If the mixture is thermally isolated from its surroundings, then it, loses thermal energy to the environment outside as it comes to a final temperature. The correct answer is d.
When the sample of lead is placed in the water, heat will flow from the lead to the water until they reach a common final temperature. Since the final temperature will be less than the initial temperature of the lead, heat must have flowed out of the lead into the surroundings, causing the lead to lose thermal energy to the environment outside the system.
Since the mixture is thermally isolated from its surroundings, no thermal energy is exchanged between the system (lead and water) and the environment during the process. However, heat can still flow within the system itself until thermal equilibrium is reached. Option d is correct.
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which generally expands more for an equal increase in temperature: solids or liquids?
Expansion of liquids is generally more than solids for an equal increase in temperature.
Why will be equal increase in temperature?When an object is heated, its particles absorb energy and begin to vibrate more rapidly.
In solids, the particles are arranged in a rigid structure, and as they vibrate, the bonds between the particles restrict the amount of expansion that can occur.
In liquids, however, the particles are not arranged in a fixed structure and are able to move more freely.
As the temperature increases, the particles move faster and farther apart, causing the liquid to expand more than a solid would for an equal increase in temperature.
Therefore, in general, liquids expand more than solids when heated.
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A 50-Ω resistor and a 28-Ω resistor are connected in series to a 12-V battery of negligible resistance.
What is the voltage difference across each resistor?
The voltage difference across the 50-Ω resistor is 7.69 V and across the 28-Ω resistor is 4.31 V.
When two resistors are connected in series, the total resistance is the sum of their individual resistances.
In this case, we have a 50-Ω resistor and a 28-Ω resistor, so the total resistance is 50 + 28 = 78 Ω.
Using Ohm's Law (V = IR), we can find the current (I) flowing through the circuit, where V is the voltage (12 V) and R is the total resistance (78 Ω):
I = V / R = 12 V / 78 Ω = 0.1538 A
Now, we can find the voltage difference across each resistor using Ohm's Law again, this time using the individual resistances and the current (0.1538 A):
The voltage across the 50-Ω resistor:
V₁ = I * R₁ = 0.1538 A * 50 Ω = 7.69 V
The voltage across 28-Ω resistor:
V₂ = I * R₂ = 0.1538 A * 28 Ω = 4.31 V
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What is transferred to the cold, dry air mass, causing it to become unstable as it moves across the lakes
As a cold, dry air mass moves across the lakes, it can pick up moisture and heat from the warm lake waters. This process is called lake-effect and can cause the air mass to become more unstable as it gains warmth and moisture. As the air rises, it can form clouds and precipitation, which can lead to heavy snowfall in areas downwind of the lakes.
When a cold, dry air mass moves across the lakes, it becomes unstable due to the transfer of heat and moisture. The warmer lake water provides heat energy, which increases the temperature of the air mass, and evaporates water into the air, adding moisture.
These combined factors lead to the development of instability in the air mass.
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1.) The atomic mass of iron is 55.845 g mol with atomic number 26. How many coulombs, Q, of positive charge are there in the protons of 20.0kg = 20, 000g of iron?
2.) The sun is mostly hydrogen (atomic mass 1.00794g/mole). The mass of the sun is 2 Ã 1030kg. Approximately how many protons are in the sun? Donât forget to convert kilograms to grams.
1) Positive charge in protons of 20.0kg of iron is 9.01 x [tex]10^{6[/tex] coulombs. 2) The total number of protons in the sun is 1.195 x [tex]10^{57[/tex]protons.
1.) To find the coulombs of positive charge in the protons of 20,000g of iron, first determine the number of moles of iron present, then the number of protons, and finally the charge. The atomic mass of iron is 55.845 g/mol, and its atomic number is 26.
