Which of the following describes a velocity vs. time graph that looks like this?
HURRY PLEASE
Explanation:
the velocity has decreasing velocity. this is my answerA 12kg object is pushed with a horizontal force of 6N due east across a horizontal table. If the force of friction between the two surfaces is 2N, what is the acceleration of the object?
The acceleration of the body is obtained as 0.33 m/s^2.
What is the acceleration of the body?Now we know that the object is acted upon by a system of forces. The net force is the effective force that acts on the body.
Hence;
ma = F -Ff
The applied force is F while the frictional force is Ff. The net force is represented as ma
Thus;
12 * a = 6 - 2
a = 4/12
a = 0.33 m/s^2
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perpetual motion machines have fascinated people especially inventors for hundreds of years before the laws of thermodynamics became known. Ideally once energy is added to start a perpetual motion machine in motion, the machine would continue to operate indefinitely. Using a law of thermodynamics, explain why such a machine cannot be produced
HELP HELP HELP
Given the fact that energy conversion is not entirely efficient, it is impossible to produce a perpetual motion machine.
What is a perpetual motion machine?The perpetual motion machine in one that is able to work continuously without stopping. This would mean that the efficiency of this machine must that the machine is 100% efficient which violates the second law of thermodynamics.
Thus, given the fact that energy conversion is not entirely efficient and energy looses cause machines not function effectively, it is impossible to produce a perpetual motion machine.
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A net force of 16 N [40° W of N] is caused by two applied forces acting on the same
object. These two forces are:
A) 10 N [W] and 12 N [N]
B) 12 N [W] and 10 N [N]
C) 14 N [W] and 12 N [N]
D) 12 N [W] and 14 N [N]
E) 10 N [W] and 14 N [N]
The two forces are 12N and 10N (option B)
What is the net force?The net force is the force that has the same effect in magnitude and direction as the two forces acting together.
This problem can be solved using a right angled triangle;
Let the forces be P and Q
sin 40 = P/16
P= 16 sin 40
P = 10 N
Cos 40 = Q/16
Q = 16 cos 40
Q = 12 N
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What is it called when data are arranged in rows and columns?
O A. Interpolation
O B. Correlation
O C. Table
OD. Bar graph
Answer:
C. Table
What is a Database table?
A organized collection of records is called a database table. The main key that uniquely identifies each row in the table. Since no two rows may have the same instantaneous value thanks to a unique key, it is simple to choose a row by its main key. A table can also contain several columns, each of which can hold a distinct kind of data. The information stored is verified using the column name and data type.
The table name is the linguistic component of a database table. It can represent expressions or variable items, and it must be typed exactly. Square brackets denote a need for the item, whereas curly braces denote an optional element. An alternate choice is indicated by a vertical bar. A main key is a single field, and a secondary key might be a combination of many fields. This kind of information is crucial.
Any field in the data table can be referenced by the secondary key. A database's data field may be a string, a number, a date, or a time. A table's first field should always be the main key, followed by any foreign keys. Actual data should never be present in a primary key. Since the immediate key value is derived from external sources, it is crucial to use it properly. Otherwise, data input mistakes may occur.
The information kept in the database table is referred to as a secondary key. This kind is a primary key, which implies it is a secondary key. A primary key can be used as an alternate key to distinguish between different records in a table and to uniquely identify a record inside a database. Multiple fields that can be either main or alternative make up a composite key.
Depending on the type of data being stored and its intended use, a database table may have a single row or several. The main key determines the number of rows, which might be 50 or more. A secondary key can be used to establish connections between various tables and to distinguish between various data types in a database. A data table also includes a secondary key, which is essential for data retrieval and is separate from the primary key.
You can have local or global database tables. The two types of tables differ in terms of names, availability, and visibility. A global table is accessible to all users and may be utilized by any other user, while a local table is only visible to the present user. It is distinct from a typical table and requires more effort to build than a straightforward one does. Its main function is to maintain a database and store data.
Rows in a database table can be of any size. A table's rows can include any number of columns. A database table's rows can be arranged in any way. The number of rows on a data page might range from one to thousands. Each row may consist of a clustered index, a row, or both. A list of columns may also be present in a row. A clustered index can only contain information in a particular sequence.
A table can be set up in two different ways. The information-containing row of data is its main key. The data column that contains the values for a row is known as a secondary key. A database that employs rows is the third form of table. Multiple primary keys are possible for a data row, and a secondary key is a secondary key that refers to a row column. A database will have a foreign key if it is formed with a single primary key.
