The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, ℓ, what combination of g and ℓ must the period be proportional to? (Acceleration has SI units of m • s-2.)

Answers

Answer 1

Answer: √(L/g)

Explanation:

Here we only work with the units:

The unit of the period is units of time, so we have:

[T] = [s]

Now, the units of the length of the pendulum are units of distance:

[L] = [m]

And the units of the acceleration are:

[g] = [m/s^2]

Now, we want to work with those two in such way that the end result is only in seconds.

First, we can see that in g we have seconds square, so we know that we should use a square root.

Then we can divide L by g in order to remove the distance unit, and to have the time unit in the numerator

[L/g] = [m*s^2/m] = [s^2]

Now we apply the square root:

[√(L/g)] = [√s^2] = [s]

Then the combination is: √(L/g)

T = k*√(L/g)

where k is the constant of proportionality.


Related Questions

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass

Answers

Answer:

the force constant  k = 2.369 N/m

Explanation:

Given that:

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair.

with period T = 0.500 s and a mass of 0.0150 kg, Then the force constant can be calculated by using the formula:

[tex]\mathtt{T = 2 \pi \ \sqrt{\dfrac{m}{k} }}[/tex]

where;

T = time period

m = mass

k = force constant.

By making k the subject of the formula; we have:

[tex]\mathtt{T^2 = 4 \pi^2 (\dfrac{m}{k})}[/tex]

[tex]\mathtt{k =\dfrac{4 \pi ^2 \ m}{T^2}}[/tex]

replacing our given values , we have:

[tex]\mathtt{k =\dfrac{4 (3.142) ^2 \ \times 0.0150 }{0.5^2}}[/tex]

[tex]\mathtt{k =\dfrac{39.49 \ \times 0.0150 }{0.25}}[/tex]

[tex]\mathtt{k =\dfrac{0.59235 }{0.25}}[/tex]

k = 2.369 N/m

According to the information available in the question, the force constant is 2.37N/m.

Using the relation;

T = 2π√m/k

T = period = 0.500 s

m = mass in kilograms = 0.0150-kg

k = spring constant = ?

Making k the subject of the formula;

k = 4π^2m/T^2

k = 4 × (3.142)^2 ×  0.0150/(0.500 )^2

k = 2.37N/m

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Which describes a grizzly bear’s habitat? all the biotic factors in the ecosystem all the abiotic factors in the ecosystem the role of the bear in the ecosystem the physical area where the bear lives

Answers

Answer:

I found this question elsewhere on brainly and the answer was verified. Here it is!

Explanation:

Grizzly bear habitats is the habitat or the physical space where the bear lives. Grizzly bears can be found in many different habitats from dense forests to subalpine meadows, arctic tundra and open plains. We can also conclude that all of the bears live in grizzly bear's habitat in order to survive.

The best description of a grizzly bear’s habitat is:

D. the physical area where the bear lives

A habitat is the natural surrounding or place where an organism lives, grows and competes with other organisms for resources. It is a physical area.

There are three major types of habitat which includes:

Freshwater habitat: This refers to the area of water where animals live. Examples of animals that live in a freshwater habitat includes: sea turtle, fishes, etc. Examples of freshwater habitat include:RiversLakesPond, etcMarine water habitat: This is where a group of organisms live. Examples include:OceansSeas, etc.Coastal habitat: This is an intersection between the land and sea habitats.

A grizzly bear is a subspecies of brown bear and is resident in the northern plains of America and their habitat is a physical location where they live.

Therefore, the correct answer is option D

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what is physics and important of physics​

Answers

Physics is the explanation of our reality, both visible and invisible. With it we can understand the world around us, why things are how they are, and why things do what they do. This understanding allows humans to develop objects that improve quality of life.

Answer:

Confusion

question:
is it multiple choice? or you have to write it

An aircraft travelling at 600km/h accelerates steadily at 10km/h per second. Taking the speed of sound as 1100km/h at the aircraft's altitude how long will it take to reach the sound barrier?​

Answers

speed of sound is the final velocity [tex] v=1100[/tex]

and initial velocity $u=600$ , $a=10$

$v=u+at$

$t=\dfrac{v-u}{a}= \dfrac{500}{10}$

$\implies t=50 h$

answer answer answer it it it

Answers

It is B. too much air resistance could cause you to fly the other way, as well as cause you damage...

Hope this helped ♥︎

Answer:

Parachutes

Explanation:

Your parachute allows you to descend more slowly because it lowers terminal velocity by increasing your air resistance. Most parachutes are designed to create a large amount of drag and allow you to land at a safe, low speed.