Moles of iron = (20,000g) / (55.845 g/mol) = 358.07 mol
Since each iron atom has 26 protons, the total number of protons is:
Protons = (358.07 mol) x (6.022 x [tex]10^{23[/tex] atoms/mol) x (26 protons/atom) = 5.62 x [tex]10^{25[/tex] protons
Each proton carries a positive charge of 1.602 x [tex]10^{-19[/tex] coulombs. So, the total positive charge, Q, is:
Q = (5.62 x [tex]10^{25[/tex] protons) x (1.602 x [tex]10^{-19[/tex] C/proton) = 9.01 x [tex]10^{6[/tex] coulombs
2.) To find the number of protons in the sun, first convert the mass of the sun to grams and then determine the number of moles of hydrogen present. The mass of the sun is 2 x [tex]10^{30[/tex] kg, and the atomic mass of hydrogen is 1.00794 g/mol.
Mass of the sun in grams = (2 x [tex]10^{30[/tex] kg) x (1000 g/kg) = 2 x [tex]10^{33[/tex] g
Moles of hydrogen = (2 x [tex]10^{33[/tex] g) / (1.00794 g/mol) = 1.986 x [tex]10^{33[/tex] mol
Since each hydrogen atom has one proton, the total number of protons in the sun is:
Protons = (1.986 x [tex]10^{33[/tex] mol) x (6.022 x [tex]10^{23[/tex] atoms/mol) = 1.195 x [tex]10^{57[/tex]protons.
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Find the current needed to achieve such a field near the center of a solenoid with radius 2.60 cmcm , length 32.0 cmcm , and 40,000 turns.
A current of 0.568 A is needed to achieve the required magnetic field near the center of the solenoid.
What is the required current?The magnetic field produced by a solenoid is given by the equation:
B = μ * n * I
where B is the magnetic field, μ is the permeability of free space, n is the number of turns per unit length, and I is the current passing through the solenoid.
The magnetic field required to achieve escape velocity near the surface of the planet depends on the mass and radius of the planet. However, assuming that the planet is Earth and using the escape velocity of 11.2 km/s, the least kinetic energy required for a projectile to escape the planet is given by:
KE = (1/2) * m * v^2 = (1/2) * m * (11200 m/s)^2
where KE is the kinetic energy of the projectile and m is its mass.
To find the current needed to achieve the required magnetic field near the center of the solenoid, we need to rearrange the above equation and solve for I:
I = B / (μ * n)
The number of turns per unit length of the solenoid is given by:
n = N / L
where N is the total number of turns and L is the length of the solenoid.
Substituting the values given, we get:
n = N / L = 40000 / 0.32 = 125000 turns/m
μ = 4π × 10^-7 T m/A
B = 11.2 × 10^3 m/s (assuming escape velocity of Earth)
Substituting these values, we get:
I = B / (μ * n) = (11.2 × 10^3 m/s) / (4π × 10^-7 T m/A × 125000 turns/m) = 0.568 A
Therefore, a current of 0.568 A is needed to achieve the required magnetic field near the center of the solenoid.
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What happens to all right plates and all left plates of capacitors in a series?
In a series combination of capacitors, the charge on all the right plates is equal and opposite to the charge on all the left plates. This is because the right plate of one capacitor is connected to the left plate of the next capacitor, and so on.
Given data ,
In a series configuration, the voltage across each capacitor is not constant. Each capacitor's capacitance is inversely proportional to the voltage drop across it. The voltage drop across a capacitor for a given charge decreases with increasing capacitance.
As a result, the first capacitor in the series has the highest voltage and the last capacitor has the lowest voltage across it. The sum of the voltages across each capacitor represents the overall voltage across the series arrangement.
The reciprocal of the sum of the reciprocals of the individual capacitances determines the overall capacitance of capacitors connected in series. As a result, the total capacitance of capacitors connected in series is always lower than the series' lowest capacitance.
Hence , the charge on the end plates of the series combination is equal to the charge on the plates of any individual capacitor.
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Which of the three terms in the formula for Newton's second law provides the direct link to the formulas for uniformly accelerated motion?
