The windings' current is 8.00 A. A location close to the solenoid's center has a magnetic field of 0.0111 T.
The magnetic field at a point near the center of a solenoid can be calculated using the following formula:
B = (μ₀xnxI) / L
Where:
B is the magnetic field
μ₀ is the permeability of free space, which is 4π x 10^(-7) Tm/A
n is the number of turns per unit length of the solenoid, in turns/m
I is the current flowing through the solenoid, in A
L, length of solenoid
Given the radius of the solenoid as 0.75 cm = 0.0075 m, and the length of the solenoid as 15.0 cm = 0.15 m, the cross-sectional area of the solenoid is:
π*(0.0075 m)² = 1.767 x 10^-5 m²
The number of turns per unit length of the solenoid can be calculated by dividing the total number of turns by the length of the solenoid:
600 turns / 0.15 m = 4000 turns/m
We can now substitute these values into the formula:
B = (4π x 10^(-7) Tm/A) * (4000 turns/m) * (8.00 A) / (0.15 m)
B = 0.0111 T
Therefore, the magnetic field at a point near the center of the solenoid is 0.0111 T.
It is worth noting that this result is valid only when the solenoid is long enough so that its ends do not affect the magnetic field inside. Also, the solenoid is considered as tightly wound and the radius of the solenoid much smaller than the length, so that the magnetic field inside the solenoid is uniform.
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the water is then released and passes through turbines to produce
The water released from the reservoir and passes through turbines to produce electricity.
What does the water do to the turbine?At the plant level, water flows through a pip also known as a penstock, and then spins the blades in a turbine, which, in turn, spins a generator that ultimately produces electricity.
What are water turbines called?Hydro turbines, it transform moving water's kinetic energy into mechanical energy, and this mechanical energy is converted into electricity using a hydropower generator. Hydropower turbines contain blades, which spin to produce electricity. Hydro turbines work on Faraday's principles.
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When a turbine's blades are turned by water, electricity is produced and sent to the power plant's users.
What occurs as water flows through the turbine? To generate energy, which is then delivered to the power plant's clients, the water can be used to turn a turbine's blades.The inner shaft of the turbine is then turned by water flowing across its blades.Once transferred to a generator, this rotational motion is used to produce energy.Turbines come in a wide variety of designs, each of which is ideally suited for a particular use.Water flow energy is transformed into mechanical energy by a hydraulic turbine.Using a hydropower generator, this mechanical energy is transformed into electricity.Potential energy, often referred to as kinetic energy, is converted to mechanical energy by a hydroelectric dam from a water reservoir behind the structure.To learn more about turbine's blades refer
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What is the magnitude of the force F on the 1.0 nC charge in the figure ?
The magnitude of the force F on the 1.0 nC charge in the figure is the positive charge and force F is 8 x 10^9 N (8 Giga Newtons).
The force F on the 1.0 nC charge in the figure can be calculated using Coulomb's law, which states that the force between two point charges is proportional to the inversely proportional to the square of the distance between the charges and a product of the charges. The magnitude of the force can be calculated using the following formula:
|F| = k x |q1| x |q2| / r^2
where k is the Coulomb constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges (in Coulombs), and r is the distance between the charges (in meters).
In this case, q1 = 1.0 nC = 1.0 x 10^-9 C and q2 = -1.0 nC = -1.0 x 10^-9 C (since the charges are opposite and the force is attractive) and r = 0.1 m.
So, the magnitude of the force F can be calculated as:
|F| = k x |q1| x |q2| / r^2 = (9 x 10^9 Nm^2/C^2) x (1.0 x 10^-9 C) x (-1.0 x 10^-9 C) / (0.1 m)^2 = 8 x 10^9 N
The magnitude of the force F is 8 x 10^9 N (8 Giga Newtons)
It's important to note that the direction of the force is from the positive charge.
