Answer:
The velocity of the ball before it hit the ground was (3.59 m/s, -3.32 m/s) in the horizontal and vertical direction
Explanation:
The velocity of the ball can be calculated using the equation of motion:
v^2 = u^2 + 2as,
where
u = initial velocity,
v = final velocity,
a = acceleration due to gravity (9.8 m/s^2),
s = vertical height fallen (0.86 m).
Solving for u:
u = sqrt(v^2 - 2as)
We know the final velocity, v = 0 (the ball lands on the ground and stops), so
u = sqrt(2as) = sqrt(2 * 9.8 * 0.86) = 3.32 m/s.
The direction of the velocity before it hit the ground can be determined using horizontal distance traveled and time of flight.
The time of flight, t, can be found using:
t = sqrt(2s/a) = sqrt(2 * 0.86 / 9.8) = 0.39 s.
The horizontal velocity, vx, can be found using:
vx = d / t = 1.4 / 0.39 = 3.59 m/s.
A container with volume 1.62 L is initially evacuated. Then it is filled with 0.293g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. If the root-mean-square speed of the gas molecules is 178 m/s, what is the pressure of the gas?
The pressure of the gas is 0.970 atm.
The pressure of a gas can be calculated using the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to find the number of moles of N2, which can be calculated using the molar mass of N2 and the mass of N2 in the container:
n = m/M
n = 0.293g / 28.02 g/mol
n = 0.0104 mol
Next, we need to find the temperature in Kelvin, which can be calculated using the root-mean-square speed of the gas molecules:
T = (2 * k * m / (3 * R))
T = (2 * 1.38 x 10^-23 J/K * 6.63 x 10^-27 kg * (178 m/s)^2 / (3 * 8.31 J/mol/K))
T = 298.15 K
Finally, we can use the ideal gas law to find the pressure:
P = nRT / V
P = (0.0104 mol * 8.31 J/mol/K * 298.15 K) / (1.62 L)
P = 0.970 atm
So the pressure of the gas is 0.970 atm.
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A 6.0-kg rock is dropped from a height of 9.0 m. At what height is the rock's kinetic energy twice its potential energy?
At a height of 4.48 meters, a rock's kinetic energy is twice its potential energy.
What are kinetic energy and potential energy?Potential energy is the energy stored in any object or system due to the position or arrangement of its parts. It is, however, unaffected by factors outside of the object or system, such as air or height. Kinetic energy, on the other hand, is the energy of moving particles in an object or system.
Given that a 6.0-kg rock is dropped from a height of 9.0 m.
Calculate the total potential energy at the initial point,
PE = mgh
PE = 6 x 9.81 x 9
PE = 530.74 J
At the zero height, the kinetic energy will be maximum and is equal to the total energy,
KE = 530.75 J
1/2 mv² = 530.75
v² = 175.85
The height at which the kinetic energy is two times the potential energy is calculated as:-
1 /2 x mv² = 2 x mgh
h = ( 4 v²) / ( 4 x 9.81 )
h = 4 ( 175.82 ) / ( 4 x 9.81 )
h = 4.48 meters
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Fluid flows through a 0.22m diameter pipe at a velocity of 2.8m/s.
Calculate the cross sectional area of the pipe.
m2
Calculate the Volumetric Flow Rate (Q) of the fluid.
m3/s
How long would it take for 3.3m3 of fluid to flow through the pipe?
Answer:
9.22 m=s
Explanation:
m=s×v
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(4 points) determine which of the following pairs of functions are linearly independent. linearly independent 1. f(t)
If there is a non-trivial linear combination of the vectors that equals 0, then a set of vectors is said to be linearly dependent.
What purposes do vectors serve in physics?Physical quantities can be represented using vectors. Vectors are most frequently employed in physics to describe displacement, velocity, and acceleration. Vectors are depicted as arrows and combine magnitude and direction.