There is no limit to the amount of rows and columns in a database table. Up to 1,024 rows are allowed in a typical user-defined table. The server's storage capacity determines how many rows can fit in a database table. A table can have characteristics added to it in addition to the column and row. A restriction can stop a row from having empty fields. The connection between two tables can be established via an important control.
Set local ground level to 700 ft, and record the inches of mercury.
What is the altimeter reading in inches of mercury (from the Kollsman window)?
The altimeter reading is 29.17 from the Kollsman window is 29.17 in Hg
How to determine the altimeter reading?The given parameters are:
Ground level = 700 ft i.e. the field elevationPressure altitude = 1450 ftThe formula to calculate the pressure altitude is:
Altitude = (29.92 – Altimeter reading) * 1,000 + Ground level
Substitute the known values
1450 = (29.92 - Altimeter reading) * 1000 + 700
Evaluate the like terms
750 = (29.92 - Altimeter reading) * 1000
Divide both sides by 1000
0.75 = 29.92 - Altimeter reading
Evaluate the like terms
Altimeter reading = 29.17
Hence, the altimeter reading is 29.17 from the Kollsman window is 29.17 in Hg
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A concave mirror
light, whereas a concave lens
light.
Answer: Answer.
1)Concave lens is transparent whereas the concave mirror is opaque. 2)concave mirrors cause reflection whereas concave lense cause refraction of light.
3)concave mirror forms both real, inverted images of various sizes and virtual, erect, and enlarged images whereas a concave lens form only virtual images.
Explanation:
A basketball player passes the ball to a teammate. The ball reaches a velocity of 5.5 m/s, 2 seconds after the ball leaves the player’s hands. What is the acceleration of the ball during those two seconds?
Answer:
acceleration = 2.25 m/s²
Explanation:
[tex]a = \frac{v - u}{t}[/tex]
where:
a = acceleration (?)
v = final velocity (5.5 m/s)
u = initial velocity (0 m/s, because the ball starts from rest)
t = time taken (2s).
Using the formula:
acceleration = [tex]\frac{5.5 - 0 }{2}[/tex]
= 2.75 m/s²
Refer to Chapter 10 in the textbook which discusses externalities. Specifically, reference section 10-2, which details public policies towards externalities.
Additionally, find an article using your subscription to the Wall Street Journal detailing one proposed solution to pollution.
In your post, summarize the selected article and discuss the following:
Explain which of the public policies detailed in section 10-2 of the textbook best describes the proposed solution in the selected article.
Which of the public policy approaches outlined in section 10-2 would work best to resolve this pollution problem and why?
You are required provide a link to the article and support your answer with relevant ideas, facts, and examples.
An externality, sometimes called a spillover, occurs when an exchange between a buyer and seller has an impact on a third party who is not part of the exchange. Externalities can be positive or negative
What are Externalities?Externalities refers to situations when the effect of production or consumption of goods and services imposes costs or benefits on others which are not reflected in the prices charged for the goods and services being provided.
Externalities Private markets offer an efficient way to put buyers and sellers together and determine what goods are produced, how they are produced, and who gets them. The principle that voluntary exchange benefits both buyers and sellers is a fundamental building block of the economic way of thinking. But what happens when a voluntary exchange affects a third party who is neither the buyer nor the seller?
Externalities can be negative or positive. If you hate country music, then having it waft into your house every night would be a negative externality. If you love country music, then what amounts to a series of free concerts would be a positive externality.
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If the pitch of the sound coming out of a speaker increases, which statement is true about the sound wave?
Answer:
frequency and amplitude increases
Why are sedimentation pond useful for reducing the affects of soil erosion?
- They provide a water source that can be used for irrigation of crops?
-They help transport soil sediments to rivers, ponds and lake.
-They provide a place to raise fish that can be use to replace fish harmed by sedimentation
-They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers
Answer: D (They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers)
Explanation: I just took the test on accelerate. :)
Sedimentation ponds are useful for reducing the effects of soil erosion because : ( D ) They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers
What are sedimentation ponds ?Sedimentation ponds are ponds that hold sediments and suspended solids discharged by runoff waters thereby preventing the soil sediments from reaching water bodies such as ponds, lakes and rivers.
The sediment ponds hold the water while allowing the debris and solids contained in the water to settle down.