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A calorimeter contains 1. 25 kg of water at 21. 5°C. A 0. 15-kg block of an unknown substance at 65. 5°C is placed in the water. The final temperature of the system is 22. 0°C. What is the specific heat of the substance? What could the substance be?
The specific heat of the substance is 0.99 J/g°C and it could be aluminum or copper.
What is the final temperature of the system after the unknown substance is placed in the water?The final temperature of the system after the unknown substance is placed in the water is 22.0°C. This can be determined by using the formula Q = mcΔT, where Q is the heat transferred, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature. In this case, the heat transferred from the unknown substance to the water results in a temperature increase of only 0.5°C, indicating a relatively low specific heat value for the unknown substance.
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2. What is the potential energy of a 3 kg ball that is on the ground?
The potential energy of a 3 kg ball that is on the ground is zero.
What is the potential energy of a ball on the ground?Zero ,It will have no kinetic energy since it is not moving, and because it is laying on the ground, it will also have no potential energy. This is equivalent to the ground's zero potential energy.energy potential = massHeight, 9.8 m/s of gravity3 kilogrammes is the size of you. I think you need to increase this by 9.8 and then convert this to grammes (3000g). Since the ball is on the ground and you are at zero height, your potential energy is also zero.A 3 kilogramme body on a planet's surface has 54 joules of potential energy.To learn more about potential energy refer to:
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sue is photographing some very small and intricate succulents growing in her backyard. she wants to capture as much detail as possible. what kind of lens would be best to use in this situation?
In this case, a macro lens would've been ideal. In her backyard, Sue is taking pictures of some incredibly tiny and complex succulents. She aims to record as many specifics as she can.
What does the lens do?A lens is a transparent piece of glass that, when light rays pass through it by refraction, either concentrates or disperses them. Lenses are employed in telescopes as well as other magnifying equipment because of their enlarging capabilities.
How do lenses function?Refraction is the process by which a lens changes the path of sun beams as the pass thru it. It follows that objects viewed through a lens appear to be either larger or less then they actually are because the rays appear to originate from a location that is closer or further distant of where they actually do.
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you are traveling by plane and reach cruising altitude, where the pilot says you are going 450.0 km/hr. you turn your laptop back on, and it takes 27.00 seconds to start up. how far have you traveled in this time?
You have travelled 3.375 km in the time it took for the laptop to start up.
What is distance travelled?Distance travelled is the total amount of distance that a person, vehicle, or object has traveled from one place to another. It is usually measured in miles, kilometers, or other units of measurement. Distance traveled is an important factor when calculating time, speed, or cost.
To calculate how far you have traveled in 27 seconds, we must first calculate the distance traveled in one second. To do that, we need to divide the speed (450.0 km/hr) by 3600, which is the number of seconds in an hour.
450.0 km/hr / 3600 = 0.125 km/s
Now that we know the distance traveled in one second, we can multiply it by the number of seconds it took for the laptop to start up (27.00 seconds).
0.125 km/s x 27.00 seconds = 3.375 km
Therefore, you have traveled 3.375 km in the time it took for the laptop to start up.
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kat and andrew are trying to move a desk kat is pulling with a force of 15N and andrew is pulling with a force of 18N north draw a picture for this situation using vectors and then determine the resultant magnitude and direction
The concept of net force is important in understanding the relationship between the force experienced by an object and its resultant magnitude.
What is magnitude?The magnitude of the result (R) can now be determined using the Pythagorean theorem. The direction of the resultant force can be determined by finding the angle it makes with the north-south or east-west vector.To draw the resulting vector, connect the end of the first vector to the beginning of her second vector and place an arrow. To determine magnitude, measure the length of the resulting R, and to find its orientation, measure its angle with the x-axis.The magnitude |r| of the resulting vector is given by |r|=√(∑xi)2+(∑yi)2 | We found | = ( ∑ x i ) 2 + ( ∑ y i ) 2 , where ∑xi ∑ x i is the sum of the x components of each individual vector and ∑yi ∑ y i is the sum of the y components of each individual vector .To learn more about magnitude from the given link:
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direction cosines tell the angle between the force vector and each of the coordinate axes. select one: true false
The given statement about “direction cosines tell the angle between the force vector and each of the coordinate axes” is true.
