You hold a string that is tied to a helium balloon that is approximately spherical with a radius of 10 cm. The balloon is in equilibrium. At atmospheric pressure and a temperature of , helium has a density of and air has a density of . (Note: the volume of a sphere is .) Assume that the densities of helium and air at room temperature are close to their densities at . The mass of the latex balloon before being inflated is 2 g.
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.
What is the approximate length of an interatomic bond between adjacent atoms in solid aluminum?
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 .
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 .
Wet 'n Wild has a waterslide called Daredevil Drop. At the steepest part of the slide, the angle is about . A girl goes down the slide. Her mass is 40 kg and the frictional force of the slide on her at its steepest angle at is 20 N.
An cart on a very low-friction track has a mass 0.4 kg and is attached to a compressible, horizontal spring. It is pulled back and released from rest. A graph of its position with respect to time is shown below. (Note that the x-axis is oriented along the direction of oscillation.)
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 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 comet orbits a star counterclockwise as shown below.
For each point shown (A, B, C, and D), answer the following questions.