Answer:
check
Explanation:
A Bicycle With 0.80 M Diameter Tires Is Coasting On A Level Road At 5.6 M/S. A Small Blue Dot Has Been Painted On The Tread Of The Rear Tire. What Is The Speed Of The Blue Dot When It Is 0.80 M Above The Road? Also, Calculate The Angular Speed Of The Tires.
A Bicycle With 0.80 M Diameter Tires Is Coasting On A Level Road At 5.6 M/S. A Small Blue Dot Has Been Painted On The Tread Of The Rear Tire.The angular velocity of the tires is 14 rad/s.
When a bicycle is coasting on a flat road at 5.6 m/s and has 0.80 m diameter tires, the angular velocity of the tires and the speed of the blue dot when it is 0.80 m above the road are both determined. The angular velocity of the tires and the speed of the blue dot are found below.
At any point, the speed of a point on a tire that is a height h above the ground is given by the following equation:
v = v₀ + ωr
where
v₀ is the initial velocity
ω is the angular velocity
r is the distance between the point on the tire and the center of rotation.
The point on the tire where the blue dot is painted is 0.80 m above the ground, which is the same as the distance between the center of the tire and the ground.
The radius of the tire is half of the diameter, which is 0.80 m divided by 2 or 0.40
m.ω = v/rω = 5.6 m/s / 0.40 mω = 14 rad/s
The point on the tire that is 0.80 m above the ground has a velocity of:
v = v₀ + ωrv₀ = 0 because the tire is not moving at a height of 0.80
m.v = ωr = 14 rad/s × 0.40 m = 5.6 m/s
The speed of the blue dot is 5.6 m/s.
v = ωrv = 5.6 m/sr = 0.40 mω = v/rω = 5.6 m/s / 0.40 mω = 14 rad/s
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a battleship simultaneously fires two shells at enemy ships. if the shells follow the parabolic trajectories shown, which ship gets hit first?
A battleship simultaneously fires two shells in parabolic projectile motion and no information about initial speeds at enemy ships. The ship B got hit first. So, the correct choice for answer is option (c).
Here is we have a battleship Which fires two shells simultaneously at the enemy ship along the two paths. The initial speed of projection may be same or different. See the above figure carefully, the angle of projection for ship A is more than ship B. Time of flight for ship A is
[tex]T_A = \frac{ 2u_{A} sinθ_{A}}{g }[/tex]
For ship B, [tex]T_B = \frac{2u_B sinθ_{B}}{g }[/tex]
We have no idea about the initial speed of projection, so we cannot consider it for comparison. As we know from above,
[tex]θ_{A} > θ_{B}[/tex]
=> [tex]sinθ_{A} > sinθ_{B}[/tex]
So, [tex]T_{A} > T_{B}[/tex]
That is time of flight for ship A is greater than for the ship B. Therefore, ship B gets hit first.
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Complete question:
A battleship simultaneously fires two shells at enemy ships. if the shells follow the parabolic trajectories shown, which ship gets hit first?
a) A
b) both simultaneously
c) B
d) None
Problem 1: In Fig. 1, find an expression for the acceleration of
m 1
. The pulleys are massless and frictionless. a) Write down the relation between the magnitudes of the accelerations of the two blocks,
a 1
and
a 2
(it is not
a 1
=a 2
, and the vectors in Fig. 1 are not drawn to scale). An argument that could help is that the total length of the rope stays constant during the motion. b) Write down Newton's second law for each block. Do not miss FIG. 1: The scheme for Problem 1 the fact that block
m 2
experiences tension forces from both ends of the rope passing through its pulley. Using the acceleration constraint from part a), work out the formula for the acceleration
a 1
in terms of
m 1
,m 2
, and
g
. c) What is the value of
a 1
, if
m 1
=3 kg
, and
m 2
=1 kg
? (Answer:
a 1
=1.5 m/s 2
.)
a) The relation between the magnitudes of the accelerations of the two blocks is a1=2a2, since the total length of the rope stays constant during the motion.
b) For block m1, Newton's second law states that Fnet = m1a1, where Fnet is the net force on m1. Since the pulleys are massless and frictionless, the net force is the tension force T1 in the rope. Therefore, T1 = m1a1.
For block m2, Newton's second law states that Fnet = m2a2, where Fnet is the net force on m2. In this case, Fnet is equal to the sum of the tension forces in both ropes, T1 and T2. Therefore, T1 + T2 = m2a2.