Because they may visually depict position, displacement, velocity, and acceleration, vectors are useful. It is crucial to indicate where the scale is being drawn at when drawing.
|v| =(x2 + y2) is the formula to calculate the magnitude of a vector in two dimensions, where v = (x, y). The equation |V| = (x2 + y2 + z2) can be used to calculate the magnitude of a vector in three dimensions, where V = (x, y, z).
Therefore, vectors because you frequently do not have enough room to draw them at the scale they represent.
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the block has a weight of 20 lb and is being hoisted at uniform velocity. determine the angle u for equilibrium and the force in cord ab.
The force in the cord ab is 37.6 lb when being lifted at a constant speed, and the angle u for balance.
Describe uniform velocity using an illustration.The rotation of the earth is an example of a body that is moving with uniform velocity when its speed is increasing throughout an interval of time.
The sum of the forces in each direction must be zero in order to lift the block at a steady speed.
XFx = 0 : F sin θ − T sin 20° = 0
XFy = 0 : T cos 20° − F cos θ − 20 = 0
The tension in cord CAD stays constant throughout because there is no friction on the pulley: F = 20 lb.
20 sin θ − T sin 20° = 0......... (1)
T cos 20° − 20 cos θ − 20 = 0 ........(2)
Solve equation (1) for T
T = 20 sin θ/sin 20
and substitute it into equation (2).
(20 sin θ/sin 20°)cos 20° − 20 cos θ − 20 = 0
cot 20°sin θ − cos θ − 1 = 0
cot 20°sin θ − 1 = cos θ
cot 20°sin θ − 1 = √1 − sin2θ
cot²20°sin²θ − 2 cot 20°sin θ + 1 = 1 − sin²θ
(cot²20° + 1) sin²θ − 2 cot 20°sin θ = 0
csc²20°sin²θ − 2 cot 20°sin θ = 0
(csc²20°sin θ − 2 cot 20°) sin θ = 0
csc²20°sin θ − 2 cot 20° = 0 or sin θ = 0
sin θ = 2 cot 20°/csc² 20°
= 2 cos 20°sin 20° = sin 40° or sin θ = 0
θ = 40° or θ ≠ 0°.
Substitute this nonzero value for θ into the formula for T.
T =20 sin θ/sin 20°
≈ 37.6 lb
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Find the number of kilometers in a light year. A light year is the distance that light travels in one year. Light travels at the rate of 3.0×10^5 km/s.Assume a year is 365 days
The light year is an unit of measure for distance. It is defined as the distance travelled by light in a vacuum over the course of a year.
Define a vacuum?A vacuum is a space area that is either devoid of matter or has a pressure so minimal that any particles there have no bearing on any processes occurring there. It is a condition that has a pressure that is measured in units of pressure and is much lower than the mean air pressure.
What is the term pressure?The quantity of force applied to a certain region is referred to as pressure. So either a strong force or a strong force applied over a short area can cause a lot of pressure (or do both).
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An initially motionless test car is accelerated uniformly to 145km/h in 8.28s before striking a simulated deer. The car is in contact with the faux fawn for .815s, after which the car is measured to be traveling at 82.0km/h. What is the magnitude of the acceleration of the car before the collision? What is the magnitude of acceleration of the car during the collision? What is the magnitude of acceleration of the car during the entire test, from when the car first begins moving until the collision is over?
The magnitude of acceleration of the car during the entire test is 4.83 m/s^2.
To calculate the magnitude of acceleration of the car before the collision, we can use the formula for uniform acceleration:
a = (v_f - v_i) / t
where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.
v_i = 0 (the car is initially at rest), v_f = 145 km/h = 40 m/s, t = 8.28 s
a = (40 - 0) / 8.28 = 4.83 m/s^2
To calculate the magnitude of acceleration of the car during the collision, we can use the formula for average acceleration:
a = (v_f - v_i) / (2t)
where v_f is the final velocity after the collision (82 km/h = 22.8 m/s), v_i is the initial velocity before the collision (145 km/h = 40 m/s), and t is the time of the collision (0.815 s).
a = (22.8 - 40) / (2 * 0.815) = -19.86 m/s^2
Finally, to find the magnitude of acceleration of the car during the entire test, we have to integrate the acceleration over the time interval from t = 0 to t = 8.28 s. The area under the acceleration versus time graph represents the velocity of the car. By finding the velocity at t = 8.28 s, we can find the acceleration required to get from rest to that velocity.
v = a * t = 4.83 * 8.28 = 40 m/s
a = v / t = 40 / 8.28 = 4.83 m/s^2
So the magnitude of acceleration of the car during the entire test is 4.83 m/s^2.