Analytical geometry defines the directional cosines of a vector as the cosines of the angles formed by the vector with the three coordinate axes. To calculate the cosine of a vector's direction, divide the relevant coordinate by the vector's length. A direction's cosine is equivalent to a unit vector's x-coordinate. One such property of the direction cosine is that the sum of the squares of all the direction cosines equals one. The cosine of the angle subtended by a line having three coordinate axes, such as the x-axis, y-axis, and z-axis, is known to be the direction cosine. The direction cosines are cos α, cos β, and cos γ if the angles subtended by these three axes α, β, and γ.
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The denity of water i 997 kg/m3. A wimming pool contain 375 m3 of water. What i the ma of thi water?
Explanation:
ρ = 997kg/m³
v = 375m³
ρ = m/v
m = ρv
m = 997×375
m = 373,875kg
the airplane travels with constant velocity. a piece of its cargo falls out of an open door. which curve best describes the motion of the piece of cargo?
The curve of a parabolic path best captures the motion of the piece of cargo.
The parcel moves in a parabolic path, always remaining underneath the aircraft. As the package falls, it encounters a vertical acceleration that alters its vertical velocity. The downward force of gravity on the package is what is causing this vertical acceleration.
If the package's velocity could be roughly compared to projectile motion, then there would be no horizontal acceleration (that is, if the impact of air resistance could be assumed to be insignificant). In the absence of horizontal forces, there would be a constant horizontal velocity. This explains why the package was dropped beneath the plane, as it were.
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the acceleration of gravity on the surface of mars at the equator is 3.699 m/s2. how long does it take for a rock dropped from a height of 1.099 m to hit the surface?
It takes total time of 74 seconds for a rock dropped from a height of 1.099 m to hit the surface.
That planet's gravitational acceleration is 3.699 meters per second squared. The height from which the object was dropped takes 0.8198 seconds to reach the surface. Because the initial velocity is zero,
H = Ut + 1/2 a[tex]t^{2}[/tex] Because u = 0, this is half multiplied by 3.699 multiplied by [tex]0.8198^{2}[/tex] divided the.81988198 right divide by 2. This gives us an estimate of 1.25 meters.
When the rock is launched upwards, it begins to decelerate immediately due to the opposing force of gravity. The rock will have reached its highest point and will then fall back down when the velocity on the ascent reaches zero.
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the rotating armature of an ac generator is connected to its external circuit through ? while a dc generator uses a(n) ? to make the connection.
With the help of slip rings, an AC generator connects the rotating armature to its external circuit.
A slip ring is an electronic device that permits the transfer of electrical currents and energy from a still structure to a spinning one. Any electrical device that needs to rotate while sending energy or currents can employ a slip ring.
A device that generates electrical energy from mechanical energy is an AC generator. Mechanical energy is provided by steam turbines, gas turbines, and combustion engines as the AC generator's input source. Alternating electrical power in the form of current and voltage is the output.
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electromagnetic waves transfer ____ from one ____ to ____ ?
Answer:
electromagnetic waves transfer energy from one place to another.
Explanation:
PART 1
The figure shows a claw hammer as it pulls a
nail out of a horizontal board. If a force of magnitude 124 N is exerted
horizontally as shown, find the force exerted
by the hammer claws on the nail. (Assume
that the force the hammer exerts on the nail
is parallel to the nail).
Answer in units of N.
PART 2
Find the force exerted by the surface on the
point of contact with the hammer head. Assume that the force the hammer exerts on the
nail is parallel to the nail.
Answer in units of N.
(1) The force exerted by the hammer claws on the nail is 67.54 N.
(2) The the force exerted by the surface on the point of contact with the hammer head is 124 N.