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When using science to investigate physical phenomena, which characteristic of the event must exist?
predictable
measurable
provable
readable
READ NEXT SECTION
ASK FOR HELP

Answers

The correct answer is B. Measurable

Explanation:

The use of science to investigate a phenomenon implies using measurements and observations to better understand a phenomenon or test a hypothesis. Moreover, science focuses on natural phenomena that can be objectively studied through measurement instruments such as a thermometer, balance, hydrometer, etc.

In this context, for a phenomenon to be studied by science this needs to be measurable because the use of precise instruments as wells as numbers allow scientist to analyze and understand a phenomenon. Moreover, phenomena that depend on personal perspectives and cannot be measure is considered as non-scientific.

Using your own word, tell me what is the difference between an element and a compound? Make sure to give an example of each.

Answers

Answer:

Hey there!

Elements only contain one type of atom, and a compound contains atoms of different elements chemically combined together. For example, gold is an element, because it only is made of gold atoms, where water or H2O is a compound.

Let me know if this helps :)

Answer:

A compound contains atoms of different elements chemically combined together in a fixed ratio. An element is a pure chemical substance made of same type of atom. Elements contain only one type of atom.

Example:

Explanation:

Match the words to the correct blanks in the sentences. Use each choice only once. a. The collapse of a protostar with less than 0.08 times the mass of the Sun is halted by________. b. As a protostar shrinks in size, its central temperature rises along with its________. c. A star that has not yet finished forming is called a_______. d. A forming star spins more rapidly as it collapses because of conservation of________. e. If a protostar has a mass too small for it to sustain nuclear fusion it becomes the type of object known as a________.A. thermal pressureB. angular momentumC. energy balanceD. degeneracy pressureE. brown dwarfF. gravitational equilibriumG. protostar

Answers

Answer:

The collapse of a protostar with less than 0.08 times the mass of the Sun is halted by DEGENERACY PRESSURE. b. As a protostar shrinks in size, its central temperature rises along with its THERMAL PRESSURE. c. A star that has not yet finished forming is called a__PROTOSTAR_____. d. A forming star spins more rapidly as it collapses because of conservation of ANGULAR MOMENTUM. e. If a protostar has a mass too small for it to sustain nuclear fusion it becomes the type of object known as a____BROWN DWARF____

famous comparative and superlative form​

Answers

Answer:

comparative----more famous, superlative----- most famous

[tex]\huge{\fbox{\red{Answer:}}}[/tex]

Word Given :

Famous

___________________✍

Comparative Form : more famous

Superlative Form : most famous

Hope you understand

What is the Opportunity Cost in textbooks from going from point A to B?

Answers

Answer:

60.00

Explanation:

you welcome

Brandon buys a new seadoo he goes 12 km north from the beach he jumps wakes for 6 km to the east the chases a boat 10 km north what distance did he cover what was his displacement

Answers

Answer:

Distance covered 28 km

displacement is 22.8 km North-East

Explanation:

Distance shows how far apart objects or points are from each other. The distance he covered is the sum of all the distance travelled. Therefore:

Distance covered = 12 km + 6 km + 10 km = 28 km

Displacement is a vector quantity (has direction). It is the overall change in position.

The total distance traveled north = 12 km + 10 km = 22 km

The distance traveled east = 6 km

The displacement (d) is:

d² = 22² + 6² = 484 + 36

d² = 520

d = √520 = 22.8 km

Therefore the displacement is 22.8 km North-East

Distance covered 28 km

displacement is 22.8 km North-East

The calculation is as follows:

Distance covered

= 12 km + 6 km + 10 km

= 28 km

Now

The total distance traveled north = 12 km + 10 km = 22 km

And,  

The distance traveled east = 6 km

So,  

The displacement (d) is:

[tex]d^2 = 22^2 + 6^2\\\\ d^2 = 520\\\\d = \sqrt520[/tex]

= 22.8 km

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An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley, the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The child’s true weight is 320 N, and the chair weighs 160 N. (a) Show that the acceleration of the system is upward and find its magnitude. (b) Find the force the child exerts on the chair.

Answers

Answer:

(a) 0.42 m/s²

(b) 83 N

Explanation:

Assuming g = 10 m/s².

Draw free body diagrams for the child and the chair.

There are three forces on the child:

Tension force T pulling up,

Weight force Mg pulling down,

and normal force N pushing up.

There are three forces on the chair:

Tension force T pulling up,

Weight force mg pulling down,

and normal force N pushing down.

Sum of forces on the child in the y direction:

∑F = ma

T + N − Mg = Ma

Sum of forces on the chair in the y direction:

∑F = ma

T − N − mg = ma

Add the equations together to find the acceleration.