Hence we can conclude that sedimentation ponds provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers
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This is a scenario common with many physics students: you push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn't this mean that the forces cancel each other, making acceleration impossible? Resolve the misunderstanding underlying this question.
Considering that the moment you provide the action force, the car will certainly apply the response force. You will consequently come into an opposing force.
What is Newton's third law of motion?
According to Newton's third law of motion, every action has an equal and opposite reaction. As well as the action and reaction are always acted in pairs.
You manually move a big automobile. You are then pushed back by the automobile with an opposing but equivalent force.
Because the automobile will undoubtedly apply the response force when you apply the action force. As a result, you will encounter an opposing force.
Hence, when you push a heavy car by hand. The car, in turn, pushes back due to the action-reaction analogy.
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Which pair of quantities includes one quantity that increases as the other decreases during simple harmonic motion? acceleration and displacement acceleration and net force velocity and displacement displacement and net force
Velocity and displacement are the two quantities that increases as the other decreases during simple harmonic motion.
In a basic harmonic motion, how are velocity and displacement related?If a body's velocity at any given moment is inversely proportional to its displacement from the mean position, its motion is said to be simple harmonic.
Angular harmonic frequency and time t are functions that can be used to explain simple harmonic motion:
Displacement from equilibrium has amplitude A:
x = Asin(ωt)
and velocity has amplitude ωA
v = dx/dt = ωAcos(ωt)
At ωt = 0, x = 0 while v = Aω (max).
At ωt = π/2, x = A (max) while v = 0.
As a result, v reaches it's maximum /2 (90°) before x does. Therefore, displacement follows velocity at a 90° angle.
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A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch. Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l minus its un-stretched length [tex]l_0[/tex]; that is, [tex]x=l-l_0[/tex] (see below). Suppose a particular bungee cord has a spring constant, for 0 ≤ x ≤ 4.88m , of [tex]k_1=204 N/m[/tex] and for x ≥ 4.88m , of [tex]k_2=111N/m[/tex]. (Recall that the spring constant is the slope of the force F(x) versus its stretch x.) (a) What is the tension in the cord when the stretch is 16.7 m (the maximum desired for a given jump)? (b) How much work must be done against the elastic force of the bungee cord to stretch it 16.7 m?
please explain if possible!
A) When the cord is stretched 16.7 m, the tension in the cord is 18537 N.
b) The work that must be done against the elastic force of the bungee cord to stretch it 16.7 m is 15.48 kJ.
What is the tension in the Bungee cord when stretched 16.7 m?
The tension or force in an elastic string is given by the formula:
Force = spring constant × extensiona) The force or tension in the cord = 111 N/m × 16.7
Tension = 18537 N
b) Work done in a string = ke²/2
where k = 111 N/m, e = 16.7
Work done = 111 × 16.7²/2 = 15,478.395 J
Work done = 15.48 kJ
In conclusion, the force constant of the cord is required to calculate the tension and work done against the elastic force of the cord.
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find the x-component of this vector.
The x-component for the vector given in the image is : [tex]B_{x}[/tex] = 18.3m
Meaning of a VectorA Vector can be defined as a quantity that possesses both magnitude and direction thereby giving more details.
A vector is very important when it comes to dealing with forces.
Analysis
[tex]B_{x}[/tex] = B cos(Θ)
Θ = 180° - 170° = 10°
[tex]B_{x}[/tex] = B cos(10°) = 18.3m
In conclusion, The x-component for this vector is : [tex]B_{x}[/tex] = 18.3m
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. In a common test for cardiac function (the “stress test”), the patient walks on an
inclined treadmill. Estimate the power required from a 75-kg patient when the
treadmill is sloping at an angle of 12° and the velocity is 3.1 km/h.
The power required from a 75-kg patient when the treadmill is sloping at required speed is 131.58 W.
Parallel force on the patient
The parallel force on the patient is calculated as follows;
F = mg sinθ
F = (75 x 9.8) x sin(12)
F = 152.82 N
Average power requiredP = FV
where;
V is speed = 3.1 km/h = 3.1/3.6 = 0.861 m/sF = 152.82 x 0.861
F = 131.58 W
Thus, the power required from a 75-kg patient when the treadmill is sloping at required speed is 131.58 W.
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After washing lettuce, you can dry the water from it using a salad spinner. You put the lettuce in the bowl, and then crank the handle, spinning and drying the lettuce.
