The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T=2πlg where l is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.

Answers

Answer 1

Answer:

Explanation:

T = 2π √l/g

The dimension for l = m

The dimension for g = m/s²

The dimension for 2π is nothing. Since it's a constant, it is dimensionless.

Now we proceed ahead. Since we are not using the 2π, for the sake of this proving, our formula will temporarily be written as

T = √l/g

Inputting the dimensions, we have

T = √(m) / (m/s²)

T = √(m * s²/m)

T = √s²

T = s

Since the unit of period itself is in s, we can adjudge that the equation is dimensionally constant.


Related Questions

Your friend says, “chemical changes are caused by an input in energy. In physical changes, there is no transfer of energy” is your friend correct? Why or why not?

Answers

Answer:

Ok, let's suppose the simplest of the physical changes:

We have an object that is not moving (so it is not accelerated)

and there is change, now the object moves.

Because there was a change, means that there was an acceleration, and by the second Newton's law.

Force equals mass times acceleration:

F = m*a

There must be a force.

So suppose that you pushed the object, then some energy that you had, you transferred it to the object, that now is moving and now has kinetic energy.

Now, is kinda true that in a closed system the total energy is always constant, but it depends on what is our system.

So if we think in our system as you and the object, then in the whole system the energy does not change because the energy that you lost is now on the object, but again, there was a transfer of energy.

So no, your friend is not correct.

Both chemical and physical changes involve energy transfer, so your friend is not correct.

A chemical change occurs when a new substance is formed or created through a process of chemical reaction which is reversible.

The addition or removal of heat energy can affect the rate of chemical reaction. This addition or removal is known as energy transfer process.

Examples of chemical changes include;

Acid-base reaction.Rusting of iron in presence of moisture and oxygen.   Cooking any food.

A physical change on the other hand doesn't involve formation of new substance and it is can be reversible or irreversible.

The addition or removal of heat energy can affect the rate of physical changes.

Examples of such physical changes include;

vaporization of liquid (liquid to gas),freezing of liquid (liquid to solid), and condensation of gas (gas to liquid).

Thus, both process (chemical and physical changes) involve energy transfer, so your friend is not correct.

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A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. After many oscillations, he finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.

Answers

Explanation:

It is given that,

Mass of a bungee jumper is 65 kg

The time period of the oscillation is 38 s, hitting a low point eight more times.It means its time period is

[tex]T=\dfrac{38}{8}\\\\T=4.75\ s[/tex]

After many oscillations, he finally comes to rest 25.0 m below the level of the bridge.

For an oscillating object, the time period is given by :

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

k = spring stiffness constant

So,

[tex]k=\dfrac{4\pi ^2m}{T^2}\\\\k=\dfrac{4\pi ^2\times 65}{(4.75)^2}\\\\k=113.43\ N/m[/tex]

When the cord is in air,

mg=kx

x = the extension in the cord

[tex]x=\dfrac{mg}{k}\\\\x=\dfrac{65\times 9.8}{113.6}\\\\x=5.6\ m[/tex]

So, the unstretched length of the bungee cord is equal to 25 m - 5.6 m = 19.4 m

The spring stiffness constant is 116.7 N/m and the the unstretched length of the bungee cord is 19.54 m.

The given parameters;

mass of the bungee jumper, m = 65 kgtime of motion, t = 38 sdistance to come to rest, d = 25 m

The period of oscillation of the bungee jumper is calculated as follows;

[tex]T = \frac{t}{n} \\\\T = \frac{38}{8} \\\\T = 4.75 \ s[/tex]

The spring stiffness constant is calculated as follows;

[tex]T = 2\pi \sqrt{\frac{m}{k} } \\\\\sqrt{\frac{m}{k} } = \frac{T}{2\pi} \\\\k = m \times \frac{T^2}{4\pi^2} \\\\k = 65 \times \frac{(4.75)^2}{4\pi ^2} \\\\k = 116.7 \ N/m[/tex]