2T − Mg − mg = Ma + ma

a = (2T − Mg − mg) / (M + m)

a = g (2T − Mg − mg) / (Mg + mg)

a = (10 m/s²) (2 × 250 N − 320 N − 160 N) / (320 N + 160 N)

a = 0.42 m/s²

Plug into either equation to find the normal force.

T + N − Mg = Ma

250 N + N − 320 N = (320 N / 10 m/s²) (0.42 m/s²)

N = 83 N

*If someone says v-u=0 ,what does it mean. *What is the relation among mometum,mass and velocity. *A moving bus a little distance forward even when breaks are applied on it which Newton's laws work here? *Under what conditions acceleration of a moving object will be zero?

Answers

Answer:

1) It means that the acceleration is 0

2) Momentum, p = Mass, m × Velocity, v

3) Newton's second law of motion

4) The conditions where there are no resultant forces acting on the object

Explanation:

1) The value v - u =  0 means that the acceleration is 0

The relation between v and u is v = u + a·t

v - u = a·t

When v - u = 0 we have;

a·t = 0

a = 0 or t = 0

Acceleration, a = 0

2) The relation between momentum, mass and velocity is

Momentum, p = Mass, m × Velocity, v

p = m × v

3) The bus moving a little distance forward even when the breaks are applied is due to the following relation;

Force = Rate of change of momentum produced

Which is Newton's second law of motion

Therefore, where the the force is low, the rate of change of the momentum and therefore, the velocity will be low, and the bus will still move further after applying the breaks

4) According to Newton's first law of motion, the conditions under which the acceleration of a moving object will be zero includes conditions where there are no resultant forces acting on the object.

Convert 85 cm/min to m/s.

Answers

Explanation:

meter=100cm

cm=10^-2 m

min=60 sec

0.0141666667 m / s

The conversion of 85 cm/min would be 0.0133 m/s

What is Velocity?

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.

As given in the problem position-time graph of an object.

As we know that slope of the position time curve represents the velocity of the object

As given in the problem we have to convert 85 cm/min to m/s.

Let us first convert the displacement in cm to meters

100 cm = 1 m

1 cm = 1/100 m

85 cm = 85×1/100 m

          = 0.85 m

similarly, convert time given in minutes to the seconds

1 min = 60 s

velocity = displacement /time

velocity  =  0.85 / 60 m/s

             =0.01333 m/s

Thus, we converted  85 cm/m into 0.0133 m/s

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please help ASAP.
these are examination questions ..
no nonsense answers .
i will mark as brainliest if you got it correct .​

Answers

Answer:

1st question c part

2nd question c part

What is The distance traveled by a vehicle in 12 minutes,if it’s speed is 35km/h

Answers

Answer: 7 km

Explanation: 12 minutes is 1/5 of an hour. 35/5=7

What is the goal of the scientific method

Answers

Answer:

Regardless of how the steps are documented, the goal of scientific method is to gather data that will validate or invalidate a cause and effect relationship.

Hope this helped!!!

Eli and Andy want to find out which of the two is stronger. Eli pushes a table with a force of 120 newtons while Andy pushes the table from the opposite side with a force of 125 newtons. Ignoring the masses of Eli and Andy, what is the resultant acceleration of the table if its mass is 10.0 kilograms?

Answers

Answer:

a = 0.5 m/s²

Explanation:

the type of problem is called a Newtons second law of motion.

and the equation would be the sum of F = m * a  where m = mass and a = acceleration

forces are 125N and the opposite direction is 120N

Eli pushes the table with a force of 120N towards Andy

and

Andy pushes the table with a force of 125N towards Eli

mass of table given as 10 kg.

using the equation

120N - 125N = 10kg * a

a = (120-125) / 10

a = -0.5 m/s² so the acceleration is in the direction of Andy's force towards Eli.

therefore a = 0.5 m/s²

Answer:

B.  

0.50 meters/second2

Explanation:

What is a potential psychological outcome of regulary playing sports

Answers

This question is incomplete because the options are missing; I found the complete question:

What is a potential psychological outcome of regularly playing sports? Select one of the options below as your answer:

a. restlessness

b. improved mood

c. depression

d. lack of energy

The answer to this question is B. Improved mood

Explanation:

Practicing a sport regularly has multiple positive effects including physical and psychological benefits. In the case of psychological effects, this includes an improved mood, this is because practicing a sport reduces stress significantly and it is often associated with positive emotions such as motivation, confidence, or pride. Moreover, interacting with others in group sports allow individuals to positively interact with others, which contributes to a better mood. Thus, one potential psychological outcome of playing sports is an improved mood.