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During a football match, the ball kicked at 45° angle of elevation went just over the goal post, height 2.4m. Assuming the goal post height is the greatest, calculate: The speed at which the ball was projected, The time taken to reach the greatest height
the horizontal distance between the point of kick and foot of the goal post bar (neglect the thickness of the bar)
Answer:
see below
Explanation:
We are here given that ,
maximum height of projectile= 2.4m (h)angle at which it is kicked = 45° speed of projection= ? (u)As we know that,
[tex]\implies h =\dfrac{u^2\sin^2\theta}{2g} \\[/tex]
substitute the respective values,
[tex]\implies 2.4 m =\dfrac{u^2\sin^245^\circ}{2\times 10} \\[/tex]
[tex]\implies 2.4m =\dfrac{u^2\times \bigg(\dfrac{1}{\sqrt2}\bigg)^2}{20}\\[/tex]
[tex]\implies u^2 = 40 \times 2.4 = 96 \\[/tex]
[tex]\implies u^2 =\sqrt{96}\\[/tex]
[tex]\implies \underline{\underline{ u \approx 9.79 \ m/s }}\\[/tex]
secondly we know that,
[tex]\implies t = \dfrac{u\sin\theta}{g}\\[/tex]
[tex]\implies t =\dfrac{9.79\times \sin45^\circ}{10} \\[/tex]
[tex]\implies t =\dfrac{9.79\times \dfrac{1}{\sqrt2}}{10} \\[/tex]
[tex]\implies \underline{\underline{ t \approx 0.69 \ s }}\\[/tex]
and we are done!
. a body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius r. (see below.) prove that the body leaves the sphere when
It has been demonstrated that the angle when the body exits the sphere is θ = cos⁻¹(2/3)
Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Every time an object moves or attempts to move, friction always acts in the direction opposing to that movement.
Force acting on a stationary particle
The following formula is used to compute the particle's force while it is stationary;
Rgcos = mgcos = mv2/R v2 —- (1)
power-saving measures
Utilizing the principle of energy conservation, one may calculate the object's ultimate speed once it begins to slide.
v2 = 1/2mR(1 - cos) = 2gR(R - Rcos) ---(2) reconcile (1) and (2)
Rgcos = 2gR (cos - 1);
cos = 2 - cos 2.
Cos1(2/3) = 3cos = 2cos = 2/3
As a result, the body exits the sphere at an angle of θ = cos⁻¹(2/3) , proved.
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The complete question is
A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. Prove that the body leaves the sphere when 0 = cos(2/3).
a pulley system has a mechanical advantage of 3, and an object weighing 9 newtons must be lifted 15 meters. how much force must be applied to lift the object? use the following equation to find the answer: ma=fo/fi
To lift the object, you must apply a force of 27 Newtons (9 Newtons divided by 3, the mechanical advantage).
The equation you can use to find the answer is MA = F0/Fi, where MA is the mechanical advantage, F0 is the input force and Fi is the output force.
MA is the mechanical advantage of a machine and is the ratio of output force to input force. For example, if an object needs to be lifted but the force required to lift it is too great, a machine such as a pulley system can be used to reduce the force needed. A pulley system has a mechanical advantage of 3, meaning that the output force is three times greater than the input force.
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how matter is identified.
Answer:
Explanation:
Matter is identified based on its physical and chemical properties.