An object moves along a straight line so that at any time t greater than or equal to 0 it's velocity is given by v(t)= 2cos(3t). What is the distance traveled by the object from t=0 to the first time that it stops?
A. 0
B. Pi/6
C. 2/3
D. Pi/3
E. 4/3
The distance traveled by the object from t=0 to the first time that it stops is 2/3. So, option C. is correct.
To find the distance traveled by the object from t=0 to the first time it stops, we first need to determine when the object stops. The object stops when its velocity v(t) is equal to 0:
v(t) = 2cos(3t) = 0
This occurs when cos(3t) = 0.
The first positive value for t that satisfies this equation is when 3t = π/2, which gives us t = π/6.
Now, we need to find the distance traveled. Since we know the velocity function v(t), we can find the position function s(t) by integrating v(t):
s(t) = ∫v(t)dt = ∫2cos(3t)dt
Integrating the function gives:
s(t) = (2/3)sin(3t) + C
As the initial condition is s(0) = 0, we find C = 0.
So, the position function is:
s(t) = (2/3)sin(3t)
Now, we can find the distance traveled by the object from t=0 to t=π/6:
Distance = s(π/6) - s(0)
= (2/3)sin(3(π/6)) - (2/3)sin(0)
= (2/3)sin(π/2) - 0
= (2/3)(1)
= 2/3
So, the correct answer is C option.
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If the efficiency of a gasoline engine is
25 percent, what happens to the missing 75 percent of the energy in the fuel?
When the efficiency of a gasoline engine is 25 percent, the remaining 75 percent of energy in the fuel is lost in the form of heat and exhaust.
This is because not all the energy produced by the combustion of gasoline can be converted into useful work by the engine. Some of the energy is lost due to friction, heat transfer, and other inefficiencies in the engine's operation. Therefore, it is important to improve the efficiency of gasoline engines to reduce energy waste and increase fuel economy.
A gasoline engine supplies a mixture of air and fuel (gasoline) into cylinders, produces combustion, and obtains power from the thermal energy generated by combustion.
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A fire truck parks 16 feet away from a building. The fire truck extends its ladder 30 feet to the very top of the building. How tall is the building? Round to the nearest tenth.
25 feet tall. By using the above data and Pythagoras theorem we can say the building is 25 feet tall.
The height of the building when a fire truck parks 16 feet away from it and extends its ladder 30 feet to the top, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this scenario, the fire truck's ladder is the hypotenuse (30 feet), one side is the distance between the truck and the building (16 feet), and the other side is the height of the building (which we want to find).
Let's denote the height of the building as 'h'. The Pythagorean theorem can be expressed as:
h^2 + 16^2 = 30^2
Now, let's solve for 'h':
h^2 + 256 = 900
h^2 = 900 - 256
h^2 = 644
h = √644
h ≈ 25.4 feet
So, the building is approximately 25.4 or 25 feet tall, rounded to the nearest tenth.
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A hoop, a uniform disk, and a uniform sphere, all with thesame mass and outer radius, start with the same speed androll without slipping up identical inclines. Rank the objectsaccording to how high they go, least to greatest.A. hoop, disk, sphereB. disk, hoop, sphereC. sphere, hoop, diskD. sphere, disk, hoop'E. hoop, sphere, disk
The kinetic energy of a rolling object is given by the expression:
KE = (1/2)mv² + (1/2)Iω²
What would happen if the objects were not rolling without slipping up the incline?The objects will all have the same potential energy at their maximum height, as they will have the same mass, radius, and height. Therefore, we can rank them based on their kinetic energy at the bottom of the incline, which will determine how high they are able to roll up.
The kinetic energy of a rolling object is given by the expression:
KE = (1/2)mv² + (1/2)Iω²
where m is the mass of the object, v is its linear speed, I is its moment of inertia, and ω is its angular velocity. For a given mass and radius, the moment of inertia is highest for a solid sphere and lowest for a hoop, with the disk in between.
