Light waves from the sun can travel through outer space and reach the earth. This suggests that light is a(n)
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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.
3) The work done is D. zero
4) The kinetic energy is B. 180 J
5) The potential energy is A. 120 J
6) The work done depends on B. position
7) The example of non-renewable energy is C. coal
8) The power expended is
9) The efficiency is A. 100%
10) The velocity ratio is 5
Explanation:
3)
The work done by a force acting an object is given by:
where :
F is the magnitude of the force
d is the displacement
is the angle between the direction of the force and the displacement
When the force is applied perpendicular to the direction of motion,
Therefore, the work done is:
4)
The kinetic energy of a body is given by
where
m is the mass of the body
v is its speed
For the girl in this problem, we have
m = 40 kg
v = 3 m/s
Therefore her kinetic energy is
5)
The potential energy of an object is given by
where
m is the mass
is the acceleration of gravity
h is the heigth of the object relative to the ground
For the ball in this problem,
m = 0.4 kg
h = 30 m
So, the potential energy is
6)
A conservative field is a field for which the work done by the field on an object does not depend on the path taken, but only on the initial and final position of the object.
Gravitational and electric fields are examples of conservative fields. In fact:
- When an object is pulled down by gravity (free fall), the work done by the gravitational field only depends on the change in height
between the two points, not on the path taken during the fall
- When an electric charge is pushed by the electric field, the work done by the field depends only on the initial and final position of the charge in the field
For any conservative field, it is possible to define a "potential" function, which represents the energy per unit mass/charge, and depends only on the position of the object.
7.
- Non-renewable energy sources are sources of energy whose rate of consumption is faster than the rate at which they are re-created. Examples of non-renewable sources are coal, oil, natural gas. These energy sources are consumed at a fast rate, while they take million of years to regenerate, so at the current rate they will eventually run out.
- Renewable energy sources are sources of energy that replenish at faster rate than the rate at which it is consumed. Examples of renewable sources are solar energy, wind, hydroelectric power.
Therefore, the example of non-renewable energy in this case is
C. Coal
8.
For an object pushed by a force F and moving at a constant velocity v, the power expended is given by
where F is the force and v is the velocity.
for the rocket in this problem, we have:
F = 10 N is the force propelling the rocket
v = 3000 m/s is its velocity
Substituting into the equation, we find the power expended:
9.
The efficiency of a machine is given by
where
is the energy in input to the machine
is the useful work in output from the machine
For a real machine, the useful work in output is always lower than the energy input, because part of the energy is "wasted" and converted into thermal energy due to the presence of internal frictions. However, for an ideal machine, all the input energy is converted into useful work, so
And therefore the efficiency is
which means 100%.
10.
The velocity ratio of a block and tackle system is the ratio between the distance moved by the effort and the distance moved by the load.
In a block and tackle system, the velocity ratio is also equal to the number of pulleys in the system.
For the system in the problem, there are 5 pulleys: therefore, this means that when the effort moves 5 metres, the load moves 1 metres, therefore the velocity ratio is
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Answer:
Explanation:
q = Charge of proton =
r = Radius of circle =
v = Velocity of proton =
Magnetic moment is given by
The magnetic moment associated with this motion is