A lighter-than-air spherical balloon and its load of passengers and ballast are floating stationary above the earth. Ballast is weight (of negligible volume) that can be dropped overboard to make the balloon rise. The radius of this balloon is 4.47 m. Assuming a constant value of 1.29 kg/m3 for the density of air, determine how much weight must be dropped overboard to make the balloon rise 148 m in 13.0 s.

A toy gun uses a spring with a force constant of 350 N/m to propel a 15.0 g steel ball. The spring is compressed 8.40 cm and friction is negligible.

a) How much force (in N) is needed to compress the spring? (Assume the gun is aimed in the positive direction. Indicate the direction with the sign of your answer.)

b)To what maximum height (in m) can the ball be shot?

c)At what angles above the horizontal (in degrees) may a child aim to hit a target 3.00 m away at the same height as the gun? (Enter your answers to at least two decimal places.) smaller angle and larger angle?

* I already answered a and b: a) -29.4 N and b) 8.52 m, I just need C *

Steam at 100°C is added to ice at 0°C.

(a) Find the amount of ice melted and the final temperature when the mass of steam is 11.0 g and the mass of ice is 48.0 g.


(b) Repeat this calculation, when the mass of steam as 1.10 g and the mass of ice is 48.0 g.

A particle with a charge of 34 μC moves with a speed of 73 m/s in the positive x direction. The magnetic field in this region of space has a component of 0.42 T in the positive ydirection, and a component of 0.83 T in the positive zdirection.

Part A

What is the magnitude of the magnetic force on the particle?

Express your answer using two significant figures.

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Part B

What is the direction of the magnetic force on the particle? (Find the angle measured from the positive z-axis toward the negative y-axis in the yz-plane.)

Express your answer using two significant figures.

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A rock has mass 1.80 kg. When the rock is suspended from the lower end of a string and totally immersed in water, the tension in the string is 12.6 N .

What is the smallest density of a liquid in which the rock will float?

Express your answer with the appropriate units.

A playground is on the flat roof of a city school, 5.00 m above the street below. The vertical wall of the building is 6.00 m high, forming a 1.00 m high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of 53.0° above the horizontal at a point 26.0 m from the base of the building wall. The ball takes 2.10 s to reach a point vertically above the wall.

(a) Find the speed at which the ball was launched.
??? m/s

(b) Find the vertical distance by which the ball clears the wall.
??? m

(c) Find the distance from the wall to the point on the roof where the ball lands.
??? m

A 0.6410-kg ice cube at -12.40°C is placed inside a chamber of steam at 365.0°C. Later, you notice that the ice cube has completely melted into a puddle of water. If the chamber initially contained 6.310 moles of steam (water) molecules before the ice is added, calculate the final temperature of the puddle once it settled to equilibrium. (Assume the chamber walls are sufficiently flexible to allow the system to remain isobaric and consider thermal losses/gains from the chamber walls as negligible.)

Part A

Calculate the magnitude of the angular momentum of the Earth in a circular orbit around the sun. The Earth has mass 5.97

A 300,000 kg- spacecraft is floating in space when it senses a 40-kg enemy missile coming toward it at 20m/s. The spacecraft fires at 60 kg lump of clay at 30m/s directly at the missile. The clay sticks to the missile. (a.) Show that the spacecraft recoils at about 6mm/s (1mm=0.001m) (b.) Show that the final velocity of the clay-laden missile is 10 m/s in a direction away from the spacecraft.

You are on an engineering team examining the feasibility of a satellite launching system that uses the electric force instead of rocket fuel. The proposed launching system consists of 4 metal spheres, each one 15 m above the ground, arranged at the corners of a square with sides 5 meters long. The satellite is placed on the ground below the center of the square. To launch the satellite, the four spheres are first each given a charge of +Q/4 and the satellite is given a charge –Q. The satellite is then released and is pulled straight upward through the center of the square.

When the satellite reaches 15 m above the ground (the same height as the spheres), the spheres are neutralized. To evaluate this idea, you decide to calculate how big Q would have to be to launch a 100 kg satellite at a speed of 8 km/s. You are also worried about dielectric breakdown of the air, which causes spontaneous sparking in the presence of electric fields larger than 3 x 10⁶ V/m and so decide to check whether that will be a problem. For this purpose, you assume that the spheres have a diameter of 1 m.

(a) Give a purely symbolic answer to the problem in terms of (only) the quantities given in the problem and known constants. Be sure to define each of the symbols you use.
(b) Give a numerical answer to the problem.

How do you find the total internal reflection angle? I know that if the incident angle is larger than the critical angle, that will lead to total internal reflection. So is it just a concept (like there no degree/ angle/ numerical value given to total internal reflection)? Thank you!!

A dye molecule has electrons that are free to travel up and down a chain of atoms, giving electron energy states that are given by the particle-in-a-box model, with En=(0.34eV)n2. What are the three longest wavelengths of visible light that the molecule will absorb?

In simple terms (so a non-physicist with an upper division math background can understand), what is a Lagrangian and what is it used for?

Ampere's Law for a long wire states that magnetic field is directly proportional to current and inversely proportional to the distance for the wire. True or False.

Ampere's Law for a loop wire states that magnetic field is indirectly proportional to current and directly proportional to the radius of the loop. True or False.

Ohm's Law is true regardless of the nature of the electric circuit. True or False

Thank you!

Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in (Figure 1) If each internal resistance is r = 0.400? , and R = 4.00 ?, what is the voltage across the resistor R?