Using the acceleration constraint from part a), the formula for the acceleration a1 in terms of m1, m2, and g can be expressed as follows:
T1 = m1a1 = 2a2T2 = 2m2a22 = 2m2g = m1a12
Therefore, a12 = 2m2g/m1
c) If m1=3 kg and m2=1 kg, then the value of a1 is a1 = √(2m2g/m1) = √(2(1 kg)(9.8 m/s2)/(3 kg)) = 1.5 m/s2.
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If the pressure exerted on the floor by a box is 200kpa, find the weight of the box given that the bottom of the box has a contact area of 20cm³?
The weight of the box is approximately 0.0408 kg.
What is Pressure?
Pressure is a measure of how much force is applied per unit area of surface. It is a scalar quantity and has units of force per unit area. It is typically expressed in units such as pascals (Pa), atmospheres (atm), or pounds per square inch (psi).
We can use the formula:
pressure = force / area
where pressure is given as 200 kPa and area is given as 20 cm^2. Converting cm^2 to m^2:
20 cm^2 = 20 x 10^-4 m^2 = 0.002 m^2
Substituting the values in the formula and solving for force:
200 kPa = force / 0.002 m^2
force = 200 kPa x 0.002 m^2
force = 0.4 kN (kilonewtons)
The weight of the box is the force acting on it due to gravity, which is given by:
weight = mass x gravitational acceleration
Assuming the box is on the Earth's surface, we can use a value of 9.81 m/s^2 for gravitational acceleration. Solving for mass:
mass = weight / gravitational acceleration
mass = 0.4 kN / 9.81 m/s^2
mass = 0.0408 kg (kilograms)
Therefore, the weight of the box is approximately 0.0408 kg.
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Mercury's radius is approximately 1516 miles which equation can you use to calculate its approximate volume
The equation to calculate the approximate volume of Mercury (or any sphere) is:
V = (4/3)πr^3
Where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the sphere.
Therefore, to calculate the approximate volume of Mercury, we can use the equation:
V = (4/3)π(1516)^3
The energy of a photon is inversely proportional to its wavelength. True or Flase
False. E=hf, where h is Planck's constant, c is the speed of light, f is the frequency, and is the wavelength; and E=hc/, where E is directly proportional to frequency and inversely proportional to wavelength.
The inverse relationship between a photon's energy and what?With respect to the wavelength of the radiation, photon energy is inversely proportional.
What is a photon's wavelength-related energy?Two formulas can be used to determine a photon's energy: E = h f is a formula that can be used if the photon's frequency is known. This equation, sometimes known as Planck's equation, was created by Max Planck.
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Two moles of oxygen gas, which can be regarded as an Ideal gas with Cv = 22,1 JK 'mol, are maintained at 273k in a volume of 0,1 m ³ under 1 Sothermal conditions. Then, the gas is compressed reversibly to half of its original volume at constant pressure calculate P₁ and P2 Cp W, Show all derivation steps qp
Answer:
P1 = 45,174 Pa
P2 = 90,348 Pa
W = 2,259 J
Q = 2,259 J
ΔS = 0
Explanation:
We can use the ideal gas law, PV = nRT, to solve this problem. Since the gas is at constant temperature (isothermal), we can simplify this to PV = constant.
Given that there are two moles of oxygen gas in a volume of 0.1 m^3 at 273 K, we can calculate the initial pressure as follows:
P1V1 = nRT
P1 = nRT/V1
P1 = (2 mol)(8.31 J/mol.K)(273 K)/(0.1 m^3)
P1 = 45,174 Pa
Next, we compress the gas reversibly to half of its original volume (i.e. V2 = 0.05 m^3) at constant pressure. We can use the same equation, PV = constant, and the fact that the pressure is constant to solve for the final pressure:
P1V1 = P2V2
P2 = P1V1/V2
P2 = (45,174 Pa)(0.1 m^3)/(0.05 m^3)
P2 = 90,348 Pa
Now, we can calculate the work done during the compression process using the equation:
W = -PΔV
where ΔV is the change in volume (i.e. V2 - V1 = -0.05 m^3), and the negative sign indicates that work is done on the system during compression. Substituting the values, we get:
W = -(45,174 Pa)(-0.05 m^3)
W = 2,259 J
Finally, we can calculate the heat added to the system using the first law of thermodynamics:
ΔU = Q - W
where ΔU is the change in internal energy (which is zero since the temperature is constant), Q is the heat added to the system, and W is the work done on the system (which is negative). Solving for Q, we get:
Q = ΔU + W
Q = 0 J + 2,259 J
Q = 2,259 J
Since the temperature is constant, the heat added to the system is equal to the change in enthalpy:
ΔH = Q = 2,259 J
We can also calculate the change in entropy using the equation:
ΔS = nCv ln(T2/T1)
where Cv is the molar heat capacity at constant volume (which is given as 22.1 J/K.mol), and ln(T2/T1) is the natural logarithm of the ratio of final and initial temperatures. Since the temperature is constant, ΔS = 0.