What is the force exerted by the hammer claws on the nail?
The force exerted by the hammer claws on the nail is calculated by applying the following formula.
Fy = W sinθ
where;
θ is the inclination of the claw on the headW is the force exertedFy = 124 N x sin ( 33 )
Fy = 67.54 N
The the force exerted by the surface on the point of contact with the hammer head is calculated as follows;
Fn = W sin (90)
Fn = 124 N
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you and your friend are running at each other from 200.0 m apart. after 10.0 seconds and having passed the 50.0 m mark on your side, you see your friend has already gone 60.0 m on his. what will your average velocity need to be for the remaining time in order for you to both have covered the same amount of total distance, assuming he maintains a constant speed?
My average velocity should be 7.5 m/sec.
Speed = [tex]\frac{distance covered }{time taken}[/tex]
Average speed = [tex]\frac{total distance}{total time}[/tex]
my friend has covered 60 m in 10s
Speed of friend =[tex]\frac{60}{10}[/tex]
= 6m/s
Friend will cover final 40 m in
[tex]\frac{40}{6}[/tex]=6.67 s
So, I need to cover final 50 m in 6.67 s
my average speed= [tex]\frac{50}{6.67}[/tex]
=7.5 m/s
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what must the charge (sign and magnitude) of a particle of mass 1.50 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 670 n/c ?
The force acting on a negative charge is in opposition to the direction of the electric field [tex]-2.194 \times 10^{-5}[/tex].
In order for a charge to stay stationary, a weight must be balanced by an electric force that acts in the opposite direction as the weight, with the electric force acting upward.
In a directed electric field, the electric charge particles are subject to a force that is directed in that direction. It can be caused by a charge imbalance, which is when there are more positively charged particles than negatively charged particles in a certain region.
A particle of mass 1.50 g
A downward-directed electric field of magnitude 670 n/c
qE=mg
q=mg/E
Substitute the value in above equation we get,
[tex]& =\frac{1.50 \times 10^{-3} \times 9.8}{670} \\& =-2.194 \times 10^{-5} \mathrm{C}[/tex]
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a girl lays on the edge of a cliff and looks down at the water below. wondering how far the drop is, she drops a pebble over the edge and counts 1.37 s from the time that she releases the pebble (from rest) to when it strikes the water. how far below the cliff is the surface of the water?
The pebble was traveling at 13.44 m/s when it impacted the water.
The speed at which something moves in a specific direction is known as its velocity. as the speed of a car driving north on a highway or the pace at which a rocket takes off.
A cliff is a group of rocks that rises nearly vertically, or straight up and down, from the ground. Cliffs are a frequent component in landscapes. Sea cliffs are one type that can occur around the coast, high in the mountains, or as the walls of canyons and valleys.
t = Time taken = 1.37 s
u = Initial velocity
v = Final velocity
s = Displacement
a = Gravitational acceleration is 9.81 m/s2 (downward direction is taken as positive)
Equation of motion
v = u + at
v = 0 + 9.81 × 1.37
v = 0 + 13.4397
v = 13.44 m/s
When the stone impacted the water, its speed was 13.44 m/s.
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a test ton used on a radio has a frequency of 1000 hz. what is the wavelength of this sound in air at normal room temperature
Explanation:
"Outlier" data can shift a Normal Bell Curve ____.
A. to get a large peak
B. to flatten out
C. to the left or right
D. up at both ends
two charges, one 2nc and the other -2nc forming a horizontal dipole, are separated by 1.5 cm. a) calculate the magnitude and direction of the electric field at a vertical distance of 1m from the center of the dipole (0,1m)
The magnitude of the electric field at a distance of 1 m is 7.33 x 10^7 N/C and direction of the electric field is from the positive charge to the negative charge.
The magnitude of the electric field at a distance of 1 m from the center of the dipole is given by:
E = k(2q)/r^2
where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q is the charge of each charge (2nc and -2nc), and r is the distance between the charges (1.5 cm).
