Answers
Answer:
0.7 m/\(s^{2}\)
Explanation:
From Newton's law of universal gravitation,
F = \(\frac{GMm}{r^{2} }\)
and from Newton's second law of motion,
F = mg
So that;
mg = \(\frac{GMm}{r^{2} }\)
⇒ g = \(\frac{GM}{r^{2} }\)
For the first planet,
7 = \(\frac{GM}{R^{2} }\)
⇒ G = \(\frac{7R^{2} }{M}\) .............. 1
For the second planet,
g = \(\frac{0.4GM}{(2R)^{2} }\)
= \(\frac{0.4GM}{4R^{2} }\)
⇒ G = \(\frac{4gR^{2} }{0.4M}\) ............. 2
Equating 1 and 2, we have;
\(\frac{7R^{2} }{M}\) = \(\frac{4gR^{2} }{0.4M}\)
g = \(\frac{7R^{2} *0.4M}{4R^{2}M }\)
= \(\frac{7*0.4}{4}\)
= \(\frac{2.8}{4}\)
g = 0.7
Therefore, the acceleration due to gravity on the new planet is 0.7 m/\(s^{2}\).
Related Questions
A group of students were playing basketball together during recess. The temperature outside was 30.5 oC (87 oF) and the sun was out. The students ran, shot baskets, and dribbled the ball for 30 minutes. When they finished their game some of the students made the following comments:
Answers
Our muscles need more oxygen to make energy (in the form of ATP) while we workout.
When the respiratory rate picks up to fulfill this need, more oxygen can enter the body and more carbon dioxide can be exhaled.
Student 3 is breathing more forcefully than usual in this situation because of the high temperature and physical activity.
The respiratory system is the organ system engaged in this process.
Learn more about the respiratory system at:
https://brainly.com/question/2619922\
#SPJ1
# complete question:
A group of students were playing basketball together during recess. The temperature outside was 30.5 oC (87 oF) and the sun was out. The students ran, shot baskets, and dribbled the ball for 30 minutes. When they finished their game some of the students made the following comments:
Student 1: Wow! I am so hot and sweaty! I need some water to cool down.
Student 2: My cheeks are really red.
Student 3: I am breathing so hard, I can barely catch my breath!
Explain what is happening to the students and how their bodies are trying to maintain homeostasis. Be sure to include any of the organ systems involved with each student.
can somewon help me with this qustion?
Answers
A light ray in glass (n=1.5) hits the air-glass interface at an angle of 10 degrees from the normal. What angle from the normal is the light ray in the air (n=1.0)? (You can use the small angle approximation.)
Answers
Answer:
The angle from the normal is 15.1°.
Explanation:
We can find the angle by using Snell's law:
\( n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2}) \)
Where:
n₁: is the first medium (glass) = 1.5
n₂: is the second medium (air) = 1.0
θ₁: is the first angle (in the glass) = 10°
θ₂: is the second angle (in the air) =?
\( \theta_{2} = arcsin(\frac{n_{1}sin(\theta_{1})}{n_{2}}) = arcsin(\frac{1.5*sin(10)}{1.0}) = 15.1 ^{\circ} \)
Therefore, the angle from the normal is 15.1°.
I hope it helps you!
A rotating heavy wheel is used to store energy as kinetic energy. If it is designed to store 1.00 x 106 J of kinetic energy when rotating at 64 revolutions per second, find the moment of inertia (rotational inertia) of the wheel. (Hint: Start with the expression for rotational kinetic energy.)
Answers
We know, \(1\ rpm = \dfrac{2\pi}{60} \ rad/s\) .
\(64\ rpm\ is = \dfrac{2\pi}{60}\times 64\ rad/s\\\\= \dfrac{32\pi}{15}\ rad/s\)
We know, kinetic energy is given by :
\(K.E = \dfrac{I\omega^2}{2}\\\\I = \dfrac{2(K.E)}{\omega^2}\\\\I = \dfrac{2\times 10^6}{\dfrac{32}{15}\times \pi}\\\\I = 298415.52 \ kg \ m^2\)
Hence, this is the required solution.