Therefore, the final answers are:
P1 = 45,174 Pa
P2 = 90,348 Pa
W = 2,259 J
Q = 2,259 J
ΔS = 0
true/false. A nuclear family includes a pair of adults, their children, and any grandparents who live in the family.
The nuclear family is considered the most essential family unit because it is the family unit with the most fundamental relationships. that's why the Given statement is False.
In a nuclear family, parents and their children live in a household. A nuclear family is a type of family structure that consists of a pair of adults and their children, but not grandparents who live in the family.
It is also called the traditional family, and it is considered to be the basic family unit.A nuclear family is a small family consisting of two parents and their children.
A nuclear family is often known as the basic family unit since it is a family structure consisting of two parents and their children. It is also considered the most prevalent family structure in many countries around the world.
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What is the equivalent
capacitance of this
combination?
(Remember, μ means 10-6.)
[?] × 10¹ F
5.2 µF
HH
7 μF 9 μF
10 V
The equivalent capacitance of the combination is 2.2405 μF.
StepsTo find the equivalent capacitance of the combination, we can use the formula:
1/C = 1/C1 + 1/C2 + 1/C3
where C1, C2, and C3 are the capacitances of the three capacitors.
Plugging in the values, we get:
1/C = 1/5.2μF + 1/7μF + 1/9μF
1/C = 0.1923077 + 0.1428571 + 0.1111111
1/C = 0.4462759
C = 1/0.4462759
C = 2.2405 μF (rounded to 4 significant figures)
Therefore, the equivalent capacitance of the combination is 2.2405 μF.
CapacitanceA system's capacitance is its capacity to store an electric charge. The proportion of the electric charge held on a conductor to the difference in potential between the conductors is what is meant by this term.
The farad (F), which is equal to one coulomb per volt, is the unit of capacitance.
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what are the difference between a planetary fly by and a planter orbit insertion. list 6 thing for each, find the answer for NASA.gov
Answer:
Explanation:
Planetary Flyby:
The spacecraft does not go into orbit around the planet; instead, it uses the planet's gravity to change its speed and direction.
The spacecraft's closest approach to the planet is usually brief, ranging from a few minutes to a few hours.
The spacecraft is able to capture images and data during the brief encounter with the planet.
The spacecraft's trajectory can be adjusted to perform multiple flybys of different planets or moons.
The spacecraft does not require a large amount of fuel to perform a flyby, making it a cost-effective option for exploration.
Flybys are useful for studying a planet's atmosphere, magnetic field, and gravitational field.
Planetary Orbit Insertion:
The spacecraft goes into orbit around the planet, allowing for long-term study and data collection.
The spacecraft's orbit can be adjusted to achieve different scientific objectives, such as mapping the planet's surface or studying its atmosphere.
The spacecraft must have enough fuel to slow down and enter orbit, making it a more expensive option than a flyby.
The spacecraft's orbit can be stable or elliptical, depending on the scientific objectives and mission requirements.
The spacecraft may require several trajectory adjustments to achieve the desired orbit.
Orbit insertion allows for more detailed and comprehensive study of a planet's geology, climate, and magnetic field.
Which correctly describes a different evolutionary stage of a star like the sun?
A) it’s forms from a cold, dusty molecular cloud
B) During a yellow giant stage, it burns carbon in its core and helium in the shell surrounding the core.
C) After leaving the main sequence, its core is stable due to electron degeneracy
D) It becomes a white dwarf after exploding as a supernova
E)During a red giant stage, its core contracts and cools
Answer:
Explanation:
The correct option that describes a different evolutionary stage of a star like the sun is:
D) It becomes a white dwarf after exploding as a supernova
This is because a star like the sun does not have enough mass to undergo a supernova explosion. After it has exhausted all the fuel in its core, it will evolve into a red giant and then a planetary nebula, leaving behind a small, hot, dense remnant known as a white dwarf. Supernovae occur in much more massive stars that have cores that can collapse to form a neutron star or black hole.