E = (8.99 x 10^9 Nm^2/C^2)(2 x 2nc)/(0.015 m)^2
E = 7.33 x 10^7 N/C
The direction of the electric field is from the positive charge to the negative charge.
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a ball is thrown upward. what is its time interval between the release of the ball and the time it reaches its maximum height?
The upward throw of a ball. The gravity acceleration is 9.8 m/s2, and its combination 1 speed is 10.8 m/s. So, 1.10 seconds pass between the ball's release and the moment it reaches its highest point.
What happens to the ball's speed when it is launched upward and returns to the spot from which it was hurled?Gravity's acceleration is constantly downward and constant, however the speed and direction of the acceleration vary. The speed of the ball is zero at its top portion in its trajectory, then it picks up speed again as it descends toward.
Why does an object being hurled upward have a zero final velocity?Because the acceleration caused by the gravitational force is operating constantly downward at the greatest point when a body was thrown vertically upwards, only that point's velocity is zero. As a result, the velocity is zero due to the acceleration.
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radiant energy is also called(1 point) responses thermal energy. thermal energy. light energy. light energy. chemical energy. chemical energy. cellular energy.
Radiant energy is also called responses thermal energy (b) light energy is correct option.
Radiant energy in physics refers to the energy of electromagnetic and gravitational radiation. Radiant energy is particularly studied via radiometry. Its SI unit for energy is the joule (J). Other than radiometry, electromagnetic energy is denoted by the letters E or W. The phrase is specifically used when electromagnetic radiation is released into the environment by a source. For the human eye, this radiation might be visible or invisible.
Energy included in electromagnetic waves is known as radiant energy. These consist of microwaves, infrared, radio waves, ultraviolet light, and visible light. The random molecular movements of substances store thermal energy, often known as heat energy.
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The half-life of francium-223 is 20 minutes. If a sample originally contains 10 g of the isotope, how much remains after an hour? Please help me!! FAST!
(20 points)
The amount of the mass of the radioactive isotope remaining after 1 hour is 1.25 g.
What is the mass of the sample remaining after an hour?The mass of the sample remaining after an hour is calculated from the half life of the isotope as shown below.
The half life of the radioactive isotope = 10 minutes
The amount of the mass of the radioactive isotope remaining after 1 hour is calculated as follows;
1 hour = 60 minutes
0 half life ---------------------------> 10 g
20 minutes ------------------------> 5 g
40 minutes -----------------------> 2.5 g
60 minutes -----------------------> 1.25 g
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which region includes the lowest pressures and highest temperatures at which the phase of x is known?
The region with the lowest pressures and highest temperatures at which the phase of x is known is the supercritical region.
This region is between the critical temperature and pressure, and is characterized by a single phase that is neither liquid nor gas, but rather a combination of the two.
This region exhibits properties that are intermediate between those of a liquid and a gas, and so the phase of X is known here.
A fluid is referred to as "supercritical" when it is subjected to pressure and temperature above the compound's critical point. The fluid exhibits specific characteristics and behaves in a manner that is in between that of a liquid and a gas in the supercritical region.
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If you were paddling up stream in a canoe at 2 m/min and the river is flowing at 1.5 m/ min? What is your net or final velocity?(This is a vector problem)
As you were paddling upstream, your net or final velocity is 0.5 m/s.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
The magnitude of velocity of river flowing: u = 1.5 m/min.
The magnitude of velocity of your canoe: v = 2 m/min.
As you were paddling upstream, that is, in opposite to the flow, your net or final velocity is = v - u
= 2 m/min - 1.5 m/min
= 0.5 m/min.
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An automobile traveling initially at a speed of 60 m/s is accelerated uniformly to a speed of 85 m/s in 12 s. How far does the automobile travel during the 12 s interval?