Physical properties, such as color, texture, density, melting point, and boiling point, can be used to identify matter without changing its composition. For example, a solid object with a high density and a high melting point is likely to be a metal, while a lighter, less dense material with a low melting point is likely to be a plastic.
Chemical properties, such as reactivity, flammability, and acidity, are also used to identify matter. For example, the reaction of a substance with a strong acid or base can provide information about its chemical composition.
In addition to physical and chemical properties, matter can also be identified based on its molecular structure and composition. This can be done using techniques such as X-ray diffraction, spectroscopy, and microscopy, which allow scientists to examine the atomic and molecular structure of matter.
Finally, the chemical formula of a substance can also be used to identify it. The chemical formula specifies the types and numbers of atoms present in the substance, which can be used to determine its chemical properties and behavior.
The equivalent resistance of 2.0 Ω, 3.0 Ω, 5.0 Ω, and 6.0 Ω resistors connected in parallel is ________.
A) 1.2 Ω
B) 7.2 Ω
C) 0.83 Ω
D) 9.3 Ω
Answer:
C) 0.83 Ω
Explanation:
Question 10 0.5 pts What is the diffusion coefficient b) for iron at 700°C, with an activation energy (Q) of 18,300 cal/mol, and D.=0.0047cm/s: 2.43E3 cm2/s O 9.08E-9 cm2/s O 3.64E-7 cm2/s 60.66 cm2/s
The diffusion coefficient based on the provided data is 3.651 x 10^(-5) cm^2/s. (Option C)
The diffusion coefficient refers to the ratio of flux density to the negative of the concentration gradient in direction of diffusion. The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:
D=Do exp (-E/RT)
Where D is the diffusion coefficient (in m2/s), Do is the maximal diffusion coefficient (at infinite temperature; in m2/s), E is the activation energy for diffusion (in J/mol), T is the absolute temperature (in K), and R ≈ 8.31446 J/(mol⋅K) is the universal gas constant.
In the given case,
Do = 0.0047 cm/s = 4.7 x 10^-5 m/s
E = 18300 cal/mol = 76567.2 J/mol
T = 700°C = 973.15 K
Hence,
D=(4.7 x 10^(-5)) exp (-76567.2/(8.31446*973.15))
D=(4.7 x 10^(-5)) exp (-9.463)
D=3.651 x 10^(-9) m^2/s or 3.651 x 10^(-5) cm^2/s
Note: The question is incomplete. The complete question probably is: What is the diffusion coefficient (D) for iron at 700°C, with an activation energy (E) of 18,300 cal/mol, and Do = 0.0047cm/s. A) 2.43E3 cm2/s B) 9.08E-9 cm2/s C) 3.64E-5 cm2/s D) 60.66 cm2/s.
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When connected to a 12V battery, the current in a car headlight is 4.0 A.
When the lamp is lit, what is its resistance?
A) 3.0 ohms
B) 16 ohms
C) 48 ohms
D) 0.33 ohms
Answer:
3Ω
Explanation:
we are here given that,
voltage= 12V current= 4A resistance= ?From Ohm's law , we know that,
[tex]\implies V = iR \\[/tex]
where ,
v is potential differencei is currentR is resistanceon substituting the respective values, we have,
[tex]\implies 12V = 4A(R) \\[/tex]
[tex]\implies R =\dfrac{12V}{4A} \\[/tex]
[tex]\implies \underline{\underline{ R = 3\Omega}} \\[/tex]
and we are done!
The following circuit diagram is partially incomplete. A device is added to the electrical circuit to vary the current in Lamp 2 only. Which of the following circuit symbols should be included in the diagram to represent this device?
The device used to vary the current in a circuit is a variable resistor. The symbol of a variable resistor is option d. The symbol with a rectangle and an arrow.
What is a variable resistor ?A variable resistor also called a rheostat is a resistor of which the electric resistance value can be adjusted. A variable resistor is in essence an electro-mechanical transducer and normally works by sliding a contact (wiper) over a resistive element.