Part A The two ropes seen in (Figure 1) are used to lower a 255 kg piano exactly 9 m from a second story window to the ground How much work is done by w? Express your answer in joules. O ACCO ? Figure 1 of 1 > Submit Request Answer Part B 1830 N 21 60° 7 1295 N How much work is done by Ti? Express your answer in joules. V AE = 0 2 ? 2500 N W= Submit Request Answer Caprub your answer ill juures. The two ropes seen in (Figure 1) are used to lower a 255 kg piano exactly 9 m from a second-story window to the ground O AO O a ? Submit Request Answer Part Figure 1 of 1 How much work is done by T2? Express your answer in joules. 1830 N 1295 N AX 60° 45° Submit 2500 N Request Answys Request Answer ovide Feedback
Answers
The work done by w is 22491 J.
The work done by Ti is 10728 J.
we have to determine the amount of work done by w. We can use the formula
W = Fd,
where W is the work done, F is the force applied, and d is the distance over which the force is applied.
The mass of the piano is given as 255 kg, and it is lowered exactly 9 m from the second-story window to the ground.
We can calculate the force required to lower the piano using the formula
F = mg,
where m is the mass of the piano and g is the acceleration due to gravity.
Therefore, \(F = 255 kg x 9.8 m/s^2 = 2499 N.\)
Using the formula for work, we can calculate the work done by w as follows:
W = Fd = 2499 N x 9 m = 22491 J
we have to determine the amount of work done by Ti. We are given the magnitude of two forces, 1830 N and 1295 N, and the angle between them is 60°.
We can find the resultant force using the law of cosines, which states that
\(c^2 = a^2 + b^2 - 2ab cos(C),\)
where c is the length of the side opposite the angle C and a and b are the lengths of the other two sides.
Therefore, \(c = sqrt(a^2 + b^2 - 2abcos(C)) = sqrt((1830 N)^2 + (1295 N)^2 - 2(1830 N)(1295 N)cos(60°)) = 2159 N.\)
The angle between the resultant force and the horizontal is 45°, so we can calculate the work done by Ti using the formula
W = Fd cos(theta),
where theta is the angle between the force and the direction of motion.
Therefore, W = 2159 N x 7 m x cos(45°) = 10728 J.
for such more question on work done
https://brainly.com/question/25573309
#SPJ11
a stationary object experiences two forces as shown in the diagram below
Answers
Answer: the answer is B
Explanation: 80 is not the same as 150 so it will go the way 150 units of force is pulling.
A 75 kg bungee jumper leaps from a bridge. When he is 30 meters above the water, and moving at a speed of 20 m/s, the bungee cord begins to stretch. The cord stops his motion exactly at the water surface. Determine the spring constant of the bungee cord. Assume no thermal losses.
Answers
Answer:
k = 52.2 N / m
Explanation:
For this exercise we are going to use the conservation of mechanical energy.
Starting point. When it is 30 m high
Em₀ = K + U = ½ m v² + m g h
Final point. Right when you hit the water
\(Em_{f}\) = K_{e} = ½ k x²
in this case the distance the bungee is stretched is 30 m
x = h
as they indicate that there are no losses, energy is conserved
Em₀ = Em_{f}
½ m v² + m g h = ½ k h²
k = \(\frac{m (v^{2} + 2 g h)}{h^{2} }\)
let's calculate
k = \(\frac{75 \ ( 20^{2} + 2 \ 9.8 \ 30)}{30^{2} }\)
k = 52.2 N / m
At time t = 0 s, a puck is sliding on a horizontal table with a velocity 3.60 m/s, 35.0° above the +x axis. As the puck slides, a constant acceleration acts on it that has the following components: a = - 2 0.360 m/s and da, = -0.980 m/s. What is the velocity of the puck at time t = 1.50 s? 2 0
Answers
The velocity of the punk at time t = 1.5 s is equal to 2.47 m/s.
What are the components of velocity?The object will have two velocities during the projectile motion, one is horizontal velocity and the other is vertical velocity. The horizontal velocity of the object is constant throughout the projectile motion but the vertical velocity is changed in the projectile motion.
Given that the velocity vector is making an angle θ with a horizontal table, θ = 35°
The vertical component of the velocity of the puck can be determined as:\(u_x = u Sin 35^o = 3.60 \times 0.573 =2.06 m/s\)
The horizontal component of the velocity of the puck can be determined as:
\(u_y = u cos 35^o = 3.60 \times 0.82=2.95 m/s\)
Given the acceleration aₓ = -0.360 m/s² and a y = -0.980 m/s²
The final vertical components of the velocity of the punk are:
\(v_x = u_x + a_xt\)
\(v_x = 2.95 - (0.360) (1.5)\\v_x = 2.41 m/s\)
and, the horizontal velocity of the punk is:
\(v_y = u_y +a_yt\\v_y = 2.06 - (0.980) (1.5)\\v_y = 0.59 m/s\)
The velocity of the punk can be determined as:
\(v = \sqrt{v_x^2 + v_y ^2}\\ v =\sqrt{(5.80)^2 + (0.35)^2}\\ v = 2.47 m/s\)
Learn more about components of the velocity, here:
https://brainly.com/question/12498991
#SPJ1
HELP PLZ HURRY :((( I NEED IT BY TONIGHT
Answers
Answer:
Please see attached image
Explanation:
The gravitational potential energy of a 4 kg book is 98 J. what is its height
Answers
The height of the 4 kilograms book with a gravitational potential energy of 98 Joules is approximately 2.5 meters.