Therefore, we can rank the objects based on their initial kinetic energy, which is proportional to (1/2)mv²:
E. hoop, sphere, disk
The hoop has the least moment of inertia, and therefore the highest initial kinetic energy. The sphere has the highest moment of inertia, and therefore the lowest initial kinetic energy. The disk is in between the two.
Therefore, the objects will reach their maximum heights in the following order:
E. hoop, sphere, disk
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The sum of the voltages on the two capacitors equals the voltage of the battery. is TRUE or FALSE.
The sum of the voltages on the two capacitors equals the voltage of the battery. So, the statement is true.
The voltage throughout the entire circuit in any series circuit with any sort of component will be equal the voltage that is supplied.
The voltage of the supply is equal to the total of the voltages across all components connected in series.
Each component in a series has a voltage across it that is proportional to their resistance. This indicates that the supply voltage is divided equally between two identical components when they are linked in series.
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A long wire carrying a current of 200 A is placed in a uniform external magnetic field of 10.0 mT. The wire is perpendicular to this magnetic field. Locate the points at which the resultant magnetic field is zero.
A) 400 cm
B) 0.004 m
C) 4.00 m
D) 0.004 cm
When a wire carrying an electric current is placed in a magnetic field, a resultant magnetic field is created around the wire. The direction of this magnetic field can be determined using the right-hand rule. In the case of a wire carrying a current of 200 A placed in a uniform external magnetic field of 10.0 mT, the magnetic field around the wire is circular and its strength can be calculated using the formula B = (μ₀I)/(2πr).
To locate the points at which the resultant magnetic field is zero, we need to consider the interaction between the external magnetic field and the magnetic field around the wire. If the wire is perpendicular to the external magnetic field, the magnetic fields will cancel each other out at certain points. These points can be found by setting the two magnetic field strengths equal to each other and solving for the distance from the wire.
Using the formula B = (μ₀I)/(2πr), we can set the strength of the magnetic field around the wire equal to the strength of the external magnetic field. Solving for r, we get r = (μ₀I)/(2πB). Plugging in the given values, we get r = (4π × 10⁻⁷ T m/A)(200 A)/(2π × 10⁻² T) = 0.004 m.
Therefore, the points at which the resultant magnetic field is zero are located at a distance of 0.004 m from the wire, which corresponds to answer choice B.
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The magnitude of the force is inversely proportional to the square of the distance. So if the distance is halfed, force is increased by a factor of ?
If the distance is halved, the force is increased by a factor of 4
Given data ,
The magnitude of the force is inversely proportional to the square of the distance.
And , F = k / d²
where F is the magnitude of the force, d is the distance between the objects, and k is a constant of proportionality.
If the distance is halved (i.e., becomes 1/2 of its original value), we can substitute 1/2d for d in the equation above and find the new force:
F' = k / (1/2d)²
Simplifying this expression, we get:
F' = k / (1/4d²) = 4k / d²
Hence , if the distance is halved, the force is increased by a factor of 4
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Are your observations consistent with the magnitude of the magnetic force be described by F=qvB where q is the charge, v is the speed of the moving charge, and B is the magnitude of the magnetic field? Explain
Yes, the observations are consistent with the equation F = qvB, which describes the magnetic force acting on a moving charge. In this equation, F represents the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnitude of the magnetic field.
What's the equation F = qvB?The equation shows that the magnetic force depends on the charge's magnitude, its speed, and the strength of the magnetic field.
As the charge, speed, or magnetic field increases, the magnetic force will also increase, and vice versa. Additionally, the direction of the magnetic force is always perpendicular to both the velocity and the magnetic field, as determined by the right-hand rule.
This equation can accurately predict the behavior of charged particles in various magnetic fields, such as the deflection of electrons in a cathode ray tube or the circular motion of ions in a mass spectrometer.
Overall, the equation F = qvB is a fundamental tool for understanding and analyzing the magnetic forces experienced by moving charges.
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How does a heat pump move thermal energy from a cold area to a warm area?