When a variable resistor is used as a potential divider by using 3 terminals it is called a potentiometer.
When only two terminals are used, it functions as a variable resistance and is called a rheostat. Electronically controlled variable resistors exist, which can be controlled electronically instead of by mechanical action. These resistors are called digital potentiometers.
Here, the resistance thereby the current through the lamp 2 can be varied by placing a resistor. Hence, option d is correct.
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The symbol used in diagram to represent the device is rheostat's symbol.
Correct option is D.
What is electric current?Electric current is defined as the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.
In given circuit,
A device is added to the electrical circuit to vary the current in Lamp 2 only,
Electrical current is varied by applying variable resistance,
The device used to apply variable resistance is rheostat, which has symbol of box with an arrow through it.
Hence, rheostat's symbol will be used in diagram to represent the device.
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Two weights are connected by a massless wire and pulled upward with a constantspeed of 1.50 m/s by a vertical pull P. The tension in the wire is T(see figure). Whichone of the following relationships between Tand Pmust be true?
A)T
B)T=P
C)P+T=125N
D)P=T+25N
The correct relationship between T and P is represented by option B)
T = P.
The net force operating on the system is represented by the tension in the wire T, which is equal to the total of the forces acting on each weight. Because only the gravitational force and the tension force are operating on each weight in this situation, the net force exerted on each weight is equal to the difference between the tension and the weight. T must therefore equal the sum of the gravitational pull P and the forces acting on each weight.
Since m represents the mass of each weight and g is the acceleration brought on by gravity, the equation for the relationship between T and P must be T = P + m * g.
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What is the magnitude of your total displacement if you have traveled due west with a speed of 23 m/s m / s for 155 s s , then due south at 12 m/s m / s for 235 s s ?
The magnitude of your total displacement is 745 m.
What is the total displacement?
The total displacement of the your motion is calculated by applying the following formula as shown below;
Δx = x₂ - x₁
where;
x₂ is the final positionx₁ is the initial positionThe magnitude of your total displacement is calculated as follows;
Δx = ( 23 m/s x 155 s ) - ( 12 m/s x 235 s )
Δx = 745 m
Thus, the magnitude of your total displacement is based on the change of your position.
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Choose one human-made object in motion on Earth. Draw a picture of the object and add arrows showing the forces acting on the object while it is in motion. Be sure to show the overall direction in which the object is moving by scaling your arrows.
Be sure to label the forces.
You need to include at least 2 forces for full credit.
The arrow pointing downward is gravitational force, F(g), The left arrow is the applied force, F(t), The right arrow is frictional force, F(f) and the arrow pointing upward is the net force, F(n).
What is a force?A force is a push or pull upon an object resulting from the object's interaction with another object. Forces can cause an object to accelerate or change its direction of motion.
Forces can be described by their magnitude and direction. In physics, forces can be caused by many interactions, including gravity, electromagnetic forces, and the strong and weak nuclear forces.
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the gravitational force exerted by the planet earth on a unit mass at a distance from the center of the planet is
The gravitational force put by the planet earth on a unit mass at a distance from the center of the planet is "the strength of the gravitational field at that location".
It is directly proportional to the mass of the planet and inversely proportional to the square of the distance between the unit mass and the center of the planet. The formula for gravitational force is
F = G * (m1 * m2) / r^2,
where
G is the gravitational constant,m1 and m2 are the masses of the planet and the unit mass, and r is the distance between the two.The strength of the gravitational field decreases with increasing distance from the planet.
