A propeller-driven airplane of mass 680 kg is turning in a horizontal circle with a constant speed of 280 km/h. Its bank angle remains during the turn. A head-on view of the airplane and a top view are shown below.
The forces on the airplane are due to Earth (gravitational force) and air. The force by the air on the airplane can be written as three components: lift (perpendicular to the wings), thrust (in the direction of the velocity), and drag (opposite to the velocity). Neglect wind.
Parasailing is a recreational activity where a person with a parachute (or rather, a parasail) is pulled by a boat, as shown below.
The boat and parasail (including the person) are traveling at a constant speed of 15 m/s in the +x direction. The person and parasail together have a mass of 120 kg. The tension in the rope is .
Suppose that in the lab, you build a set of identical balls connected by identical springs, as shown below.
The masses of the balls and springs are negligible compared to the block that you hang from the apparatus. If you hang a 0.25-kg block in equilibrium, the apparatus stretches 0.050 m from its relaxed length.
A certain tin wire (white tin, as opposed to gray tin) has a length of 1.5 m and a square rectangular cross section that is (1 mm x 1 mm). With a tension of 200 N applied to the wire, it stretches 6 mm. Use a simple ball-and-spring model of a solid, and assume that tin's crystal lattice is simple cubic, with atoms essentially stacked next to and on top of one another, like inflated basketballs stacked in a box. From these measurements, approximate the bond stiffness of tin. The density of white tin is . Its atomic weight is 118.7 g/mol.
Spring A of stiffness 10 N/m is hung vertically from a ringstand. From the lower end of this spring, a different spring (Spring B) of stiffness 20 N/m is hung. And from the lower end of this spring, a 0.25-kg block is hung in equilibrium. When springs are connected in this orientation, they are said to be in series. Neglect the mass of the springs.
What is the approximate length of an interatomic bond between adjacent atoms in solid aluminum?
A centrifuge is used to separate white blood cells, red blood cells, and blood plasma by rotating the sample at a high angular speed. Suppose that a sample of blood is placed in a test tube and is swung in a circle of radius 0.0375 m at an angular speed of 360 rad/s. A picture of the test tube at a certain instant is shown below. The mass of the blood and tube (combined) is 0.0069 kg.
There are only two forces acting on the tube, the gravitational force on the tube and the force by the holder on the tube. Define the system to be the tube and blood sample together. What is the force by the holder on the tube at the instant shown.
A bobber is attached to a string and submerged in a jar of water. The jar travels around a circle of radius at a constant speed . What is the angle of the string with respect to the vertical?
A comet orbits a star counterclockwise as shown below.
For each point shown (A, B, C, and D), answer the following questions.
Suppose that in a theatre, a steel rod of length 1.2 m and cross-sectional radius 1 cm hangs vertically from the ceiling and supports a 10-kg spotlight that hangs in equilibrium from the end of the rod. Steel has a density of 7860 kg/m .