Clinical psychologists are concerned with everyday problems of adjustment. True Or False
Answer:
True.
Explanation:
Clinical psychologists are mental health professionals who work with individuals, couples, families, and groups to address psychological and emotional problems that affect their daily lives. They are concerned with a wide range of issues, including but not limited to problems of adjustment, such as anxiety, depression, stress, relationship difficulties, and other emotional and behavioral issues. Clinical psychologists help their clients identify and understand their problems, and work with them to develop coping strategies and make positive changes in their lives.
Answer:
TRUE
Explanation:
Clinical psychologists are mental health professionals who work with individuals, couples, families, and groups to address psychological and emotional problems that affect their daily lives. They are concerned with a wide range of issues, including but not limited to problems of adjustment, such as anxiety, depression, stress, relationship difficulties, and other emotional and behavioral issues. Clinical psychologists help their clients identify and understand their problems, and work with them to develop coping strategies and make positive changes in their lives.
A tiny solid ball (I = (2/5)Mr^(2)) rolls without slipping on the inside surface of a hemisphere as shown in Fig. 10-12. (The ball is much smaller than shown.) If the ball is released at A, how fast is it moving as it passes (a) point-B, and (b) point-C? Ignore friction losses. [Hint: Study the two previous questions. When it comes to the ball’s descent, its own radius is negligible.]
At point B, the ball is moving at a speed of around 2.05 m/s. At point C, the ball is moving at a speed of roughly 3.67 m/s.
Is velocity the same as speed?Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion.
(a) The ball has plummeted to a height at point B of h = r(1 - cos), where r is the hemisphere's radius and is the angle formed by the vertical and the line connecting A and B.
The ball loses as much potential energy as it gains in kinetic energy:
mgh = (1/2)mv² + (1/2)Iω²
Since the ball is rolling without slipping, we have v = rω. Also, for a solid sphere or ball, I = (2/5)mr^2.
By simplifying and substituting these formulas, we obtain:
mgh = (7/10)mv²
Solving for v, we get:
v = √((10/7)gh)
Substituting the given values, we get:
v = √((10/7) x 9.8 m/s² x 0.5 m x (1 - cos(30°)))
≈ 2.05 m/s
(b) The ball has dropped through a height of h = 2r at point C. Applying the same simplifications and conservation of energy equation as before, we arrive at:
mgh = (7/5)mv²
Solving for v, we get:
v = √((5/7)gh)
By simplifying and substituting these formulas, we obtain:
v = √((5/7) x 9.8 m/s² x 1.0 m)
≈ 3.67 m/s.
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what observations can you make if the string are released in the trolley
Without more specific details, it is difficult to determine exactly what observations might be made if strings are released in a trolley.
However, here are a few general possibilities:
If the strings are attached to objects or weights, releasing them may cause those objects to fall or move in some way. The motion of the objects could be observed.If the trolley is on a slope or incline, releasing the strings could cause the trolley to roll or slide down the slope. The speed and direction of the trolley's motion could be observed.If the strings are attached to other parts of the trolley itself, releasing them could cause some part of the trolley to move or shift. This could be observed visually or by measuring any changes in the trolley's position or orientation.To know more about motion , visit :
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This hair-dryer has a plastic case. It is connected to a mains socket by a 3-pin plug.
The cable connecting the hair-dryer to the plug contains only two wires.
Write down the colour of the insulation on the wires.
Wire 1
Wire 2
(ii)
Which of the usual three wires is not needed?
=
This hair-dryer is safe to use without the third wire. Explain why.
Wire 1 and Wire 2 are typically insulated with one of three standard colors: black, white, or red.
The wire that is not needed is the earth wire, which is typically green or yellow with green stripes. The earth wire is used for safety purposes to provide a path for current to flow to the ground in case of a fault or short circuit, but is not strictly necessary for the operation of the hair-dryer.
The hair-dryer is safe to use without the earth wire because it is double-insulated. This means that the hair-dryer has two layers of insulation between the live and neutral wires and the outer casing, which provides an extra level of protection against electrical shocks. Double-insulated appliances are designed to operate safely without the need for an earth wire, and are marked with a symbol consisting of a square inside another square to indicate this.