The extension of the cord is calculated as follows;

[tex]F = kx\\\\mg = kx\\\\x = \frac{mg}{k} \\\\x = \frac{65 \times 9.8}{116.7} \\\\x = 5.46 \ m[/tex]

The unstretched length of the bungee cord is calculated as;

[tex]\Delta x = l_2-l_1\\\\l_1 = l_2 - \Delta x\\\\l_1 = 25 - 5.46\\\\l_1 = 19.54 \ m[/tex]

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If one object (a) is moving at 60m/s^2, and the other object (b) is moving at 65m/s^2, at what time will the faster moving object be 10m ahead of the other object?

Answers

Answer:

a is moving at 60m and the other object

Two 100kg bumper cars are moving towards eachother in oppisite directions. Car A is moving at 8 m/s and Car B at -10 m/s when they collide head on. If the resulting velocity of Car B after the collision is 8 m/s, what is the velocity of Car A after the collision

Answers

Answer:

[tex]-10 m/s[/tex]

Explanation:

When two cars collide then the momentum of two cars will remains conserved

Mass of two cars = 100 kg Speed of car A = 8 m/s Speed of car B = - 10 m/s After collision the speed of car B = +8 m/s

By momentum conservation equation

               [tex]m1v1i+m2v2i=m1v1f + m2v2f[/tex]

               [tex](100)(8)+(100)(-10)=(100v)+(100)(8)\\ v=-10 m/s[/tex]

Two equal charges are 2m2m apart. If the charges and the distance are divided by two, how is the force between the charges affected? g

Answers

Answer:

The force between the charges are not affected.

Explanation:

Given;

distance between two equal charges, R = 2m

The force between the charges is given by;

[tex]F = \frac{kq^2}{R^2}\\\\F_1 = \frac{kq_1^2}{R_1^2}\\\\When\ the \ charges \ and \ the \ distance \ are \ divided \ by \ two \ (q_2 = \frac{q_1}{2}, \ R_2 = \frac{R_1}{2} )\\\\ F_2 = \frac{kq_2^2}{R_2^2}\\\\F_2 = \frac{k(q_1/2)^2}{(R_1/2)^2}\\\\F_2= \frac{4k*q_1^2}{4*R_1^2}\\\\F_2 = \frac{k*q_1^2}{R_1^2}\\\\F_2 = F_1[/tex]

Therefore, the force between the charges are not affected.

Which scientist determined that electrons had predicted zones orbiting the nucleus?

Answers

Answer:

Rutherford

Explanation:

Because

Schrödinger I just took the unit review

When charges qa, qb, and qc are placed respectively at the corners a, b, and c of a right triangle, the potential at the midpoint of the hypotenuse is 20 V. When the charge qa is removed, the potential at the midpoint becomes 15 V. When, instead, the charge qb is removed (qa and qc both in place), the potential at the midpoint becomes 12 V. What is the potential at the midpoint if only the charge qc is removed from the array of charges?

Answers

Answer:

8v

Explanation:

First we apply super position principle

Vt= v1 + v2+ v3

Remove qa

But vt= 20v

So V = v2+v3

V1= 20-15

= 5v

Remove qb

V= v1+v3

V=8v

So the potential when qa and qc are remove is the potential due to qb

Which is 8v

What is the binary number system? ​

Answers

Explanation:

binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" and "1".

How does sleep affect your ability to handle stress?

Answers

Answer: Stress can adversely affect sleep quality and duration, while insufficient sleep can increase stress levels. Both stress and a lack of sleep can lead to lasting physical and mental health problems.

Explanation:

Many report that there stress increases when the length and quality of their sleep decreases. When you do not get enough sleep, 21 percent of adults report feeling more stressed.

Sleep affects your ability to handle stress because when you have more sleep you are able to think more clearly and you’re more energized and happy throughout the day.

