An astronaut landed on a far away planet that has a sea of water. To determine the gravitational acceleration on the planet's su
1 answer:
The concept required to solve this problem is hydrostatic pressure. From the theory and assuming that the density of water on that planet is equal to that of the earth we can mathematically define the pressure as
Where,
= Density
h = Height
g = Gravitational acceleration
Rearranging the equation based on gravity
The mathematical problem gives us values such as:
Replacing we have,
Therefore the gravitational acceleration on the planet's surface is
You might be interested in
Explanation:
Work done by gravity is given by the formula,
W = ......... (1)
It is known that when levels are same then height of the liquid is as follows.
h = ......... (2)
Putting value of equation (2) in equation (1) the overall formula will be as follows.
W =
=
= 0.689 J
Thus, we can conclude that the work done by the gravitational force in equalizing the levels when the two vessels are connected is 0.689 J.
E) The number of moles of the helium of the balloon can be found by using the ideal gas law, which states:
where p is the gas pressure, V is the gas volume, n is the number of moles, R is the gas constant and T the gas temperature. Since we know p,V and T of the gas, we can find the number of moles n by re-arranging the equation:
F) The car uses an internal combustion engine. In an internal combustion engine, the fuel (gasoline) burns releasing heat, which moves the pistons of the engine. The motion of the pistons is then converted into motion of the wheels of the car.
The second law of thermodynamics states that the entropy of an isolated system can never decrease. If we take the engine as an isolated system, the this law applied also to it. In fact, at the beginning the engine containes fuel, which has a certain degree of "order" (entropy). When the fuel burns, the chemical bonds of the fuel are converted into heat, which has a higher degree of "disorder" (=more entropy) than the initial state.
G1) The ice cubes in the drink undergo melting: they go from solid state into liquid state (water).
G2) Since the temperature of the ice cubes is lower than the temperature of the surrounding liquid drink, the drink releases heat to the ice cubes. This heat makes the molecules of the ice cubes to vibrate faster and faster, eventually breaking the bonds between the molecules. When this occurs, the ice cubes start melting.
G3) If the drink continues to heat, it will undergo evaporation, which is the transition between the liquid state and the gas state. This transition occurs when the energy given to the molecules of the drink is large enough to remove the intermolecular forces between the molecules of the liquid, allowing them to escape from each other.
H) Entropy is the amount of thermal energy of a system (per unit temperature) which cannot be used to do work. In practise, the entropy of a system gives a measure of the degree of "disorder" of a system. When the ice cubes melt, the entropy of the system (the ice cubes) increases, because they move from a state with higher degree of "order" (the solid state) to a state with lower degree of "order" (the liquid state).
A) This nuclear equation is an example of alpha-decay, where an unstable nucleus (uranium-235) decays into a daughter nucleus (thorum-231) releasing an alpha particle (a nucleum of helium, consisting of 2 protons and 2 neutrons).
B) The other three types of decay are:
- beta minus decay: in an unstable nucleus, a neutron decays into a proton, releasing a fast moving electron and an antineutrino. Following this decay, the atomic number of the nucleus increases by 1 unit while its mass number remains the same
- beta plus decay: in an unstable nucleus, a proton decays into a neutron, releasing a fast moving positron and a neutrino. Following this decay, the atomic number of the nucleus decreases by 1 unit while its mass number remains the same
- gamma decay: a nucleus in excited states decays to its ground state by emitting a gamma photon, whose energy is equal to the difference in energy between the two nuclear levels.
C) The length of time of a decay process is usually expressed by using the concept of half life. The half life of a substance is the time it takes for the substance to decrease to half of its original amount. The equation that gives the amount left of a substance at time t is given by:
where m0 is the original mass of the substance,and
is the half life.
7B1) In nuclear fusion, two smaller nuclei combine together (fuse) to form a new larger nucleus. An example of this process is the hydrogen-to-helium fusion, which occurs inside the stars, where two nuclei of hydrogen (one proton each) fuse together to form a nucleus of helium-4. In the nuclear fusion process, the sum of the masses of the initial nuclei is larger than the mass of the final nucleus, so the mass lost in the process has converted into energy, according to Einstein's formula:
.