An object is moving along a circular track of radius 7 m with constant speed 11 m/s. Its average velocity after 8 second of the start is

Answers

Answer:

0 m/s

Explanation:

Average velocity is displacement over time.

v_avg = Δx / Δt

Displacement is the distance between the start and the finish.

The circumference of the track is:

C = 2πr

C = 2π (7 m)

C ≈ 44 m

The distance covered by the object is:

d = vt

d = (11 m/s) (8 s)

d = 88 m

So the object travels 2 circumferences, meaning it ends back where it started.  Therefore, the displacement is 0 m, and the average velocity is 0 m/s.

Describe the motion of water waves.

Answers

Answer:

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases.

A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 4 : 45 4:45 p.m. At this time, he started pumping gas into the tank. At exactly 4 : 50 4:50, the tank was full and he noticed that he had pumped 12.5 12.5 gallons. What is the average rate of flow of the gasoline into the gas tank

Answers

Answer:

Explanation:

Average rate = gallons / minutes

If 12.5gallons in 5mins

Xgallons in 1mins

12.5/5 = 2.5gallons per minute

Once a scientist has made a hypothesis, what would they typically do next? (2 points)
a
Analysis
b
Testing
C
Research
d
Sharing

Answers

Answer:Testing

Explanation:Once a scientist has made a hypothesis, what would they typically do TESTING nextn

Once a scientist has made a hypothesis, they would typically do testing, therefore the correct answer is option B

What is the scientific claim?

Scientific claims are statements made in science based on an experiment.

These Scientific claims are backed by the experimental data and their true results obtained from scientific investigation and experimentation.

When a scientist performs a fair test is one in which all other circumstances are maintained while just one variable is changed at a time.

Scientists frequently discover that their hypotheses and predictions were not supported by the results of their experiments. In these situations, they will communicate the findings of their experiment before revising their original hypotheses and predictions in light of the new knowledge they have gained.

The right response is option B because once a scientist has made a theory, they usually do testing.

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why do objects in equilibrium have a net force of 0?

Answers

Answer:

Because there is no net force acting o an object in equilibrium.

Explanation:

When object is in equilibrium (either at rest or moving with constant velocity, the net force acting o it is zero.A vector can only have zero magnitude fall of its components are zero this means that all forces acting on the object are balanced.

Hi :) how to do this?

Answers

Answer:

The answer is b

Hope this helps you!

A train travels southwest from point A to point B through the Arizona desert at 55 mi/h. How far will the train travel six-and-a-half hours?

Answers

Explanation:

Distance = speed × time

d = (55 mi/hr) (6.5 hr)

d = 357.5 mi

i)Distinguish between different methods of charging. ii) You are provided with a positively charged gold leaf electroscope. State and explain what happens when a. a glass rod rubbed with silk is brought near the disc of electroscope. b. an ebonite rod rubbed with fur is brought near the disc of electroscope. c. an uncharged metal rod is brought near the disc of electroscope d. a glass rod rubbed with silk is rolled on the disc of electroscope.

Answers

Answer:

Explanation:

On rubbing a glass rod with silk, the electrons from the glass rod get transferred to the silk. The silk now has an excess of electrons and so is negatively-charged. On the other hand, the glass rod is deficient in electrons and hence is positively-charged.

In the above case, the silk undergoes negative electrification.

Now, when the positively charged glass rod is touched on the disc of a negatively charged gold leaf electroscope, the electrons shifts towards rod, hence amount of charge on gold leaves decreases and the divergence between the gold leaves decreases as unlike charges attract each other.

Hence, the divergence decreases when a glass rod rubbed with silk is brought near the disc of negatively charged electroscope.

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At a camp site there are tents of 2 shades. 1 made with black fabric and the other with white fabric. Which one will you prefer for resting on a hot summer afternoon. Give reason for your choice

Answers

Answer:

Explanation:

On a hot summer afternoon the tent made up of white fabric will be preferred because white colour is a bad absorber and good reflector of heat. Hence, it will be more convenient to stay under fabric tent made of white during this season because heat will be reflected which makes shade provided by such tent to be cool and enjoyable.

While the black fabric tent will be preferred during winter because black materials are good absorber of heat and are poor reflector.

If a car has a speed of 36m/s how long will it take to go 100 m

Answers

It will take 2.77..... seconds
The answer to this question is 2.77..... seconds.

a metre rod on wedge is example of unstable equilibrium.why

Answers

Answer:

because it has no balance

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