In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so
1 answer:
Answer:
(a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°
Explanation:
Given that,
Radius of the circle = 0.681 m
Angular acceleration = 67.7 rad/s²
Angular speed =18.6 rad/s
We need to calculate the centripetal acceleration of the ball
Using formula of centripetal acceleration
Put the value into the formula
We need to calculate the tangential acceleration of the ball
Using formula of tangential acceleration
Put the value into the formula
(a). We need to calculate the magnitude of the total acceleration of the ball
Using formula of total acceleration
Put the value into the formula
(b). We need to calculate the angle of the total acceleration relative to the radial direction
Using formula of the direction
Put the value into the formula
Hence, (a). The magnitude of the total acceleration of the ball is 239.97 m/s².
(b). The angle of the total acceleration relative to the radial direction is 11.0°
You might be interested in
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.
Answer:
The acceleration is about 9.8 m/s2 (down) when the ball is falling.
Explanation:
The ball at maximum height has velocity zero
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.8 m/s² (positive downward and negative upward)
The accleration 9.8 m/s² will always be acting on the body in opposite direction when the body is going up and in the same direction when the body is going down. The acceleration on the body will never be zero