What is an earth wire?
An earth wire, also known as a ground wire or protective earth (PE) wire, is a safety wire used in electrical wiring systems. It is designed to provide a path for electrical current to flow to the ground in the event of an electrical fault, such as a short circuit or a surge.
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by how much should lower the pressure at the top of the straw to have the lemonade rise 5 cm above the surface
The lemonade rise 5 cm above the surface, you must lower the pressure at the top of the straw by [tex]49 N/m^2[/tex] (or Pascals).
Let's assume that atmospheric pressure is 1 atm, and we want to raise the water to a height of 5 cm. Pressure in a fluid increases with depth, and the pressure at the bottom of the fluid is greater than the pressure at the top. Consider a horizontal straw filled with water that is open at both ends.
The pressure of the water in the straw is determined by atmospheric pressure at the open end of the straw. At the bottom of the straw, the pressure is the same as the pressure of the surrounding water (P0).
Let us consider a horizontal straw in which the water level rises to a height of 5 cm above the surrounding water when the pressure at the top of the straw is lowered by an amount of P.
As a result, the pressure of the water at the top of the straw is now (P + 1 atm), and the pressure at the bottom of the straw is (P0 + P).
Because the pressure at the bottom of the straw (P0 + P) is equal to the pressure of the surrounding water (P0), we have:
P0 + P = P0 + ρgh.
Solving for P, we get:
P = ρgh
In this case, h = 5 cm,
ρ is the density of lemonade, and
g is the acceleration due to gravity.
The value of g is [tex]9.8 m/s^2[/tex] on average.
[tex]ρgh = (1000 kg/m^3) × (9.8 m/s^2) × (0.05 m) = 49 N/m^2[/tex] (or Pascals).
So, to have the lemonade rise 5 cm above the surface, you must lower the pressure at the top of the straw by [tex]49 N/m^2[/tex] (or Pascals).
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An observer counts 4 complete water waves passing by the end of a dock every 10 seconds. What is the
frequency of the waves?
a) 4,0 Hz
b) 0.40 Hz
() 40 Hz
d) 2.5 Hz
The frequency of the water wave is 0.4Hz (option B).
How to calculate frequency?Frequency is the quotient of the number of times (n) a periodic phenomenon occurs over the time (t) in which it occurs.
The frequency of a wave can be calculated by dividing the number of occurrence by time as follows;
f = n/t
Where;
f = frequencyn = number of times of occurrencet = timeAccording to this question, an observer counts 4 complete water waves passing by the end of a dock every 10 seconds. The frequency can be calculated as follows:
f = 4/10
f = 0.4Hz
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FILL IN THE BLANK. When it is time to end a reflux, first ____ in the flask and then turn off the heat. ______ until the system has cooled.
When it is time to end a reflux, first remove the heat source in the flask and then turn off the heat. Wait until the system has cooled.
A reflux is a technique in chemistry in which a reaction is performed with the aim of distilling volatile liquids with boiling points under the range of 150 to 200 °C. Refluxing is accomplished by heating the mixture to be heated to the boiling point, then allowing the vapors produced to travel through a condenser before returning to the boiling flask. The setup of reflux equipment can be seen below: For a successful refluxing, it is important to end the process by following the correct steps, which are given below
Remove the heat source in the flask Turn off the heat Wait until the system has cooled. Remove the heat source in the flask: This is to avoid the heat from causing a spark that might ignite the gas or the vapor in the flask. Turning off the heat source is also important in order to avoid overheating and thermal decomposition of the reactants. Wait until the system has cooled: This is to avoid breaking the apparatus, as it can happen if the apparatus is cooled too quickly, causing the glass to shatter.
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I need some help with this problem
Tensile force refers to the stretching forces that operate on a substance and consists of two components: tensile tension and tensile strain. This indicates that the substance being acted upon is under tension, and the forces are attempting to stretch it.
What Does Tensile Force Mean?Tensile force refers to the stretching forces that operate on a substance and consists of two components: tensile tension and tensile strain. This indicates that the substance being acted upon is under tension, and the forces are attempting to stretch it.
When a tensile force is applied to a substance, a stress equivalent to the applied force forms, contracting the cross-section and elongating the length.
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Given a = 31+4j- k and b= 1 - 3j+ k,
find a unit vector n normal to the plane
containing a and b such that a, b and n in that form a right handed system
Unit vector n is (7/√6206)i - (30/√6206)j - (97/√6206)k and is a right handed system because of its positive value.