How to determine the height of an object with a gravitational potential energy?Gravitational potential energy is simply the potential energy an object possessse in relation to another object due to gravity.
It is expressed as;
U = m × g × h
Given that:
Gravitational potential energy of the book U = 98 Joules
Mass of the book m = 4 kilograms
Acceleration due to gravity g = 9.8 m/s²
Height h = ?
Plug these values into the above formula and solve for height.
U = m × g × h
h = U / ( m × g )
h = 98 / ( 4 × 9.8 )
h = 98/39.2
h = 2.5 meters
Therefore, its height is 2.5 meters.
Learn more about gravitational potential energy here: brainly.com/question/3884855
#SPJ1
Answer #49 please and thank you
Answers
when Force (N) is 10.0 Length (m) is 0.60
when Force (N) is 8.0 Length (m) is 0.40
when Force (N) is 4.0 Length (m) is 0.20
when Force (N) is 4.0 Length (m) is 0.20
when Force (N) is 2.0 Length (m) is 0.10
chatgpt
49. To find the length of a pendulum that has a period of 2.3 seconds on the Moon, where the gravitational acceleration (g) is 1.6 N/kg, we can use the formula:
Period (T) = 2π√(Length (L) / g)
Substituting the given values:
2.3 = 2π√(L / 1.6)
To solve for L, we can rearrange the formula:
L = (2.3 / (2π))^2 * 1.6
L ≈ 0.781 meters (or 78.1 centimeters)
So, the pendulum must be approximately 0.781 meters (or 78.1 centimeters) long to have a period of 2.3 seconds on the Moon.
50. Ranking Task:
To rank the pendulums according to their periods, we need to consider both the length and mass of each pendulum.
Ranking from least to greatest period:
1. A: 10 cm long, mass = 0.25 kg
2. C: 20 cm long, mass = 0.25 kg
3. B: 10 cm long, mass = 0.35 kg
There is a tie between pendulums A and C, as they have the same length but different masses.
BEST ANSWER = BRAINLIEST
An object with a charge of +1 C is 10 mm from an object with a charge of +1 C. Based on the data in the table, which type and amount of electrical force will there most likely be between the two objects? Explain your answer
Answers
Answer: Weak or repulsive
Explanation: The amount of electrical force would be weak based on the distance between the two objects.
Based on the data in the table, the two objects will have a repulsive force of medium strength.
How to find type and amount?This is because the two objects have the same charge, and like charges repel each other. The force is calculated using the following formula:
F = k × (Q₁ × Q₂) / r²
where:
F = force in newtons
k = Coulomb's constant (8.988 x 10⁹ N m²/C²)
Q₁ and Q₂ = charges in coulombs
r = distance between the charges in meters
In this case:
F = medium
k = 8.988 x 10⁹ N m²/C²
Q1 = Q2 = +1 C
r = 10 mm = 0.01 m
Substituting these values into the formula gives:
F = (8.988 x 10⁹ N m²/C²) × (+1 C × +1 C) / (0.01 m)²
= 8.988 x 10⁶ N
Therefore, the two objects will have a repulsive force of medium strength.
Find out more on repulsive force here: https://brainly.com/question/23498984
#SPJ1
the sound travels _______ in liquid as compare to solid
Answers
Answer:
in mechanical waves
Explanation:
A mechanical wave is a disturbance that moves and transports energy from one place to another through a medium. In sound, the disturbance is a vibrating object. And the medium can be any series of interconnected and interactive particles.
The volume of an ideal gas is increased from 0.6 m3 to 2.4 m3 while maintaining a constant pressure of 1000 Pa (1000 N/m2). Determine, in J, the amount of work done by the gas in this expansion.
Answers
The amount of work done by the gas in the given expansion is 1800 J.