Answer:
870 m
Explanation:
d = Vit + 1/2at²
a = ΔV/Δt = (85 m/s - 60 m/s) / (12 s) = (25 m/s) / 12 s = 2.08 m/s²
d = (60 m/s)(12 s) + 1/2 (2.08 m/s²)(12 s)² = 870 m
Answer:
The automobile traveled 870 meters during the 12 second interval.
Explanation:
We can use this kinematics equation to evaluate how far the automobile traveled.
[tex]\overline v=\frac{\Delta x}{\Delta t}[/tex]
Note
[tex]\overline v[/tex] is the average velocity
[tex]\Delta x[/tex] is the change in position (displacement)
[tex]\Delta t[/tex] is the change in time (time interval)
The formula for average velocity is
[tex]\overline v=\frac{V_f-V_o}{2}[/tex]
We are given
[tex]V_f=85\\V_o=60\\\Delta t=12[/tex]
First lets evaluate the average velocity.
[tex]\overline v=\frac{85-60}{2}[/tex]
[tex]\overline v=72.5[/tex]
Rearranging our kinematics equation to isolate [tex]\Delta x[/tex] we get
[tex]\Delta x=\overline v \Delta t[/tex]
Now lets evaluate [tex]\Delta x[/tex].
[tex]\Delta x=72.5*12\\\Delta x=870[/tex]
There are many different ways you can solve this; I could have used a different equation.
A box is attached to the ceiling and the wall with two ropes. The force of tension in the top rope is T1=√3 N and the force of tension in the side rope is T2=1 N. If the box has a mass of m=2kg, what force FA do you have to apply to break the ropes and accelerate the box with a=1 m/s2?
So the force you have to apply to break the ropes and accelerate the box with a=1 m/s^2 is 2 + √3 + 1 N
Calculating the problem:To determine the force FA that must be applied to break the ropes and accelerate the box with a=1 m/s^2, you can use the equation of motion:
F = ma
where F is the net force acting on the box, m is the mass of the box, and a is the acceleration of the box.
We know that the net force acting on the box is equal to the force applied to it minus the forces of tension in the top and side ropes.
So, F = FA - T1 - T2
and the acceleration of the box is 1 m/s^2
Given that,
FA = m×a + T1 + T2
Substitute the given values for m, a, T1 and T2,
FA = 2 kg × 1 m/s² + √3 N + 1 N
FA = 2 kg × 1 m/s² + √3 N + 1 N
= 2 + √3 + 1 N
What is movement?An object's movement or shift in position in relation to its surroundings over time is referred to as the motion. A subfield of physics that deals with the behavior of physical systems and objects is mechanics, the study of motion.
There are various kinds of motion, such as:
Motion in a line:This is straight-line motion. The linear velocity and acceleration of an object are calculated using the distance and time it takes to travel in a particular direction.
Motion by rotation:An axis is in motion here. When describing an object's rotational motion, the terms "angular displacement," "angular velocity," and "angular acceleration" are utilized.
Rhythmic oscillation: This is a motion that happens over and over again and revolves around a central point. It's called oscillation. A pendulum that swings or a guitar string that vibrates are two examples.
Motion of a projectile: This is the movement of an object that is projected into the air, like a ball that is thrown into the air or a gunshot.
Relational movement: This is how an object moves in relation to a reference point, like how a car moves on a road in relation to the earth.
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what must the charge (sign and magnitude) of a 1.55 g particle be for it to remain balanced against gravity when placed in a downward-directed electric field of magnitude 635 n/c ?
The 1.55 g particle must have a positive charge that is equivalent to 635 N/C times (1.55 g / 9.8 m/s2) = 11.9 C. To maintain equilibrium against gravity.
for a)
a particle's charge must be opposite in sign and magnitude to the electric force acting on it.
mg = qe
1.55 X 10 ⁻³ X 9.81 = q X 635
q = - 0.023 X 10⁻³ C
it willl be negative
We get at q = F / E = 15.09 N / 635 N/C = 0.0237 C after solving for the charge.