Which statement best defines inertia? An object's motion is unaffected by any external forces acting upon it. An object responds to a force by tending to move in the direction of that force. An object opposes any motion, naturally returning to a state of rest on its own. An object opposes any change in its velocity, either to its direction or to its speed.

Answers

Answer:

An object opposes any change in its velocity, either to its direction or to its speed.

Explanation:

Edmentum Answer

which water molecules have the greatest kinetic energy

Answers

The higher the temperature the substance is, the more energy in it because the particles are moving a lot more around in it. So therefore, steam which has the highest temperature, has the greatest kinetic energy.



What quantity do units represent in a value?

A. size

Answers

Question:

What quantity do units represent in a value? A. Size B. Direction C. Magnitude D. Dimension

Answer:

D. Dimension

Explanation:

A unit is simply the measurement given to a dimension. In other words, units represent dimensions. For example, consider a ruler that is 20m long.

i. The value is 20m.

ii. The magnitude of the measurement is 20

iii. The unit of the measurement is meters(m) and that essentially represents the dimension (length) of the ruler.

What happens to the temperature as altitude increases in the exosphere? Does it increase or decrease the higher it goes?

Answers

Answer:

it gets colder the higher you go

You are driving your car at a speed of 19.0 m/s and you hit the brakes. The car accelerates at -3.50 m/s2. (a) How long does it take the car to cover 10.0 m? (b) What is the final velocity of the car?

Answers

Recall the formulas,

[tex]x_f=x_i+v_it+\dfrac12at^2[/tex]

[tex]v_f=v_i+at[/tex]

(a)

[tex]10.0\,\mathrm m=\left(19.0\dfrac{\rm m}{\rm s}\right)+\dfrac12\left(-3.50\dfrac{\rm m}{\mathrm s^2}\right)t^2[/tex]

[tex]\implies \boxed{t\approx0.555\,\mathrm s}[/tex]

(b)

[tex]v_f=19.0\dfrac{\rm m}{\rm s}+\left(-3.50\dfrac{\rm m}{\mathrm s^2}\right)(0.555\,\mathrm s)[/tex]

[tex]\implies \boxed{v_f\approx17.1\dfrac{\rm m}{\rm s}}[/tex]

A stone is thrown vertically upward with a speed of 28.0 m/s how much time is required to reach this height

Answers

A stone is thrown vertically upward with a speed of 17.0 m/s. How fast is it moving when it reaches a height of 11.0 m? How long is required to reach this height?

Let’s review the 4 basic kinematic equations of motion for constant acceleration (this is a lesson – suggest you commit these to memory):

s = ut + ½ at^2 …. (1)

v^2 = u^2 + 2as …. (2)

v = u + at …. (3)

s = (u + v)t/2 …. (4)

where s is distance, u is initial velocity, v is final velocity, a is acceleration and t is time.

In this case, we know u = 17.0m/s, a = -g = -9.81m/s^2, s = 11.0m and we want to know v and t, so from equation (2):

v^2 = u^2 + 2as

v^2 = 17.0^2 -2(9.81)(11.0)

v = √73.18 = 8.55m/s

now from equation (3):

v = u + at

8.55 = 17.0 – 9.81t

t = (8.55 – 17.0)/(-9.81) = 0.86s

The speed of a bus increases uniformly from
15 ms- to 60 ms in 20 seconds. Calculate
a. the average speed,
b. the acceleration,
C. the distance travelled during the entire
period The speed of a bus increases uniformly from
15 ms- to 60 ms in 20 seconds. Calculate
a. the average speed,
b. the acceleration,
C. the distance travelled during the entire
period​