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In the following problems you will be asked to calculate the net gravitational force acting on the Moon. To do so, please use the following variables. Mass msun = m1 mEarth = m2 mMoon = m3Initial Position Sun =< 0,0,0 > PEarth =< 1,0,0 > Moon =< L, h,0 > (a) Calculate the gravitational force on the Moon due to the Earth. "G" is the universal gravitational constant. (b) Calculate the gravitational force on the Moon due to the Sun. (c) Determine the net gravitational force on the Moon. < >
The net gravitational force is terms of L and h and is equal to[tex]f_{net} = G m_3*(m_2 / ((L - 1)^2 + h^2) + m_1 / (L^2 + h^2))[/tex]
(a) The gravitational force on the Moon due to the Earth can be calculated using the equation:
f_gravity = G * (m2 * m3) / d^2
where d is the distance between the Earth and the Moon. The distance between the Earth and the Moon can be calculated using the Pythagorean theorem:
d = sqrt((L - 1)^2 + h^2)
Plugging in the values, we get:
[tex]f_{gravity} = G * (m_{Earth} * m_{Moon}) / d^2 = G * (m_{2} * m_{3}) / d^2 \\\\= G * (m_{2} * m_{3}) / (sqrt((L - 1)^2 + h^2))^2[/tex]
(b) The gravitational force on the Moon due to the Sun can be calculated using the same equation as above:
f_gravity = G * (m1 * m3) / d^2
where d is the distance between the Sun and the Moon. The distance between the Sun and the Moon can be calculated using the Pythagorean theorem:
d = sqrt(L^2 + h^2)
Plugging in the values, we get:
[tex]f_{gravity} = G * (m_{Sun} * m_{Moon}) / d^2 \\= G * (m_{1} * m_{3}) / d^2 = G * (m_{1} * m_{3}) / (sqrt(L^2 + h^2))^2[/tex]
(c) The net gravitational force on the Moon is the sum of the gravitational forces due to the Earth and the Sun:
f_net = f_gravity_Earth + f_gravity_Sun
Substituting the values of f_gravity_Earth and f_gravity_Sun, we get:
[tex]f_{net} = G * (m_2 * m_3) / (sqrt((L - 1)^2 + h^2))^2 + G * (m_1 * m_3) / (sqrt(L^2 + h^2))^2[/tex]
[tex]f_{net} = G * (m_2 * m_3) / ((L - 1)^2 + h^2) + G * (m_1 * m_3) / (L^2 + h^2)[/tex]
[tex]f_{net} = G m_3*(m_2 / ((L - 1)^2 + h^2) + m_1 / (L^2 + h^2))[/tex]
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If there were no such thing as friction, what would happen to the motion of the soccer ball? (Please answer quickly, it's due today)
**a person kicking a soccer ball**
The soccer ball would gradually slow down.
The soccer ball would travel only a short distance.
The soccer ball would keep traveling until it hit something else.
The soccer ball would stop instantly.
Answer:
The soccer ball would keep traveling until it hit something else.
Explanation:
Friction acts as a force that opposes motion and slows objects down. When friction is absent, there is no force slowing the soccer ball down. So, without friction, the soccer ball would continue to move in a straight line at a constant velocity (assuming no other forces are acting on the ball) until it encounters an obstacle such as a wall or the ground, at which point it would stop.
he circular orbits of satellites 1 and 2 coincide. Satellite 2 has twice the mass of satellite 1. Compare their accelerations. A) 1's acceleration is half as much. B) 1's acceleration is the same as 2's C) 1's acceleration is twice as much as 2's D) It depends on the periods of their orbits.
The correct answer is (a): satellite 1's acceleration is half as much as satellite 2's.
This is due to the fact that the acceleration of two satellites in a circular orbit depends on their masses and orbital periods. Satellite 2 accelerates more quickly because it has twice as much mass as satellite 1. As a result, satellite 1 accelerates at a rate that is half that of satellite 2.
This results in a divergence in the orbits of the two spacecraft since satellite 1's speed will rise more slowly than satellite 2's. Over time, this difference will become more obvious, with satellite 1's orbit straying from a circular form more so than satellite 2's.
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two tennis balls fall through the air from a tall building. one of them is filled with lead pellets. the ball to reach the ground first is the
From a towering building, 2 tennis balls fall into the air. Lead pellets are contained within one of them. The lead-filled ball becomes the first to touch the ground.
