Exam 1: A: Foundations

A locomotive is pulling 19 freight cars,each of which is loaded with the same amount of weight.The mass of each freight car (with its load)is 37,000 kg.If the train is accelerating at 0.22 m/s² on a level track,what is the tension in the coupling between the second and third cars? (The car nearest the locomotive is counted as the first car,and friction is negligible.)

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg • m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s.The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).What is the angular velocity of the turntable just after the ball is caught?

The root-mean-square speed (thermal speed)for a certain gas at 100°C is 0.500 km/s.If the temperature of the gas is now increased to 200°C,the root-mean-square (thermal)speed will be closest to

A wire segment 1.2 m long carries a current I = 3.5 A,and is oriented as shown in the figure.The +x-axis points directly into the page.A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown.What is the magnetic force vector on the wire segment?

While spinning down from 500.0 rpm to rest,a solid uniform flywheel does 5.1 kJ of work.If the radius of the disk is 1.2 m,what is its mass?

In a ballistics test,a 1.50-g bullet is fired through a 28.0-kg block traveling horizontally toward the bullet.In this test,the bullet takes 11.4 ms to pass through the block as it reverses the block's velocity from 1.75 m/s to the right to 1.20 m/s to the left with constant acceleration. Find the magnitude of the force that the bullet exerts on the block during this ballistics test.

An object weighing 44.1 N hangs from a vertical massless ideal spring.When set in vertical motion,the object obeys the equation y(t)= (6.20 cm)cos[(2.74 rad/s)t - 1.40]. (a)Find the time for this object to vibrate one complete cycle. (b)What are the maximum speed and maximum acceleration of the object? (c)What is the TOTAL distance the object moves through in one cycle? (d)Find the maximum kinetic energy of the object. (e)What is the spring constant of the spring?

An ideal Carnot engine operates between reservoirs having temperatures of 125°C and -20°C.Each cycle the heat expelled by this engine is used to melt 30.0 g of ice at 0.00°C.The heat of fusion of water is 3.34 × 10⁵ J/kg and the heat of vaporization of water is 2.25 × 10⁶ J/kg. (a)How much work does this engine do each cycle? (b)How much heat per cycle does this engine absorb at the hot reservoir?

Three point charges of -2.00 μC,+4.00 μC,and +6.00 μC are placed along the x-axis as shown in the figure.What is the electrical potential at point P (relative to infinity)due to these charges? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits,and the pattern is viewed on a screen 1.20 m away.The fifth bright fringes (not counting the central fringe)occur at ±2.12 cm on either side of the central bright fringe.The entire apparatus is now immersed in a transparent liquid.When the experiment is repeated,the fifth bright fringes now occur at ±1.43 cm from the central bright fringe.(c = 3.00 × 10⁸ m/s) (a)How far apart are the slits? (b)What is the index of refraction of the liquid?

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m.The electric field at a point P,which is 0.50 m from the center of the sphere,is 15,000 N/C and is directed radially outward.At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

The special theory of relativity predicts that there is an upper limit to the speed of a particle.It therefore follows that there is also an upper limit on the following properties of a particle.

The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at x = 2.00 m,what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m,as shown in the figure.The sphere carries a net excess charge of -500 nC.A point charge of +300 nC is present at the center. (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C)The radial component of the electric field at a point that is 1.50 m from the center is closest to

A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges equal to zero?

Upon being struck by 240-nm photons,a metal ejects electrons with a maximum kinetic energy of 1)45 eV.What is the work function of this metal? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

When an object 1.15 cm tall is placed 12 cm from a lens,the lens produces an upright image of the object that is 5.75 cm tall.What is the focal length of the lens?

Ocean tides are waves that have a period of 12 hours,an amplitude (in some places)of 1.50 m,and a speed of 750 km/hr.What is the distance between adjacent crests of these waves?

The focal lengths of the objective and eyepiece in a compound microscope are 0.80 cm and 2.5 cm,respectively.The image formed by the objective is 16 cm from it and the final image is 25 cm from the eye.What is the total overall magnification of the microscope?

A convex lens has a focal length f.An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens.The image is located at what distance from the lens?