7. As a mass tied to the end of a string swings from its highest point down to its lowest point, it is acted on by three forces: gravity, tension, and air resistance. Which force does (a) positive work? (b) negative work? (c) zero work?

What is the Schwarzschild radius of the black hole at the center of the Milky Way? What

      is the ratio of the gravitational acceleration the Sun feels from this black hole to the

      gravitational acceleration the Sun feels from the entire Milky Way? Comment on the

      gravitational significance the black hole has on our Solar System.

A boy standing on top of a building throws a small ball from a height of H₁ = 45.0 m. (See figure.) The ball leaves with a speed of 26.9 m/s, at an angle of 61.0 degrees from the horizontal, and lands on a building with a height of H₂ = 12.0 m. Calculate for how long the ball is in the air. (Neglect air friction, and use g = 9.81 m/s².)

Suppose you find a magnifying glass in a junk drawer at home. You place it directly in between a light bulb and the wall, which are separated by 95 cm. When the lens is 15 cm from the wall it creates a focused image of the bulb. (a) Determine the focal length of the magnifying glass lens. (b) Without moving the light bulb (or the wall) at what other location would the lens project a focused image of the bulb on the wall? (c) Find the ratio of the image sizes of the two cases. (d) If the bulb is moved too close to the wall there will be no way possible to project a focused image – determine this distance and explain.

What are possible reasons for the differences between the measured and calculated values of centripetal force?

Two capacitors, C₁ = 15.0 µF and C₂ = 44.0 µF, are connected in series, and a 18.0-V battery is connected across them.

(a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor.

equivalent capacitance ________uF

total energy stored ________J

(b) Find the energy stored in each individual capacitor.

energy stored in C1 ______J

energy stored in C2 ______J

Show that the sum of these two energies is the same as the energy found in part (a). Will this equality always be true, or does it depend on the number of capacitors and their capacitances?

(c) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)?

______V

Need a simple explanation as to how gyroscope precession occur in a  spinning wheel which is held up by one end of its axle.

A projectile is launched vertically given the following: 1. The initial velocity of the projectile is 3 m/s. 2. The mass of the projectile is 0.57 kg. 3. Air resistance acts on the projectile with a force of 0.5v at any given time. If the projectile is launched from an initial height of 3 m., what is its maximum height?

You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators. If state law mandates that elevators cannot accelerate at greater than 2.70 m/s2 or travel faster than 15.3 m/s, what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor?

A 10 kg ball moving at 6 m/s strikes a 5 kg ball that is at rest, with contact of 0.5 seconds. The 10 kg ball comes to a complete stop.
(a) What average force was exerted on the 10 kg ball?
(b) What average force was exerted on the 5 kg ball?
(c) What is the final momentum of the 5 kg ball?
(d) What is the initial momentum of the 10 kg ball?

The arrangement in the drawing shows a block (mass = 15.2 kg) that is held in position on a frictionless incline by a cord (length = 0.580 m). The mass per unit length of the cord is 1.28 × 10-2 kg/m, so the mass of the cord is negligible compared to the mass of the block. The cord is being vibrated at a frequency of 150 Hz (vibration source not shown in the drawing). What is the smallest angle θ between 15.0 ° and 90.0 ° at which a standing wave exists on the cord?

An object is undergoing uniform circular motion. True or False: A graph of its position oscillates back and forth, but not with simple harmonic motion.

A.) True

B.) False

Very large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index ( ?? ), defined as ??=?5/2? . In the expression, ? is the duration of the accleration, but ? is not equal to the acceleration. Rather, ? is a dimensionless constant that equals the number of multiples of ? that the acceleration is equal to. In one set of studies of rear-end collisions, a person's velocity increases by 12.5 km/h with an acceleration of 35.5 m/s2 . Let the +? direction point in the direction the car is traveling. What is the severity index for the collision? ??= How far ? does the person travel during the collision if the car was initially moving forward at 5.70 km/h ? ?= m

A 335 kg box is pulled 6.00 m up a 30° frictionless, inclined plane by an external force of 5425 N that acts parallel to the plane.

Calculate the work done by the external force.

Calculate the work done by gravity.

Calculate the work done by the normal force.

An LC circuit like that in the figure below consists of a 3.30-H inductor and an 832-pF capacitor that initially carries a 134-μC charge. The switch is open for t < 0 and is then thrown closed at t = 0. Compute the following quantities at t = 5.00 ms. (a) the energy stored in the capacitor (b) the total energy in the circuit (c) the energy stored in the inductor