What do you call air?The invisible atmospheric mixture that envelops Earth is called air. Most organisms depend on vital elements like oxygen and nitrogen to thrive, which are found in air. Of course, a member of this species is human people (Homo sapiens). In some cases, "atmosphere" is substituted in place of "air."
What purpose does air serve?Respiration is a procedure that includes breathing. A living organism breathes by taking intake oxygen from the environment and exhaling carbon dioxide. This process provides the energy necessary for plants and animals to absorb, grow, and sustain life.
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A 67 kg high jumper leaves the ground with a
vertical velocity of 6.4 m/s.
How high can he jump? The acceleration
of gravity is 9.8 m/s².
Answer in units of m. Answer in units of m.
The height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.
What is Kinetic and Potential energy?Potential energy is defined as the energy stored in an object or system by virtue of its position or arrangement of parts while kinetic energy is defined as the energy of the moving particles of an object or system.
Potential energy is represented as :
P.E.= mgh
Kinetic energy is represented as :
[tex]K.E.= 1/2mv^2[/tex]
where, m = mass of the object
h= height
v= velocity
g= acceleration due to gravity which is [tex]9.8m/s^2[/tex]
For above given example,
m= 67kg, v= 6.4m/s
we first find out Kinetic energy,
K.E.=[tex]\frac{1}{2} 67* (6.4)^2[/tex]= 2744.32/2= 1372.16 J
As we know, K.E.= P.E.
So, P.E.= 1372.16J = mgh
1372.16= 67* 9.8* h
height= 2.089 m
Thus, the height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.
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Energy Essay Question 1
You do work on something when you lift it against gravity. How does this work relate to gravitational potential
energy? If the lifted object is released, what becomes of this energy? Be sure to define all terms that you use.
Posted Mon Jan 30, 2023 at 1:16 pm
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DS Immersive Reader Grade: N/A O
As the object is raised, the gravitational potential energy of the system grows. When you drop something, the potential energy of the object is transformed into kinetic energy, which is the energy of the moving object, when it strikes the ground.
What is kinetic and potential energy?
Potential energy is the energy stored in an object or system due to its position or arrangement of elements. It is unaffected by the environment outside the installation or system, such as air or altitude. Conversely, kinetic energy refers to the energy of moving particles in a system or object.
An object's kinetic energy, unlike potential energy, relates to other stationary and moving objects in its immediate vicinity. Thus, the lifted object is in kinetic motion when released.
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When a stone is projected, its horizontal range is 24m and greatest height 6m. Find its velocity of projection.
Answer:
15.33 m/s
Explanation:
We are here given that ,
Range = 24m (R)Maximum height= 6m (h)velocity of projection= ? (u)As we know that,
[tex]\longrightarrow R = \dfrac{u^2\sin2\theta}{g} \dots (1)\\[/tex]
And ,
[tex]\longrightarrow h =\dfrac{u^2\sin^2\theta}{2g} \dots (2)\\[/tex]
Divide equation 1 and 2 ,
[tex]\longrightarrow \dfrac{R}{h}=\dfrac{4 \cos\theta}{\sin\theta} \\[/tex]
[tex]\longrightarrow \dfrac{24m}{6m}=4 \cot\theta \\[/tex]
[tex]\longrightarrow \cot\theta = 1 \\[/tex]
[tex]\longrightarrow \theta = \cot^{-1}(1) \\[/tex]
[tex]\longrightarrow \underline{\underline{\theta = 45^{\circ}}}\\[/tex]
Now we may substitute this value in equation 1 as ,
[tex]\longrightarrow 24 =\dfrac{ u^2\sin(2\times 45^{\circ} )}{g} \\[/tex]
[tex]\longrightarrow 24g = u^2\sin90^\circ \\[/tex]
[tex]\longrightarrow u^2 = 24 \times 9.8 \\[/tex]
[tex]\longrightarrow u =\sqrt{235.2} m/s \\[/tex]
[tex]\longrightarrow \underline{\underline{ u \approx 15.33 \ m/s }}\\[/tex]
and we are done!