A heat pump moves thermal energy from a cold area to a warm area by using a refrigerant that evaporates and condenses in a closed loop system.
First, the heat pump absorbs thermal energy from the cold area using a refrigerant, which evaporates into a gas. The gas is then compressed by a compressor, which raises its temperature and pressure.
Next, the hot gas is pumped to a heat exchanger, where it transfers its thermal energy to the warm area, and condenses back into a liquid state. The liquid refrigerant is then expanded through an expansion valve, which lowers its temperature and pressure, and the cycle repeats.
This process allows a heat pump to move thermal energy from a cold area to a warm area, against the natural flow of heat, by using mechanical work to compress and expand the refrigerant. The net effect is to transfer thermal energy from the cold area to the warm area, increasing the temperature of the warm area while decreasing the temperature of the cold area.
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A force is equivalent to a rate of transfer of momentum
T/F
The statement "a force is equivalent to a rate of transfer of momentum" is true.
A force is equivalent to a rate of transfer of momentum. This is known as Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.
In mathematical terms, Newton's second law can be written as:
F = ma
where F is the net force acting on an object, m is the mass of the object, and a is the acceleration of the object.
The unit of force is the Newton (N), which is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg m/s²).
Similarly, the unit of momentum is the kilogram-meter per second (kg m/s), and the rate of transfer of momentum is given by the force applied to an object.
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Why is it dangerous to turn on a light when you are in a bathtub?
It is dangerous to turn on a light when you are in a bathtub because it increases the risk of electric shock.
Water is a good conductor of electricity, and when a person is in a bathtub filled with water, their body becomes a conductor as well. If there is any electrical fault in the lighting circuit, such as a short circuit or a ground fault, the electricity can flow through the water and into the person's body, causing electric shock.
Electric shock can range from mild to severe, depending on the amount of current flowing through the body. Mild shocks can cause a tingling sensation, while severe shocks can cause muscle contractions, burns, and even cardiac arrest.
When a person is in a bathtub, their muscles are relaxed, which can make it harder for them to let go of an electrified object or move away from the source of electricity, increasing the risk of severe injury or death.
To avoid the risk of electric shock, it is important to keep electrical appliances away from water and to never touch electrical devices when you are in a bathtub or shower.
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please help me out (answer step by step show all work) I WILL MARK BRAINLIEST<33
The plot of the graph of the force obtained from the mass on the table and the Displacement of the spring indicates;
a) Please find attached the graph of the force on the spring (y-axis) versus displacement (x-axis), created with MS Excel
b) The spring constant is about 0.18
What is the force on the spring?The force acting on the spring is due to the application of the mass on the spring, which is a product of the mass and the acceleration due to gravity.
Let the force on the spring be due to the mass attached to the spring, we get;
Mass (g) [tex]{}[/tex] Force N
100 g = 0.1 kg [tex]{}[/tex] 0.1 kg × 9.81 m/s² = 0.981 N
200 g = 0.2 kg [tex]{}[/tex] 0.2 kg × 9.81 m/s² = 1.996 N
300 g = 0.3 kg [tex]{}[/tex] 0.3 kg × 9.81 m/s² = 2.943 N
400 g = 0.4 kg [tex]{}[/tex] 0.4 kg × 9.81 m/s² = 3.942 N
Hooke's law states that the force, F, applied on the spring is the product of a constant K, and the displacement of the spring, x
Therefore; F = -k·x
The spring constant k = F/x
Therefore, the extension of a spring, Δx, due to the addition of a force, ΔF, indicates;
ΔF = k × Δx
k = ΔF/Δx
The data from the force and the extension of the spring, produces a graph with a line of best fit equation of, y = 0.1828·x + 0.0027, which indicates;
k = Δy/Δx = ΔF/Δx ≈ 0.1828
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Did you observe a significant difference in the currents flowing at these 2 locations in the circuit, or was the current the same?
If there is a significant difference in the currents flowing at two locations in the circuit, it is likely due to differences in the resistance of the components present.