From the Earth frame of reference, what causes the water on the lettuce to come off the lettuce and go to the walls of the bowl?
The centrifugal force
The centripetal force
Newton's first law of motion
The force of gravity
A. The force that causes the water on the lettuce to come off the lettuce and go to the walls of the bowl is centrifugal force.
What is centrifugal force?
Centrifugal force is an inertial force that appears to act on all objects when viewed in a rotating frame of reference.
This force is directed away from the center around which the body is moving.
What is centripetal force?This is force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.
While centripetal force is directed towards to the center, the centrifugal force is directed away.
Thus, the force that causes the water on the lettuce to come off the lettuce and go to the walls of the bowl is centrifugal force.
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Centripetal force causes the water on the lettuce to come off the lettuce and go to the walls of the bowl.
What is centripetal force?Centripetal force is the force that is necessary to keep an object moving in a curved path and that is directed inward toward the center of rotation. This force can move the body in the circular direction.
So we can conclude that Centripetal force causes the water on the lettuce to come off the lettuce and go to the walls of the bowl.
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A particle with mass 3×10−2 kg
k
g
and charge +3 μC
μ
C
enters a region of space where there is a magnetic field of 1 T
T
that is perpendicular to the velocity of the particle. When the particle encounters the magnetic field, it experiences an acceleration of 12 m/s2
m
/
s
2
. What is the speed of the particle when it enters the magnetic-field region?
The speed of the particle when it enters the magnetic-field region is 120,000 m/s.
Speed of the particle
Magnetic force on the particle is given as;
F = qvB
where;
q is magnitude of the chargev is speed of the particleB is magnetic field strengthFrom Newton's second law, force on an object is given as;
F = ma
where;
m is mass of the particlea is accelerationma = qvB
v = ma/qB
v = (3 x 10⁻² x 12)/(3 x 10⁻⁶ x 1)
v = 120,000 m/s
Thus, the speed of the particle when it enters the magnetic-field region is 120,000 m/s.
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A small ball is tied to a string and set rotating with negligible friction in a vertical circle. If the ball moves over the top of the circle at its slowest possible speed (so that the tension in the string is negligible), what is the tension in the string at the bottom of the circle, assuming there is no additional energy added to the ball during rotation?
An explanation would be very much appreciated as there are a few things I am confused about
- why is tension negligible at the top? Isn't there still a tension force pulling inward? I thought there would be two forces acting on the ball at the top of the circle, Fg and [tex]F_T[/tex] ?
- is finding a numerical value for this answer even possible? we don't have the mass of the ball
Since the tension in the string over the top of the circle is negligible, the tension in the string at the bottom of the circle will be zero.
What is Circular Motion ?Circular motion is the same as rotational motion. That is, motion moving in a circle.
Given that a small ball is tied to a string and set rotating with negligible friction in a vertical circle. If the ball moves over the top of the circle at its slowest possible speed (so that the tension in the string is negligible)
Since the tension in the string over the top of the circle is negligible, the tension in the string at the bottom of the circle, assuming there is no additional energy added to the ball during rotation will be zero.
The tension is negligible at the top in order to allow the ball rotate. And since the tension is negligible, there no tension force pulling inward
Therefore, the numerical value of the answer is Zero.
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A record of travel along a straight path is as follows:
1. Start from rest with constant acceleration of 2.10 m/s2 for 14.0 s.
2. Maintain a constant velocity for the next 1.90 min.
3. Apply a constant negative acceleration of −9.06 m/s2 for 3.25 s.
m/s
a) What was the total displacement for the trip?
b) What were the average speeds for legs 1, 2, and 3 of the trip, as well as for the complete trip?
The total displacement for the trip is 5510 m
During part 1, the distance travelled is
(1/2) a t^2
= (1/2)(2.77)(225)
= 311.6 m
The final speed gotten is (2.77)(15)
= 41.55 m/s.
The average speed for that interval is half of that or 20.8 m/s
During part 2, the distance traveled is
41.55 m/s*2.05 min*60 sec/min
= 5110 m/s
During part 3, the speed drops from 41.55 m/s to
41.55 - (9.47)(4.39)
= 0
The average speed during this interval is
41.55/2 - 20.78 m/s
The distance travelled is 20.78*4.39
= 91.2 m/s
Total distance travelled = 312 + 5110 + 91 = 5513 m
The average speeds for legs 1,2,and 3 of the trip as well as for the complete trip are:
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A rectangle has a length of (2.5 ± 0.2) m and a width of (1.5 ± 0.2) m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value.