A material has a stress–strain relationship that can be approximated by the equation
ε=0.3x10-16xσ3
where the stress is in psi. Find the secant modulus and the tangent modulus for the stress level of 50,000 psi.
The secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.
What is secant modulus?Secant modulus is a measure of a material's ability to resist deformation under stress. It is the ratio of stress to strain in a material and is equal to the slope of a line drawn between two points on a stress-strain curve.
The secant modulus is the slope of the line connecting two points on the stress-strain curve. In this case, the two points we need to consider are (50,000 psi, ε) and (0 psi, 0).
Therefore, the secant modulus is given by:
secant modulus = (ε - 0) / (50,000 psi - 0 psi)
Plugging in the equation for ε, we get:
secant modulus = (0.3x10-16x50,0003 - 0) / (50,000 psi - 0 psi)
secant modulus = 4.5x10-9 psi-1
The tangent modulus is the slope of the tangent line to the stress-strain curve at a given point. In this case, the point is (50,000 psi, ε).
Therefore, the tangent modulus is given by:
tangent modulus = dε/dσ
Plugging in the equation for ε, we get:
tangent modulus = (3x10-16x50,0002) / (1 psi)
tangent modulus = 4.5x10-9 psi-1
Therefore, the secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.
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3. A stopped roller coaster cart (velocity = 0 m/s) with a mass of 12,000 kg starts from the top of
the track at a height of 35 meters. It begins to roll down to the bottom (where height will be 0
meters).
(a.)What is the kinetic energy of the roller coaster cart at the bottom? KE PE
(b.)What is the velocity of the cart at the bottom?
bottom
top
A stopped roller coaster cart (velocity = 0 m/s) with a mass of 12,000 kg starts from the top of
the track at a height of 35 meters. It begins to roll down to the bottom (where height will be 0 meters).
KE = PE = mgh
KE = (12,000)(9.8)(35)
= 4,116,000
What is height?
Despite the fact that height is typically measured in relation to a plane of reference, most height measurements in the real world are based on sea level, which is a zero surface. The position of a point above mean sea level is typically used to define altitude and elevation, two synonyms for height. The sea-level surface beneath the continents can be extended; naively, one might picture a large number of little canals running through the continents. In reality, gravity measurements must be used to calculate the sea level beneath a continent; various computing techniques are available; see Geodesy, heights.To know more about heights, click the link given below:
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A simple circuit exists with one light bulb. A resistor of equal resistance to the bulb gets placed in the circuit in parallel. Which of the following would occur?
A. The current would increase.
B. The total voltage would decrease.
C. The current would stay the same.
D. The total resistance would remain the same.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
If we add a new residence in the circuit in parallel to the bulb of same resistance, the resultant resistance will get half the value of initial resistance [ when only bulb was connected in the circuit ], the current will increase as resultant resistance is half the original. and same current will flow in both the parallel wires.
So, by above information :
A.) Current would increase ? [ Yes ], As by ohms law, V = IR
and, if R is halfed, to maintain the same potential difference, current in the circuit will increase.
B.) Total voltage will decrease ? [ No ]... voltage will remain constant
C.) The current would stay the same ? [ yes ], it would increase...
D.) Total resistance would remain same ? [ No ], it will decrease...
how much work w is done in lifting a 35-kg sandbag to a height of 4.5 m? (use 9.8 m/s2 for g. round your answer to the nearest integer.)
After applying the gravitational potential energy, the amount work done in lifting a 35 kg sandbag to a height of 4.5 m would be 1,544 Joule
Gravitational potential energy is another name for work done against gravity. Because of this, if a mass (m) object is lifted through a height (h), the work done on it will be [m × g × h], and this energy will be stored as gravitational potential energy in the body.
Thus, the amount work done would be:
Work = m × g × h
= 35 kg × 9.8 m/s² × 4.5 m
= 1,543.5 Nm
= 1,543.5 Joule
= 1,544 Joule
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