It is difficult to answer your question without knowing the specific locations in the circuit you are referring to. However, in general, the current flowing through different parts of a circuit can vary depending on the components present and their respective resistances.
If there are resistors in one part of the circuit that are higher than those in another part, the current may be lower in the former. Conversely, if there are fewer resistors in one part of the circuit,
the current may be higher there. It is important to note that current is conserved in a circuit, meaning that the total current flowing in is equal to the total current flowing out.
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A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by a = (4.0 m/s2)i-(3.0 m/s2)j. The torque, relative to the origin, acting on it at the end of 2.0 s is: (Torque as a Vector) a. 0 b. (-18N m)k c. (+24 N m)k d. (-144 N m)k e. (+144 N m)k
The angular momentum is constant in this case (no external torque is acting on the block), the torque is zero.
If the acceleration of the block was given by a = (3.0 m/s²)i + (4.0 m/s²)j, what would be the torque acting on it at the end of 2.0 seconds?To find the torque acting on the block, we first need to find the angular momentum of the block relative to the origin at the end of 2.0 seconds.
The angular momentum of an object is given by the cross product of its position vector and its momentum vector, which can be expressed as:
L = r x p
where L is the angular momentum, r is the position vector, and p is the momentum vector.
In this case, the block starts from rest, so its initial momentum is zero.
We only need to consider the momentum of the block after it has accelerated for 2.0 seconds.
The velocity of the block after 2.0 seconds can be found using the kinematic equation:
v = v0 + at
where v0 is the initial velocity (zero), a is the acceleration, and t is the time elapsed.
Substituting the given values, we get:
v = (4.0 m/s2)(2.0 s)i - (3.0 m/s2)(2.0 s)j
v = 8.0 m/s i - 6.0 m/s j
The momentum of the block can then be calculated as:
p = mv
p = (2.0 kg)(8.0 m/s)i - (2.0 kg)(6.0 m/s)j
p = 16.0 kg m/s i - 12.0 kg m/s j
Next, we need to find the position vector of the block relative to the origin. Since the block starts 3.0 m from the origin on the positive x-axis, its position vector after 2.0 seconds can be expressed as:
r = (3.0 m + 8.0 m/s(2.0 s))i
r = 19.0 m i
Finally, we can calculate the angular momentum of the block relative to the origin:
L = r x p
L = (19.0 m i) x (16.0 kg m/s i - 12.0 kg m/s j)
L = (19.0 m)(-12.0 kg m/s) k
L = -228.0 N m k
Since torque is defined as the time derivative of angular momentum, we can find the torque acting on the block as:
τ = dL/dt
The angular momentum is constant in this case (no external torque is acting on the block), the torque is zero.
The answer is (a) 0.
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946 J of work are required to carry a 23 C charge from point 1 to point 2. What is the magnitude if the potential difference between point 1 and point 2 in units of V?
946 J of work are required to carry a 23 C charge from point 1 to point 2. The magnitude of the potential difference between point 1 and point 2 is 41.1 volts.
To answer this question, we need to understand the relationship between work, charge, and potential difference. Work is defined as the product of force and displacement, and in the case of moving a charge between two points, the force is the electric force and the displacement is the distance between the points. The work done in moving a charge is equal to the potential difference between the two points multiplied by the charge. Mathematically, this is expressed as:
W = qΔV
where W is the work done, q is the charge, and ΔV is the potential difference.
In this case, we are given the work done (946 J) and the charge (23 C) and we need to find the potential difference (ΔV). Rearranging the equation above, we can solve for ΔV as:
ΔV = W/q
Substituting the given values, we get:
ΔV = 946 J / 23 C = 41.1 V
Therefore, the magnitude of the potential difference between point 1 and point 2 is 41.1 volts.
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Is it possible to move in a curved path in the absence of a force?
Answer:
No
Explanation:
No, it is not possible to move in a curved path in the absence of a force. According to Newton's first law of motion, an object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity (that is, in a straight line at a constant speed), unless acted upon by a net external force.