7B2) In nuclear fission, a nucleus of a heavy element absorbs a slow moving neutron, becoming unstable and decaying into smaller nuclei. An example of this process is the fission of uranium-235, which occurs inside nuclear power plants on Earth. In the process, uranium-235 decays into lighter nuclei and many neutrons, which are used to further induce other fission reactions with other nuclei of uranium-235. In the nuclear fission, the mass of the initial nucleus is greater than the masses of the final products, so the mass lost in the process has been converted into energy according to Einstein's formula:
8) An alternative energy source that involves the Earth is wind power: the air flows through turbines, which are put in motion by the wind. The motion of the turbines is then converted into electrical energy.
where p is the gas pressure, V is the gas volume, n is the number of moles, R is the gas constant and T the gas temperature. Since we know p,V and T of the gas, we can find the number of moles n by re-arranging the equation:
F) The car uses an internal combustion engine. In an internal combustion engine, the fuel (gasoline) burns releasing heat, which moves the pistons of the engine. The motion of the pistons is then converted into motion of the wheels of the car.
The second law of thermodynamics states that the entropy of an isolated system can never decrease. If we take the engine as an isolated system, the this law applied also to it. In fact, at the beginning the engine containes fuel, which has a certain degree of "order" (entropy). When the fuel burns, the chemical bonds of the fuel are converted into heat, which has a higher degree of "disorder" (=more entropy) than the initial state.
G1) The ice cubes in the drink undergo melting: they go from solid state into liquid state (water).
G2) Since the temperature of the ice cubes is lower than the temperature of the surrounding liquid drink, the drink releases heat to the ice cubes. This heat makes the molecules of the ice cubes to vibrate faster and faster, eventually breaking the bonds between the molecules. When this occurs, the ice cubes start melting.
G3) If the drink continues to heat, it will undergo evaporation, which is the transition between the liquid state and the gas state. This transition occurs when the energy given to the molecules of the drink is large enough to remove the intermolecular forces between the molecules of the liquid, allowing them to escape from each other.
H) Entropy is the amount of thermal energy of a system (per unit temperature) which cannot be used to do work. In practise, the entropy of a system gives a measure of the degree of "disorder" of a system. When the ice cubes melt, the entropy of the system (the ice cubes) increases, because they move from a state with higher degree of "order" (the solid state) to a state with lower degree of "order" (the liquid state).
A) This nuclear equation is an example of alpha-decay, where an unstable nucleus (uranium-235) decays into a daughter nucleus (thorum-231) releasing an alpha particle (a nucleum of helium, consisting of 2 protons and 2 neutrons).
B) The other three types of decay are:
- beta minus decay: in an unstable nucleus, a neutron decays into a proton, releasing a fast moving electron and an antineutrino. Following this decay, the atomic number of the nucleus increases by 1 unit while its mass number remains the same
- beta plus decay: in an unstable nucleus, a proton decays into a neutron, releasing a fast moving positron and a neutrino. Following this decay, the atomic number of the nucleus decreases by 1 unit while its mass number remains the same
- gamma decay: a nucleus in excited states decays to its ground state by emitting a gamma photon, whose energy is equal to the difference in energy between the two nuclear levels.
C) The length of time of a decay process is usually expressed by using the concept of half life. The half life of a substance is the time it takes for the substance to decrease to half of its original amount. The equation that gives the amount left of a substance at time t is given by:
where m0 is the original mass of the substance,and
7B1) In nuclear fusion, two smaller nuclei combine together (fuse) to form a new larger nucleus. An example of this process is the hydrogen-to-helium fusion, which occurs inside the stars, where two nuclei of hydrogen (one proton each) fuse together to form a nucleus of helium-4. In the nuclear fusion process, the sum of the masses of the initial nuclei is larger than the mass of the final nucleus, so the mass lost in the process has converted into energy, according to Einstein's formula:
7B2) In nuclear fission, a nucleus of a heavy element absorbs a slow moving neutron, becoming unstable and decaying into smaller nuclei. An example of this process is the fission of uranium-235, which occurs inside nuclear power plants on Earth. In the process, uranium-235 decays into lighter nuclei and many neutrons, which are used to further induce other fission reactions with other nuclei of uranium-235. In the nuclear fission, the mass of the initial nucleus is greater than the masses of the final products, so the mass lost in the process has been converted into energy according to Einstein's formula:
8) An alternative energy source that involves the Earth is wind power: the air flows through turbines, which are put in motion by the wind. The motion of the turbines is then converted into electrical energy.