factory at 25.0 m/s? (b)What frequency is perceived by the occupant of a car traveling away from the factory at 30.0 m/s?

Two in-phase loudspeakers are some distance apart.They emit sound with a frequency of 1536 Hz.You move between the speakers,along the line joining them,at a constant speed of 2.8 m/s.What beat frequency do you observe? The speed of sound in the room is 330 m/s.

A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long. (a)Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline. (b)Determine the angular speed of the sphere about its center at the bottom of the incline. (c)Through what angle (in radians)does this sphere turn as it rolls down the incline? (d)Does the linear speed in (a)depend on the radius or mass of the sphere? Does the angular speed in (b)depend on the radius or mass of the sphere?

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represents the direction of the acceleration of the object at point P?

When a fixed amount of ideal gas goes through an isobaric expansion

A ball is thrown directly upward and experiences no air resistance.Which one of the following statements about its motion is correct?

Kieran takes off from rest down a 50 m high,10° slope on his jet-powered skis.The skis have a thrust of 280 N parallel to the surface of the slope.The combined mass of skis and Kieran is 50 kg (the fuel mass is negligible).Kieran's speed at the bottom is 40 m/s.What is the coefficient of kinetic friction of his skis on snow?

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window.A loudspeaker is located outdoors,78 m away and facing the window.The intensity level of the sound entering the window space from the loudspeaker is 79 dB.Assume the acoustic output of the loudspeaker is uniform in all directions and that the acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window.The threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power entering through the window space is closest to

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A.If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s,how fast is the current changing?

A 56.0 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion.If the period of oscillation is 11.2 s,what is the spring constant of the bungee cord,assuming it has negligible mass compared to that of the jumper?

Two small insulating spheres are attached to silk threads and aligned vertically as shown in the figure.These spheres have equal masses of 40 g,and carry charges q₁ and q₂ of equal magnitude 2.0 μC but opposite sign. The spheres are brought into the positions shown in the figure,with a vertical separation of 15 cm between them.Note that you cannot neglect gravity.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The tension in the lower thread is closest to

A piece of wood is floating in a bathtub.A second piece of wood sits on top of the first piece,and does not touch the water.If the top piece is taken off and placed in the water,what happens to the water level in the tub?

An LRC series circuit has R = 15.0 Ω,L = 25.0 mH,and C = 30.0 μF.The circuit is connected to a 120-V (rms)ac source with frequency 200 Hz. (a)What is the impedance of the circuit? (b)What is the rms current in the circuit? (c)What is the rms voltage across the resistor? (d)What is the rms voltage across the inductor? (e)What is the rms voltage across the capacitor?

The acceleration of an object as a function of time is given by a(t)= (3.00 m/s³)t,where t is in seconds. If the object has a velocity 1.00 m/s at time t = 1.00 s,what is the displacement of the object between time T = 2.00 s and time t = 4.00 s?