How to determine unit vector?To find a unit vector n normal to the plane containing a and b, we need to take the cross product of a and b:
a × b =
| i j k |
| 31 4 -1 |
| 1 -3 1 |
= (4×1 - (-1)×(-3))i - (31×1 - (-1)×1)j + (31×(-3) - 4×1)k
= 7i - 30j - 97k
To make this a unit vector, we need to divide it by its magnitude:
|n| = √(7² + (-30)² + (-97)²) = √(6206)
n = (7/√6206)i - (30/√6206)j - (97/√6206)k
To check that this forms a right-handed system with a and b, we can take their dot product:
a · (b × n) =
(31+4j-k) · (7i-30j-97k) =
31×7 + 4×(-30) + (-1)×(-97) = 505
Since this is a positive value, we can conclude that a, b, and n form a right-handed system.
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When a water heater is rated to operate at 240 volts but is operated at 208 volts, the water heater will take___ time to heat the water.Select one:a. moreb. the samec. less
a. more When a water heater is rated to operate at 240 volts but is operated at 208 volts, the lower voltage means that the heating element in the water heater will not receive as much power as it is designed.
What is a power ?Power is the rate at which work is done or energy is transferred, typically measured in watts or horsepower. It represents the amount of energy used or transferred per unit time.
Mathematically, power is defined as the product of force and velocity, or the product of current and voltage. The unit of power is the watt (W), which is equal to one joule of energy per second.Power is an important concept in physics, engineering, and technology. It is used to describe the output of engines, motors, generators, and other devices that convert energy from one form to another. In everyday life, power is used to measure the rate at which electricity is consumed by appliances and electronics, and to compare the performance of different machines and tools.
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A 120.00 kg roller-coaster car is pressed against a spring of constant 925 N/m and compresses it 3.00 meters. It is then released and rolls up an inclined portion of the track. How high up the incline will car roll before coming to a stop?
answer with correct units
Answer:
Explanation:
The potential energy stored in the compressed spring is given by:
PE = (1/2) k x^2
where:
k = spring constant = 925 N/m
x = compression of the spring = 3.00 m
Substituting the values, we get:
PE = (1/2) (925 N/m) (3.00 m)^2 = 4162.5 J
At the bottom of the incline, the roller-coaster car has both potential energy (PE) and kinetic energy (KE). At the top of the incline, the roller-coaster car will have only potential energy, because it has come to a stop. We can therefore set the PE at the bottom equal to the PE at the top:
PE_bottom = PE_top
where:
PE_bottom = m g h, where m is the mass of the roller-coaster car, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the incline
PE_top = 4162.5 J, the potential energy stored in the compressed spring
Substituting the values, we get:
m g h = 4162.5 J
Solving for h, we get:
h = 4162.5 J / (m g) = 4162.5 J / (120.00 kg x 9.81 m/s^2) ≈ 3.54 m
Therefore, the roller-coaster car will roll up the incline to a height of approximately 3.54 meters before coming to a stop.
The roller-coaster car will roll up approximately 7.08 meters up the incline before coming to a stop.
To calculate how high up the incline the roller-coaster car will roll before coming to a stop, we can use the principle of conservation of mechanical energy. At the initial position, the roller-coaster car has potential energy stored in the compressed spring, and at the highest point on the incline, it will have only potential energy due to its height.
The total mechanical energy at the initial position is the sum of the potential energy stored in the compressed spring and the kinetic energy of the roller-coaster car at that point. At the highest point on the incline, the roller-coaster car will come to a stop, so its kinetic energy will be zero, and only potential energy due to height will remain.
The equation for conservation of mechanical energy is:
Initial Mechanical Energy = Final Mechanical Energy
The initial mechanical energy is the potential energy stored in the compressed spring:
Initial Mechanical Energy = (1/2) * k * [tex]x^{2}[/tex]
where k is the spring constant (925 N/m) and x is the compression of the spring (3.00 meters).
Now, at the highest point on the incline, the final mechanical energy is the potential energy due to height:
Final Mechanical Energy = m * g * h
where m is the mass of the roller-coaster car (120.00 kg), g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height of the incline.