Therefore, if an object is moving in a curved path, it must be experiencing a net external force that is causing it to deviate from its original straight-line path. This force can be a result of gravity, friction, or other external factors. In the absence of any external force, an object will move in a straight line at a constant speed.
How far does a 1. 2g bullet with kinetic energy of 1. 2j go in 2 seconds?
The 1.2g bullet with kinetic energy of 1.2J would travel a distance of 80 meters in 2 seconds, under the assumptions and simplifications we made.
To determine the distance traveled by a 1.2g bullet with kinetic energy of 1.2J in 2 seconds, we need to use the equations of motion. However, we do not have enough information to directly use these equations. We need to make some assumptions and simplifications to solve this problem.
Let's assume that the bullet is fired horizontally, without any air resistance or any other forces acting on it besides gravity. In this case, the motion of the bullet is a projectile motion, and we can use the following equation to determine its horizontal distance traveled:
d = v_x * t
where d is the horizontal distance traveled, v_x is the horizontal velocity of the bullet, and t is the time elapsed.
To find v_x, we need to use the kinetic energy of the bullet:
KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the bullet, and v is the velocity of the bullet. Rearranging this equation to solve for v, we get:
v = sqrt(2 * KE / m)
Substituting the given values, we get:
v = sqrt(2 * 1.2 J / 0.0012 kg) = 40 m/s
Now we can use the equation for d to find the distance traveled by the bullet:
d = v_x * t = v * cos(theta) * t
where theta is the angle between the initial velocity and the horizontal direction. Since the bullet is fired horizontally, theta = 0, and cos(theta) = 1. Thus, we have:
d = v * t = 40 m/s * 2 s = 80 meters
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Assume (for this question only) that g is 10 N/kg for Ontario. What would g be at an altitude equal to the radius of the Earth, in N/kg?
- More information is needed
- 0
- 2.5
- 20
- 5.0
The value of g at an altitude equal to the radius of the Earth would be 0 N/kg.
The value of g at any point in space is determined by the mass of the object and the distance between the center of mass of the object and the point. At the surface of the Earth, the radius is included in the distance between the center of mass and the point, resulting in a non-zero value of g.
However, at an altitude equal to the radius of the Earth, the distance between the center of mass and the point is infinite, resulting in a zero value of g. This is because the gravitational force becomes weaker as the distance between two objects increases, and at an infinite distance, it becomes negligible. Therefore, the correct answer is 0.
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A particle moves in a circle in such a way that the x and y-coordinates of its motion are given in meters as functions of time t in seconds by:
x = 5 cos (3t) y = 5 sin (3t)
Which of the following is true of the speed of the particle?
a. It is always equal to 5 m/s.
b. It is always equal to 15 m/s
c. It oscillates between 0 and 5 m/s
d. It oscillates between 0 and 15 m/s
e. It oscillates between 5 and 15 m/s.
The speed of the particle is always equal to option b. 15 m/s when equation of motion is x = 5 cos(3t) and y = 5 sin(3t).
The x and y-coordinates of the particle's motion are given by x = 5 cos(3t) and y = 5 sin(3t). To determine the speed of the particle, we need to find the magnitude of the velocity vector. First, let's find the components of the velocity vector by taking the time derivatives of the position functions:
dx/dt = -15 sin(3t)
dy/dt = 15 cos(3t)
Now, we can find the speed by calculating the magnitude of the velocity vector:
Speed = [tex]\sqrt{((dx/dt)^2 + (dy/dt)^2)[/tex]
= [tex]\sqrt{((-15 sin(3t))^2 + (15 cos(3t))^2)[/tex]
= [tex]\sqrt{(225(sin^2(3t) + cos^2(3t)))[/tex]
Since[tex]sin^2(x) + cos^2(x) = 1[/tex] for any angle x, the expression simplifies to:
Speed = [tex]\sqrt{(225)[/tex]
= 15 m/s
Therefore, the correct answer is (b) - the speed of the particle is always equal to 15 m/s.
