A helium-filled balloon (whose envelope has a mass of m = 0.260 kg) is tied to a uniform string of length = 2.50 m and mass m = 0.049 9 kg. The balloon is spherical with a radius of r = 0.398 m. When released in air of temperature 20°C and density Pair = 1.20 kg/m³, it lifts a length h of string and then remains stationary as shown in the figure below. We wish to find the length of string lifted by the balloon. He (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? O the ideal fluid model a particle in equilibrium model a particle under constant velocity model O a particle under constant acceleration model (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight F of the balloon, the weight FHe of the helium, and the weight F of the segment of string of length h. (Use any variable or symbol stated above along with the following as necessary: . Follow the sign convention that upward is the positive direction.) = 0 sty (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass me of the segment of string of length h in terms of m, r, the density of air pa, and the density of helium PHe (Use any variable or symbol stated above along with the following as necessary: TT.) m₂ = (d) Find the numerical value of the mass m₂. kg (e) Find the length h numerically. m

In 2085, your company wins a contract to deliver oxygen to several asteroid-based habitats from another asteroid with plenty of oxygen locked up in ice. Since there is no drag in space, the size of the oxygen containers is not an issue, and the most economical method turns out to be to enclose about 6 x 105 kilograms of cold but gaseous oxygen at about half atmospheric pressure in a Mylar sphere 100 m in diameter. To the sphere, you have strapped a small rocket engine. While the engine is firing, the engine presses into the sphere roughly 10 meters, like a finger pushing in on a balloon, as the sphere accelerates. The engine exerts a constant thrust until the sphere reaches its interasteroidal cruising speed of 100 m/s. The sphere travels about 5.0 km while the engine is firing. What fraction of the energy the rocket engine has given to the sphere ends up as internal energy in the gas just before the engine shuts off?

A simple thermometer is formed by taking a large spherical container of volume 1.13m³ and filling it with an ideal gas. Then, a U-shaped tube is attached that is very narrow so that very little fluid/gas can fit inside the tube. The tube has a small quantity of a fluid of density 1200kg/m³ placed in it. In equilibrium at room temperature - 21.9°C - the height of the fluid on both sides of the U-shaped tube are level. This is illustrated in the image below. What is the temperature of the gas in the spherical container when the left side of the fluid is 13.25cm higher than the right side of the fluid in the U-shaped tube? Atmospheric pressure is 101000Pa. °C

What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature? Surface tension of mercury at that temperature (20°C) is 4.65 x 10 N m. The atmospheric pressure is 1.01 x 10° Pa. Also give the excess pressure inside the drop.

A 0.527 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. The cylinder comes to rest some distance above the plunger. The plastic tube has an inner radius of 6.56 mm and is frictionless. Neither the plunger nor the metal cylinder allow any air to flow around them. If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 1.35, what is the initial acceleration ? of the metal cylinder? Assume the pressure outside of the tube is 1.00 atmand that the top of the tube is open to the air.

A typical hot air balloon can carry 3–5 passengers in a wicker basket and has a total mass of  m = 470 kg  including passengers, not including the mass of air inside the balloon. The density of hot air inside the stationary balloon is  ?hot = 0.960 kg/m3  and the density of the cooler outside air is  ?cool = 1.22 kg/m3. Determine the volume of hot air required for the balloon to be in equilibrium so that it neither sinks nor rises in the air.

Consider a spherical ash particle of diameter 65 µm, falling from a volcano at a high elevation in air whose temperature is −50°C and whose pressure is 55 kPa. The density of air is 0.8588 kg/m3 and its viscosity is 1.474 × 10−5 kg/m⋅s. The density of the particle is 1240 kg/m3. The drag force on a sphere in creeping flow is given by FD = 3??VD. The terminal velocity of this particle at this altitude is (a) 0.096 m/s (b) 0.123 m/s (c) 0.194 m/s (d ) 0.225 m/s (e) 0.276 m/s

Suppose you spray your sister with water from a garden hose. The water is supplied to the hose at a rate of 0.529 × 10-3 m³/s and the diameter of the nozzle you hold is 5.67 x 10-3 m. At what speed v does the water exit the nozzle? U = m/s

A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3600 N/m. The piston has a negligible mass and a radius of 0.010 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring?   * I know that a is = 0.0088422743 m  but b is NOT 8.950712099 J (wrong) please show work of how to work part b.

A 0.504 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. The cylinder comes to rest some distance above the plunger. The plastic tube has an inner radius of 5.88 mm and is frictionless. Neither the plunger nor the metal cylinder allow any air to flow around them. If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 3.03, what is the initial acceleration a of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm and that the top of the tube is open to the air.