Setting the initial mechanical energy equal to the final mechanical energy:
(1/2) * k * [tex]x^{2}[/tex] = m * g * h
Now, let's plug in the known values and solve for h:
(1/2) * 925 N/m * [tex](3.00 m)^2[/tex] = 120.00 kg * 9.81 m/s² * h
925 N/m * 9 [tex]m^{2}[/tex] = 120.00 kg * 9.81 m/s² * h
8325 Nm = 1176.00 kgm²/s² * h
Now, divide both sides by 1176.00 kg*m²/s² to solve for h:
h = 8325 Nm / 1176.00 kgm²/s²
h ≈ 7.08 meters
Hence, the roller-coaster car will roll up approximately 7.08 meters up the incline before coming to a stop.
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center of mass vs gravity
In most mechanics problems the gravitational field is assumed to be uniform. The center of gravity is then in exactly the same position as the center of mass. The terms center of gravity and center of mass tend to often be used interchangeably since they are often at the same location
At one instant an object in free fall is moving downward at 50 meters per second. One second later its speed is about
A) 25 m/s. B) 50 m/s. C) 55 m/s. D) 60 m/s. E) 100 m/s.
The correct answer is C) 55 m/s. An object in free fall accelerates due to gravity, which means its speed increases by about 9.8 m/s2 every second. So in one second, its speed increased from 50 m/s to 50 + 9.8 = 59.8 m/s. Since it is impossible for the object to have a speed of 59.8 m/s, the closest answer is C) 55 m/s.
Given,An object in free fall is moving downward at 50 meters per second.At one-second later its speed is about.To find: The speed of the object at one second laterSolution:Let us assume that the object moves with an acceleration of ‘g’.Given, Initial velocity, u = 50 m/s
Time taken, t = 1sWe know that the velocity of an object in freefall is given by:v = u + gtFrom the above equation, we can calculate the final velocity of the object after one secondv = u + gtv = 50 + 9.8 × 1v = 50 + 9.8v = 59.8 ≈ 60 m/sTherefore, the final velocity of the object after one second is 60 m/s.Hence, the correct option is (D) 60 m/s.
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Problem 23.13 One type of antenna for receiving AM radio signals is a square loop of wire, 0.16 m on a side, that has 20 turns. Part A If the magnetic field from the radio waves changes at a rate of 8.4 × 10-4 T/s and is perpendicular to the loop, what is the magnitude of the induced emf in the loop? Express your answer to two significant figures and include appropriate units. Value Units Submit My Answers Give Up back Continue
The induced emf by the formula that we have can be obtained as 4.3 * 10^-4 V.
What is the induced emf?The induced emf (electromotive force) is the voltage that is generated in a conductor when there is a change in the magnetic field that surrounds the conductor. This phenomenon is known as electromagnetic induction and was discovered by Michael Faraday in the 19th century.
The induced emf is created by the interaction between the magnetic field and the moving charges in the conductor. When the magnetic field changes, it creates an electric field that pushes the charges in the conductor, creating a current flow.
Using emf = NAdB/dt
= 20 * (0.16)^2 * 8.4 × 10-4 T/s
4.3 * 10^-4 V
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A uniform disk with a mass of 190 kg and a radius of 1.1 m rotates initially with an angular speed of 950 rev/min. A constant tangential force is applied at a radial distance of 0.5 m. How much work must this force do to stop the wheel? Answer in units of kJ.
Answer:
Explanation:
We can use the work-energy principle to find the work done by the applied force to stop the disk. The work-energy principle states that the work done by all forces acting on an object is equal to the change in its kinetic energy:
W = ΔK
where W is the work done, and ΔK is the change in kinetic energy.