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what is the Fixed point that a force must pass through in order to move that object in a linear manner?
The fixed point that a force must pass through in order to move an object in a linear manner is called the pivot point. This point is typically located at the center of mass of the object.
Point is where the force can be applied in a way that will cause the object to move in a straight line, or in a linear manner. By applying the force at the pivot point, any rotational motion of the object can be minimized, allowing for a more efficient and controlled linear movement.
The electron transport chain is a collection of proteins found in the plasma membrane of prokaryotic cells or the inner mitochondrial membrane of eukaryotic cells. The ETC is made up of four multi-enzyme complexes: cytochrome c oxidase (complex IV), succinate dehydrogenase (complex III), and NADH dehydrogenase (complex I). Adenosine triphosphate (ATP) generation depends on the movement of electrons across the cell membrane, which is carried out by these enzyme complexes.
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What equation describes the size of the magnetic field produced by a straight wire?
The magnetic field produced by a straight wire carrying a current I at a distance r from the wire is given by B = μ₀I / 2πr, where μ₀ is the permeability of free space.
The magnetic field produced by a straight wire can be calculated using Ampere's law, which relates the magnetic field around a closed loop to the electric current passing through the loop.
If we consider a straight wire carrying a current I, the magnetic field B at a distance r from the wire can be given by the equation:
B = μ₀I / 2πr
where μ₀ is the permeability of free space, a fundamental constant with a value of approximately 4π x 10^-7 T·m/A.
This equation is known as the "Biot-Savart law", and it gives the magnitude of the magnetic field produced by a straight wire carrying a steady current. The direction of the magnetic field can be determined using the "right-hand rule". If you wrap your fingers around the wire in the direction of the electric current, the direction of the magnetic field is given by the direction your thumb points.
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Two massive objects have -500 J of gravitational potential energy stored between them. What does that mean?
a) This situation is impossible
b) None are correct
c) The objects have 500 J more energy than they would have infinitely far away from each other
d) The objects must have a kinetic energy of 500 J each
e) It would take 500 J of work to completely separate them
It would take 500 J of work to completely separate them. Option e is the answer.
Gravitational potential energy is the energy stored in the gravitational field between two objects. A negative value for gravitational potential energy indicates that work would need to be done to separate the objects to an infinite distance, meaning that the objects are attracted to each other. Therefore, in this scenario, it would take 500 J of work to completely separate the objects. Option e is correct choice.
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A gardener feels it is taking too long to water a garden with a 3/8-in diameter hose. By what factor will the time be cut using a 5/8-in diameter hose instead?
If it took the gardener one hour to water the garden, it would take approximately 21.6 minutes to water the same garden with a 5/8-in diameter hose.
The gardener's concern about the time taken to water the garden with a 3/8-in diameter hose is valid as the smaller the diameter of the hose, the longer it will take to water the garden. Using a 5/8-in diameter hose instead of a 3/8-in diameter hose will increase the flow of water.
To calculate the factor by which the time will be cut, we need to use the formula:
Time taken with 3/8-in diameter hose / Time taken with 5/8-in diameter hose
Assuming that the water pressure and flow rate remain constant, we can calculate the factor as follows:
The area of a 3/8-in diameter hose is (3.14/4) x [tex](3/8)^2[/tex] = 0.044 square inches.
The area of a 5/8-in diameter hose is (3.14/4) x [tex](5/8)^2[/tex] = 0.122 square inches.
So the ratio of the areas is 0.122/0.044 = 2.77.
This means that the time taken to water the garden with a 5/8-in diameter hose will be reduced by a factor of approximately 2.77 compared to the 3/8-in diameter hose.
Therefore, if it took the gardener one hour to water the garden with a 3/8-in diameter hose, it would take approximately 21.6 minutes (60 minutes / 2.77) to water the same garden with a 5/8-in diameter hose.
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