The given parameters;
initial volume of the ideal gas, V₁ = 0.6 m³final volume of the ideal gas, V₂ = 2.4 m³constant pressure of the gas, P = 1000 PaThe amount of work done by the gas in the given expansion is calculated as follows;
W = PΔV
where;
ΔV is the change in volume of the gasSubstitute the given parameters and solve for the work done;
W = 1000(2.4 - 0.6
W = 1800 J
Thus, the amount of work done by the gas in the given expansion is 1800 J.
Learn more here:https://brainly.com/question/14978695
The equipotential surfaces associated with a point charge are
Answers
The equipotential surfaces associated with a point charge are concentric shells.
What is an electric charge?Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge. You can have a positive or negative electric charge.
The equipotential surface is the region where all points with the same potential are located. On the equipotential surface, a charge can be moved from one point to another without exerting any effort.
Thus,a point charge's related equipotential surfaces are concentric shells.
Learn more about an electric charge from here
brainly.com/question/8163163
#SPJ1
please answer asap!! thank you for the help, will mark brainliest if correct!
The color of visible light depends on the wavelength of the light.
Please select the best answer from the choices provided
T
F
Answers
Answer:
Its true
Explanation:
but im answering so the other person can get brainliest :3
To everyone who sees this, have a wonderful day or night!
A car is stopped at a traffic light. It then travels along a straight road so that its distance from the traffic light is given by x(t)=bt2−ct 3, where b=2.40ms −2 and c=0.120ms −3.The instantaneous velocity of the car at t=5.0s is?
Answers
The instantaneous velocity of the car at t = 5.0 s is -3 m/s. The negative sign indicates that the car is moving in the opposite direction from the traffic light at that moment.
What is instantaneous velocity ?Instantaneous velocity is the velocity of an object at a specific point in time. It is the rate of change of the object's position at that particular moment, and it is represented by the derivative of the object's position with respect to time. Instantaneous velocity is a vector quantity, meaning it has both magnitude and direction. It can be determined by taking the limit of the average velocity as the time interval approaches zero. It is also the limit of the average acceleration when the time interval approaches zero.
This can be found by taking the derivative of the equation \(x(t) = bt2 − ct3\)with respect to t. The derivative of this equation is \(v(t) = 2bt - 3ct^2.\)Plugging in the given values of b and c, and evaluating the equation at t=5.0s gives the instantaneous velocity of the car.
To learn more about instantaneous velocity visit
brainly.com/question/2234298
#SPJ4
two forces x and y are acting at 120 degrees to each other, if the magnitude are 8N and 10N respectively determine their resultant
Answers
The resultant force of both forces is 15.62 N.
What is resultant?The Resultant of forces is a single force obtained when two or more forces are combined.
To calculate the resultant of the force, we use the formula below.
Formula:
R = √[a²+b²-2abcos∅]..................... Equation 1Where:
R = Resultant of the forces.∅ = Angle between both forcesFrom the question,
Given:
a = 8 Nb = 10 NSubstitute these values into equation 1
R = √[8²+10²-2×8×10cos120°]R = √[64+100-160cos120°]R =√ [164-160(-0.5)]R = √[164+80]R = √(244)R = 15.62 NHence, the resultant force of both forces is 15.62 N.
Learn more about resultant force here: https://brainly.com/question/25239010
#SPJ1
Using the parallelogram law of vectors to obtain the resultant, we have the value 16 N.
What is the resultant force?The resultant force is that force that has the same effect in magnitude and direction as two forces acting together. In this case, we have two forces , 8 N and 10 N inclined at an angle of 120 degrees
Using the parallelogram law of vectors to obtain the resultant;
R = √([8²+10²)-2×8×10cos120°]
R = √164 +80
R = 16 N
Learn more about resultant force:https://brainly.com/question/16380983
#SPJ1
How much heat energy is needed to raise the temperature of 291 grams of silver from 18.1 degrees Celsius to 59.4 degrees Celsius
Answers
Answer: Amount of heat needed = 2884.392 J
Explanation:
The formula for calculating the quantity of heat needed to raise the temperature of a bodyis expressed as
H = mcθ
where
H is the quantity of heat
m is the mass of the body
c is the specific heat capacity of the body
θ is the change in temperature
From he information given,
m = 291 grams
specific heat capacity of silver = 0.240 J/gC
initial temperature = 18.1
Final temperature = 59.4
θ = 59.4 - 18.1 = 41.3
Thus,
H = 291 x 0.240 x 41.3
H = 2884.392 J
Amount of heat needed = 2884.392 J
How fast must the space shuttle go to cover 20,000 meters in 4.0 seconds?