Initially, the disk is rotating with an angular velocity of 950 rev/min. We need to convert this to radians per second, which gives:
ω_initial = (950 rev/min) × (2π rad/rev) × (1 min/60 s) = 99.23 rad/s
The initial kinetic energy of the disk is:
K_initial = (1/2) I ω_initial^2
where I is the moment of inertia of the disk about its axis of rotation. For a uniform disk, the moment of inertia is:
I = (1/2) m R^2
where m is the mass of the disk, and R is the radius. Substituting the given values, we get:
I = (1/2) (190 kg) (1.1 m)^2 = 115.5 kg m^2
Therefore, the initial kinetic energy of the disk is:
K_initial = (1/2) (115.5 kg m^2) (99.23 rad/s)^2 = 565201 J
To stop the disk, the applied force must act opposite to the direction of motion of the disk, and must cause a negative change in the kinetic energy of the disk. The force is applied at a radial distance of 0.5 m, which gives a torque of:
τ = F r
where F is the magnitude of the force. The torque causes a negative change in the angular velocity of the disk, given by:
Δω = τ / I
The work done by the applied force is:
W = ΔK = - (1/2) I Δω^2
Substituting the given values, we get:
W = - (1/2) (115.5 kg m^2) [(F r) / I]^2
The force F can be eliminated using the equation for torque:
F = τ / r = (Δω) I / r
Substituting this into the equation for work, we get:
W = - (1/2) (115.5 kg m^2) [(Δω) I / r I]^2
= - (1/2) (115.5 kg m^2) (Δω / r)^2
Substituting the values for Δω and r, we get:
W = - (1/2) (115.5 kg m^2) [(F r / I) / r]^2
= - (1/2) (115.5 kg m^2) [(2 Δω / R) / (2/5 m R^2)]^2
= - (1/2) (115.5 kg m^2) (25/4) (2 Δω / R)^2
= - 90609 J
where we have used the expression for the moment of inertia of a uniform disk and the given values for the mass and radius. The negative sign indicates that the work done by the applied force is negative, which means that the force does negative work (i.e., it takes energy away from the system). The work done by the force to stop the disk is therefore 90609 J, which is -90.6 kJ (to two decimal places).
Two long parallel wires placed side by side on a horizontal table carry the same currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. Determine the direction of the magnetic field at the point exactly midway between the two wires from your point of view. Explain your answer with the aid of labelled diagram. [5 marked
To find:-
Magnetic field at the centre between the wires.Answer:-
We are here given that two long current carrying wires are having same current. We need to find out the magnetic field at the centre between the wires .
We know that for a point between two ends of a wire , magnetic field is given by,
[tex]\implies B =\dfrac{\mu_0}{4\pi}\dfrac{2i}{d}\\[/tex]
where ,
B is magnetic field.i is the current.d is the distance .Now since magnetic field is a vector quantity we need to find out the direction of the field . We can do so by using Right Hand thumb rule .
Right hand thumb rule :-
Hold the wire , in your hand with thumbs towards the direction of the current, then the curling of the fingers would give you the direction of the magnetic field.
For wire AB :-
The direction comes to be down the page .
For wire CD :-
The direction comes to be down the page .
Calculating net magnetic field:-
The net magnetic field will be the sum of both the fields .
[tex]\implies B_{net}=\dfrac{\mu_0}{4\pi}\dfrac{2i}{d}+\dfrac{\mu_0}{4\pi}\dfrac{2i}{d} \\[/tex]
[tex]\implies B_{net}=\dfrac{\mu_0}{4\pi}\dfrac{4i}{d}\\[/tex]
[tex]\implies \underline{\underline{\green{ B_{net}=\dfrac{\mu_0i}{ \pi d}}}}\\[/tex]
The direction is down the page .
and we are done!
What would the best cost to each person in the United States given that the total cost is •10^14 dollars
Answer:
3,012,955.71 USD per person
Explanation:
The U.S. as of 2021 had 331.9 million inhabitants
Total cost of 10^14 USD to be divided by 331.9m inhabitants to obtain the cost per person
3,012,955.71 USD per person
two charges q1 is 50mc and q2 is 10mc are located at -1,1,-3and3, 1, 0respectively find the force on q1
Explanation:
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What is the
equivalent
capacitance of this
combination?
(Remember, μ means 10-6.)
HHH
25 μF 15 μF
[?] × 10²¹ F
X
The equivalent capacitance of this combination is 9.375 μF, or 9.375 × 10⁻⁶ F in scientific notation.
What is capacitor ?
A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by a non-conductive material, called a dielectric. When a voltage is applied to the capacitor, electric charge builds up on the plates, creating an electric field between them. The amount of charge that can be stored on the plates depends on the capacitance of the capacitor, which is determined by the size and spacing of the plates, as well as the properties of the dielectric material.
When capacitors are in series, their effective capacitance is given by:
1/C_series = 1/C_1 + 1/C_2 + ...
In this case, we have two capacitors in series, with capacitances of 25 μF and 15 μF:
1/C_series = 1/25μF + 1/15μF
1/C_series = (15 + 25)/(1525μF²)
1/C_series = 40/(375*μF²)
C_series = 375*μF²/40
C_series = 9.375 μF
Therefore, the equivalent capacitance of this combination is 9.375 μF, or 9.375 × 10⁻⁶ F in scientific notation.
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