Exam 1: A: Foundations

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above the horizontal.If T is the tension in this wire,then

A perfect Carnot engine operates between the temperatures of 300K and 700K,drawing 60 kJ of heat from the 700K reservoir in each cycle.How much heat is dumped into the 300K reservoir in each cycle?

If = 3 - + 4 and = x + - 5 ,find x so will be perpendicular to .

If we double only the mass of a vibrating ideal mass-and-spring system,the mechanical energy of the system

X and Y are two uncharged metal spheres on insulating stands,and are in contact with each other.A positively charged rod R is brought close to X as shown in Figure (a). Sphere Y is now moved away from X,as in Figure (b). What are the final charge states of X and Y?

You swing a bat and hit a heavy box with a force of 1500 N.The force the box exerts on the bat is

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible oil and capped at both ends with tight-fitting pistons.The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm.The car rests on the piston on the wider arm of the U-tube.The pistons are initially at the same level.What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem,you can neglect the weight of the pistons.)

A diffraction grating has 450 lines per mm.What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?

An apple falls from an apple tree growing on a 20° slope.The apple hits the ground with an impact velocity of 16.2 m/s straight downward.What is the component of the apple's impact velocity parallel to the surface of the slope?

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

A camera used for aerial surveillance has a lens with a 30-cm maximum aperture and a 42-cm focal length.Assume light of 550-nm wavelength is used and that the resolution of the camera is limited solely by diffraction.What is the angular resolution of the camera at maximum aperture?

A slender uniform rod 100.00 cm long is used as a meter stick.Two parallel axes that are perpendicular to the rod are considered.The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark.What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

The figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s (a)what is the length of the path the object followed? (b)what is the displacement of the object?

A closed loop conductor that forms a circle with a radius of 2.0 m is located in a uniform but changing magnetic field.If the maximum emf induced in the loop is 5.0 V,what is the maximum rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies?

An 800-kHz radio signal is detected at a point 4.5 km distant from a transmitter tower.The electric field amplitude of the signal at that point is 0.63 V/m.Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed.What is the magnetic field amplitude of the signal at that point? (c = 3.0 × 10⁸ m/s,μ₀ = 4π × 10^-7 T • m/A, Ε₀ = 8.85 × 10^-12 C²/N • m²)

The diameter of a 12-gauge copper wire is 0.081 in. The maximum safe current it can carry (in order to prevent fire danger in building construction)is 20 A. At this current,what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm³ of copper is 8.5 × 10²² and e = 1.60 × 10^-19 C.

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 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 = 0.024 m,what is the kinetic energy of the block?

The figure shows a steady electric current passing through a wire with a narrow region.What happens to the drift velocity of the moving charges as they go from region A to region B and then to region C?

In the figure,the magnitude of vector is 18.0 units,and the magnitude of vector is 12.0 units.What vector must be added to the vectors and so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer,and express vector by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

Alice and Tom dive from an overhang into the lake below.Tom simply drops straight down from the edge,but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s.Neither person experiences any significant air resistance.Just as they reach the lake below