This indicates that the particle's charge must be positive and equal to 0.0237 Coulombs in order for it to balance against gravity in the 635 N/C-magnitude downward electric field.
qe = mg
1.6 X 10 ⁻¹⁹ E = 1.67 X 10 ⁻²⁷ X 9.81
E = 1.02 X 10⁻⁷N/C
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the rate of change of the downward velocity of a falling object is the acceleration of gravity (10 meters/sec^2) minus the acceleration due to air resistance. suppose that the acceleration due to air resistance is 0.2 inverse seconds times the downward velocity. write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.
Assume that the downhill velocity is multiplied by 0.25 inverse seconds to get the acceleration caused by air resistance. Describe the initial value issue and its resolution.
How well does air resistance impact the rate at which items fall?Because air resistance slows down the motion of the falling object, it impacts acceleration during a fall to a lesser extent than gravity (g). The object's surface area and speed both influence the amount it slows down.
What are the issue and solution with initial value?A initial and boundary problem (IVP) in multivariable calculus consists of a normal differential equation and an initial condition that specify exact amount of the unknown variable at a specific location in the domain. In physics or even other sciences, modeling a system typically entails resolving an initial value dilemma.
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You and your friend throw balloons filled with
water from the roof of a several story apartment house. You simply drop a balloon from
rest. A second balloon is thrown downward
by your friend 3.4 s later with an initial speed
of 66.64 m/s. They hit the ground simultaneously.
How high is the apartment house? The
acceleration of gravity is 9.8 m/s
2
. Neglect
air resistance.
Answer in units of m. Answer in units of
m.
The height of the apartment is 127.5 m.
What is the height of the apartment?
The height of the apartment is calculated by applying the following equation.
first equation for your throw; h = ¹/₂g(t +3.4)²
second equation for your friend's throw; h = vt + ¹/₂gt²
h = vt + ¹/₂gt²
h = 66.64t + ¹/₂gt²
now equate the two equations;
¹/₂g(t+3.4)² = 66.64t + ¹/₂gt²
¹/₂(9.8)(t² + 6.8t + 11.56) = 66.64t + ¹/₂(9.8)t²
4.9(t² + 6.8t + 11.56) = 66.64t + 4.9t²
4.9t² + 33.32t + 56.64 = 66.64t + 4.9t²
33.32t = 56.64
t = 1.7 seconds
The height of the apartment is calculated as;
h = ¹/₂g(t +3.4)²
h = ¹/₂(9.8)(1.7 +3.4)²
h = 127.5 m
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How high above the ground is a 10 kg boulder that has 2400 J of gravitational potential energy? use g = 10 m/s2 (Hint: PE = mgh which rearranges to h = PE/mg)
Answer: Therefore, the rock that has a mass of 10 kg and a gravitational energy of 2400 J must be at a height of 24 meters.
Explanation:
How high above the ground is a 10 kg boulder that has 2400 J of gravitational potential energy?
Data:
m = 10 kg
Epg = 1200 J
h = ?
g = 10 m/s²
The formula for gravitational potential energy is:
Epg = m * g * hWhere
Epg = Gravitational potential energym=massg = gravityh = heightWe must calculate the height, for which we clear the formula, then
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{Ep_g}{m*g} } \end{gathered}$}}[/tex]
We substitute data in the formula and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ J}{10 \ kg*10\frac{m}{s^2} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ J}{100 \ kg*\frac{m}{s^2} } } \end{gathered}$}}[/tex]
Before continuing to answer, we must work with the units of Joules, so
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ N*m}{100 \ kg*\frac{m}{s^2} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \not{kg}*\not{\frac{m}{s^2}} *m}{100 \not{kg}*\not{\frac{m}{s^2}} } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h=\frac{2400 \ m}{100} } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{h\cong24 \ m } \end{gathered}$}}}[/tex]
Therefore, the rock that has a mass of 10 kg and a gravitational energy of 2400 J must be at a height of 24 meters.
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