(a)Calculate the area and give its uncertainty. (Enter your answers in m2.)
(b)Calculate the perimeter of the rectangle and give its uncertainty. (Enter your answers in m.)
The area of the rectangle obtained is (3.75 ± 0.03) m². The perimeter of the rectangle obtained is (8 ± 0.64) m.
Given dimensions:
Length (L) = (2.5 ± 0.2) m
Width (W) = (1.5 ± 0.2) m
(a) Area of the rectangle (A) is given by:
A = L × W
A = (2.5 ) × (1.5 )
A = 3.75 m²
The relative uncertainty in area = ΔA / A
ΔA = (ΔL / L) × A + (ΔW / W) × A
ΔA = (0.2 / 2.5) × 3.75 + (0.2 / 1.5) × 3.75
ΔA = 0.03 m²
Therefore, the area of the rectangle is (3.75 ± 0.03) m².
(b) Perimeter of the rectangle (P) is given by:
P = 2 × (L + W)
P = 2 × (2.5 + 1.5)
P = 2 × 4
P = 8 m
Relative uncertainty in perimeter = ΔP / P
ΔP = (ΔL / L) × P + (ΔW / W) × P
ΔP = (0.2 / 2.5) × 8+ (0.2 / 1.5) × 8
ΔP = 0.64 m
Therefore, the perimeter of the rectangle is (8 ± 0.64) m.
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A ball is thrown directly downward with an initial speed of 8.75 m/s, from a height of 29.4 m. After what time interval does it strike the ground?
After time 1.74 seconds ball will strike the ground.
A ball is thrown directly downward and information we have-
Initial velocity of ball (u) = 8.75m/s
distance/height (s) = 29.4m
Ball is thrown downward means there are gravitation force also worked and the acceleration of ball is-
acceleration (a) = g = 9.8 m/s²
When ball strike the ground then it's velocity should be 0 means-
Final velocity of ball (v) = 0 m/s²
For getting time period we can use 2nd equation of motion as-
s = ut + (1/2)at²
Now, 29.4 = (8.75 × t) + (1/2× 9.8 × t²)
29.4 = 8.75t + 4.9t²
Now we have a quadratic equation as -
4.9t² + 8.75t - 29.4 = 0
After solving it we get two values of t -
time = 1.74 and time = -3.5
But time can not be negative so we will reject the negative values.
so t = 1.74 seconds
So to conclude that after applying the second equation of motion the time taken by the ball to reach ground is 1.74 seconds.
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Which prathogen is often controlled by beneficial bacteria
Answer:
antibiotics
Explanation:
im not sure if this is right hope this helps lol
your manger wants everyine to make setting up seasonal aisle display their top priority you noticed one if associate benn focusing on other task mostly likly to do or least likly to do
The manager is both most and least likely to lead seminars and provide everyone skills.
What is seasonal aisle?When a store has a “seasonal aisle,” it suggests it has extra money to spend on items that are in season. Festivals, special days, seasons, and other things are examples of seasonal components.
An operational strategy focused on creating profit. Seasonal goods are required by a supply chain. A manager wants everyone to prioritize setting up the seasonal aisle displays because of this.
Hence, the significance of the seasonal aisle is aforementioned.
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Two blocks are connected by a massless rope over a massless, frictionless pulley, as shown in the figure. The mass of block 2 is 2=11.3 kg , and the coefficient of kinetic friction between block 2 and the incline is =0.200 . The angle of the incline is 31.5° . If block 2 is moving up the incline at constant speed, what is the mass 1 of block 1?
The mass of block 1 is 1.30176 kg.
What is tension in physics?A tension force in physics is a force developed in a rope, string, or cable when stretched under an applied force.
Tension is acted along the length of the rope/cable in a direction that is opposite to the force applied on it.