Answers
Answer:
5000 m/s
Explanation:
If an airplane is accelerating down a runway at 2.5 m/s^2, how much is it’s velocity changing each second?
Answers
If an airplane is is accelerating down a runway at 2.5 m/s². It's velocity changes 2.5 m/s in each second.
What is acceleration?Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.
Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.
Hence, the velocity of the airplane changes 2.5 m/s in each second when it is accelerating down a runway at 2.5 m/s².
Learn more about acceleration here:
brainly.com/question/12550364
#SPJ1
H
Question 12 of 15:
Select the best answer for the question.
12. A 150-lb block of ice has a temperature of 22 F. How much heat will the ice absorb before it begins to melt?
O A. 1500.0 Btu
O B. 1663.2 Btu
C. 756.0 Btu
OD. 2419.2 Btu
Answers
Answer:
I think it is A
Explanation:
It is A because if you calculate the weight minus the F, then you have to divide that by the amount of absorbation (the lb) before timsing it by 1000.
A hollow ball weighs 40 newtons. In a water tank, it displaces 15 newtons of water. What is the buoyant force on the ball? Will the ball float or sink? Explain your reasoning.
Answers
Answer:
25N
it will float since the water displaced is less than the weight. buoyancy = 25n down
Explanation:
40 newtons - 25 newtons = 25 newtons
The buoyant force on the ball is 25 Newton and the ball will float.
From the information given, we're informed that a hollow ball weighs 40 newtons and a water tank displaces 15 newtons of water.
Therefore, the buoyant force on the ball will be:
= 40N - 15N = 25N
Since we got a positive value, it means that the ball will float on water.
Read related link on:
https://brainly.com/question/25594887
I want you to think about each of these scenarios, what do you think will happen after? I just want you to think about it, and write a little about what is going to happen.
2. A truck is moving at 20 mph. Your car is standing still at a light and the truck crashes into you before the driver has a chance to step on the brakes.
3. You are driving your car at 20 mph. A bicycle right ahead of you suddenly stops and you crash into it before you have a chance to step on the brakes.
4. A bicycle is moving at 20 mph. Your car is stopped for a light and the bicycle crashes into you.
Answers
Find the force (N) on a 7.36cm radius piston on the other end of a hydraulic system that is driven by 23.37N of force from a 2.98cm radius piston.
Answers
The force (N) on a 7.36cm radius piston would be 142.55 Newtons, if on the other end of a hydraulic system that is driven by 23.37 N of force from a 2.98cm radius piston.
What is pressure?The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
Pressure = Force / Area
As given in the problem we have to find out the force (N) on a 7.36cm radius piston on the other end of a hydraulic system that is driven by 23.37N of force from a 2.98cm radius piston,
By using the Pascal Law,
F₁ / A ₁ = F₂ / A₂
23.37 / 2.98² = F₂ / 7.36²
F₂ = 23.37 × 7.36² / 2.98 ²
= 142.55 Newtons
Thus, the force (N) on a 7.36cm radius piston would be 142.55 Newtons ,
To learn more about pressure, refer to the link given below ;
brainly.com/question/28012687
#SPJ1
What advantage is there in measuring your distance from I1 to I1' and dividing by 2 rather than measuring the distance OI1 directly
Answers
Measuring the distance from \(I_1 \ to \ I_1'\) and dividing by 2 has advantage of achieving a more accurate result compared to measurement taking directly.
Measuring the distance from \(I_1 \ to \ I_1'\) is equivalent to the double of the distance.
This method of measurement gives a more accurate result because it minimizes error that may result from taking readings form the intervals. It ensures more accurate result compared to the measurement obtained when \(OI_1\) is measured directly.
\(OI_1 = \frac{I_1 + I_1'}{2}\)
Thus, we can conclude that measuring the distance from \(I_1 \ to \ I_1'\) and dividing by 2 has advantage of achieving a more accurate result compared to measurement taking directly.
Learn more about grating measurement here: https://brainly.com/question/15712101
During a home run, the batter only needs to run around all 4 bases if he wants to, since the ball cleared the outfield fence.
True
False
Answers
Answer: False
Explanation:
What are the three factors discussed in our live session that can lead to success through challenging physical activities:
Talent, flexibility, and stamina
Strength, balance, and endurance
Knowledge, attitude, and fitness level
Attitude, motivation, and determination
Answers
Answer:
Attitude, motivation and determination
Explanation:
Let me know if I'm right.
The factors leading to the success through the challenging physical activities are Attitude, motivation and determination.
Although the information regarding the live session is not mentioned, but as a general point of view, the major factors that need to considered while undergoing through the challenging physical activities are as follows:
Attitude - Attitude is one of the major factor leading to the management of challenges. A positive attitude always creates a base to face the initials of physical activities.Motivation - Motivation is another aspect that needs to be considered while undergoing the physical activities. Motivation comes from some sort of positive words from a specific person, thereby reducing the changes of poor start.Determination - The half battle is conquered with self-determination, a highly determined person is always has an add-on advantage for the task that he/she is going to start.Thus, we can conclude that the factors leading to the success through the challenging physical activities are Attitude, motivation and determination.
Learn more about the factors affecting the success here:
https://brainly.com/question/13958968
A pulse of sound takes 1 second to travel about 25 feet to the seafloor
100
and back. A ship stops in an area where the seafloor extends to the bottom
of the Sunlight Zone. At this spot an echosounder gives a pulse of sound
that takes 26 second to travel to the seafloor and back. How deep is the
100
ocean at the bottom of the Sunlight Zone?
HELP!!! I’m stumped!! Get max points ( if it lets me! )
Answers
Answer: The depth of the ocean is 650 feets at the bottom of the sunlight zone.
The distance travelled by echo sound is given by the formula -
Speed = 2×distance/time
So, calculating the speed of sound from the formula using distance and time
Speed = 2×25/(1/100)
Speed = 50×1000
Speed of sound = 5000 feet/second
Now, calculating the distance or depth of ocean at the bottom of the sunlight zone -
Distance = (speed×time)/2
Distance = (5000×26/100)/2
Distance = 1300/2
Distance = 650 feets
Hence, the depth of ocean is 650 feets.
Learn more about echo -
brainly.com/question/19579065
Answer:
We can start by using the formula:
distance = speed x time
where distance is twice the depth of the ocean at the bottom of the Sunlight Zone (since the pulse travels down to the seafloor and then back up), speed is the speed of sound in water, and time is the round-trip time of the pulse.
The speed of sound in water is approximately 1,500 meters per second (or 4,921 feet per second).
Converting the round-trip time to seconds, we have:
26 seconds - 1 second = 25 seconds
Substituting the values into the formula:
2 x depth = 4,921 feet/second x 25 seconds
2 x depth = 123,025 feet
depth = 61,512.5 feet
Therefore, the ocean at the bottom of the Sunlight Zone is about 61,512.5 feet deep.
An 82 kg hiker climbs to the summit of Mount Mitchell in Western NC. During one 2.0 h period, the climber's vertical elevation increases 540 m. The change in gravitational potential energy of the climber-Earth system is 433,944. Determine the power of the process in watts needed to increase the gravitational energy.
Answers
The power of the process needed to increase the gravitational energy of the hiker-Earth system is approximately 60.06 watts.
How to determine the power of the process in watts needed to increase the gravitational energy.We can use the formula for gravitational potential energy to determine the power of the process:
ΔPE = mgh
Where
ΔPE is the change in potential energym is the mass of the hiker g is the acceleration due to gravityh is the change in heightFirst, we need to determine the value of g at the location of Mount Mitchell. The acceleration due to gravity varies with altitude and latitude. At sea level and at the equator, the value of g is approximately 9.81 m/s^2.
However, at the summit of Mount Mitchell, which has an altitude of 2037 m, the value of g is slightly lower due to the increased distance from the center of the Earth. According to measurements, the value of g at the summit of Mount Mitchell is approximately 9.78 m/s^2.
Using this value of g, we can calculate the change in potential energy of the hiker:
ΔPE = mgh = (82 kg)(9.78 m/s^2)(540 m) = 432,403.2 J
The given value for the change in potential energy is 433,944 J. The difference may be due to rounding errors.
The power of the process is the rate at which energy is transferred, which is given by:
P = ΔPE / t
Where
t is the time interval for the change in potential energy. In this case, t = 2.0 h = 7200 s.Substituting the values, we get:
P = ΔPE / t = 432,403.2 J / 7200 s = 60.06 W
Therefore, the power of the process needed to increase the gravitational energy of the hiker-Earth system is approximately 60.06 watts.
Learn more about gravitational energy here : brainly.com/question/3120930
#SPJ1