According to the question,
Mass of block 2= 11.3 kg
Kinetic friction μ=0.200
The component of the weight in the direction of the incline
W = m₂gsinθ
T = [tex]F_{f} - W[/tex]........(1)
When the force of friction
[tex]F_{f}[/tex] = μ[tex]_k[/tex]N
[tex]F_{f}[/tex] = μ[tex]_k[/tex](m₂gcosθ)
Here , Put the value in equation 1
T = m₂gcos 31.5° - μ[tex]_k[/tex]m₂gcos 31.5°
We know that ,
T - m₁g = 0
T = m₁g
So,
m₁g = m₂g (Sin 31.5° - 0.200 x cos 31.5°)
m₁ = 11.3 x (0.0840 - 0.2 x 0.996)
m₁ = 11.3 x (0.1152)
m₁ = 1.30176 kg
Hence, the mass of block 1 is 1.30176 kg.
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4
Select the correct answer from each DROP-DOWN MENU.
A graph plots time in seconds versus position (m). A line rises from a point A (0, 0) to a point B (4, unit 6) extends linearly through a point C (11, unit 6), and rises to a point D (12, unit 7 point 5).
The graph describes the motion of an object.
The object moves with
from A to B. It
from B to C. It moves with
from C to D.
Reset Next
(a) The object moves with uniform velocity from A to B.
(b) The object moves with constant velocity from B to C.
(c) The object moves with increasing velocity from C to D.
Velocity of the object from point A to B
V(A to B) = (6 - 0)/(4 - 0) = 1.5 m/s
Velocity of the object from point B to CV(B to C) = (6 - 6)/(11 - 4) = 0 m/s
Velocity of the object from point C to DV(C to D) = (7 - 6)/(12 - 11) = 1 m/s
final velocity = 1 + 1.5 m/s = 2.5 m/s
Thus, we can conclude the following;
The object moves with uniform velocity from A to B.
The object moves with constant velocity from B to C.
The object moves with increasing velocity from C to D.
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Answer:The object moves with
positive accelaration
from A to B. It
speeds up
from B to C. It moves with
constant velocity
from C to D.
Explanation:I took the test
A section of a high speed test track is circular with a radius of curvature R = 1860 m.
At what angle of θ should the track be inclined so that a car traveling at 61.0 m/s (136 mph) would keep moving in a circle if there is oil on that section of the track, i.e., it would not slip sideways even with zero friction on that section. (Hint: The car's vertical acceleration is zero.)
The banking angle of curved road to allow to move without slipping is 11.53 ⁰.
Banking angle of curved roadThe banking angle of curved road is calculated as follows;
V(max) = √(rg tanθ)
where;
r is radius of the curveg is acceleration due to gravityV² = rg tanθ
tanθ = V²/rg
tanθ = (61²)/(1860 x 9.8)
tanθ = 0.204
θ = arc tan(0.204)
θ = 11.53 ⁰
Thus, the banking angle of curved road to allow to move without slipping is 11.53 ⁰.
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What percentage of the area under the normal distribution is shaded?
What buoyant force is exerted on a 6,000-mL toy balloon by the air surrounding the balloon? The density of air is 0.0009 g/mL
The buoyant force exerted on a 6,000-mL toy balloon by the air surrounding the balloon is 52.97N.
How to calculate buoyant force?The buoyancy needed for an object can be calculated using the formula;
B = ρ × V × g
where;
ρ and V are the object's density and volume respectivelyg is the acceleration due to gravity (9.81m/s²)B = 6000 × 0.0009 × 9.81
B = 52.97N
Therefore, the buoyant force exerted on a 6,000-mL toy balloon by the air surrounding the balloon is 52.97N.
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Two rocks of identical mass sit high above the river. One rock is 10 meters above the river, and the other is 20 meters above the river. Which rock has the greatest potential energy?
Answer:
Gravitational potential energy is greater for the rock [tex]20\; {\rm m}[/tex] above the river.
Explanation:
The gravitational field near the surface of the earth is approximately uniform. Let [tex]g[/tex] denote the strength of the gravitational field near the surface of the earth.
Let [tex]m[/tex] denote the mass of each rock. Assume that the gravitational potential energy of the two rocks is [tex]0[/tex] when the rocks are at the surface of the river.
When the rock is at a height of [tex]h[/tex] above the river, the gravitational potential energy ([tex]\text{GPE}[/tex]) of that rock would be [tex]\text{GPE} = m\, g\, h[/tex]. In other words, the [tex]\text{GPE}\![/tex] of the rock is proportional to its height relative to the ground.
Hence, among the two rocks, [tex]\text{GPE}[/tex] would be greater for the rock that is higher above the ground ([tex]20\; {\rm m}[/tex]) than the rock [tex]10\; {\rm m}[/tex] above the ground.