Answers

Explanation:

a. For constant acceleration:

v_avg = ½ (v + v₀)

v_avg = ½ (60 m/s + 15 m/s)

v_avg = 37.5 m/s

b. a = (v − v₀) / t

a = (60 m/s − 15 m/s) / 20 s

a = 2.25 m/s²

c. x = v_avg t

x = (37.5 m/s) (20 s)

x = 750 m

4. Lead has a density of 11.5g/cmº. A rectangular block of lead measures 7cm x5cmx2cm.
a) Find the volume of the block of lead.
b) Find the mass of the block of lead

Answers

Answer:

(a) 70cm³

(b) 805 grams

Explanation:

(a) V = L×B×H

= 7cm×5cm×2cm

= 35cm×2cm

= 70cm³

(b) Mass = Volume × Density

= 70cm³ × 11.5g/cm³

= 805 grams

Finally, consider the expression (6.67 x 10^-11)(5.97 x 10^24)/(6.38 x 10^6)^2 Determine the values of a and k when the value of this expression is written in scientific rotation. Enter a and k, separated by commas.

Answers

Explanation:

We need to find the value of following expression :

[tex]\dfrac{(6.67 \times 10^{-11})(5.97 \times 10^{24})}{(6.38 \times 10^6)^2}[/tex]

Firstly, solving the numerator of the above expression :

[tex]=\dfrac{39.8199\times 10^{-11+24}}{40.7044\times 10^{12}}\\\\=\dfrac{39.8199\times 10^{13}}{40.7044\times 10^{12}}\\\\=9.7827[/tex]

Rounding off the result = 9.78

In scientific notation : [tex]9.78\times 10^0[/tex]

The value of a = 9.78 and k = 0.

A 10 kg object is dropped from rest. a. How far will it drop in 2s? b. How long will it take a 5 kg object to drop the same distance?

Answers

Answer:

Explanation:

Using the equation of motion S = ut + 1/2at² to get the height of drop where

u is the initial velocity of the object = 0m/s

a is the acceleration due to gravity = +9.81m/s² (downwards motion of object)

t is the time it takes the object to drop = 2secs

Substituting the given parameters into the formula to get the height of drop S, we will have;

S = 0(2)+1/2(9.81)(2)²

S = 0+9.81*2

S = 19.62m

Hence the object will drop at a distance of 19.62m

b.) To determine the time it will take a 5 kg object to drop the same distance, we will use the same formula S = ut+1/2at²

Since the 5kg object also drops at the same distance, then S = 19.62m

Substituting this values into the equation we will have;

19.62 = 0(t) + 1/2(9.81)t²

19.62 = 4.905t²

t² = 19.62/4.905

t² = 4

t =2secs

This shows that it will take 5kg object 2secs to fall from the  same distance. This means that no matter the mass of the object, it will take them the same time to fall at the same distance because they are all falling under the same influence of gravity.

2. If a cyclist in the Tour de France traveled southwest a distance of 12,250 meters in one hour, what would the velocity of the cyclist be?​

Answers

Answer:

12,25 km/h

≈ 3,4 m/s

Explanation:

v = d/t

= 12250m/h

= 12,25km/h

or

v = d/t

= 12250m/h

1h = 60m×60s = 3600s

= 12250m/3600s

≈ 3,4 m/s

if a cart goes around a turn at 20 km/h ,what remains constant

1.position
2.velocity
3.direction
4.speed

Answers

Answer: 4.speed

Explanation:

In this case, we know that the cart remains at a constant 20km/h.

Now, one could say that "the velocity remains constant, because it always is 20km/h"

But remember that velocity is a vector, so this has a direction, and if the cart is going around a turn, then the direction of motion is changing, which tell us that there is acceleration.

But the module of the velocity, the speed, remains constant at 20km/h.

Then the correct option is 4, speed.

Difference between calorimeter and thermometer ?

Answers

A calorimeter is can be used to measure the amount of heat released or involved in a chemical reaction. Whereas thermometer can only measures temperature or hotness of a substance. It cannot be used to measure the thermal rate or amount of heat energy of a reaction.

Answer:

A calorimeter is can be used to measure the amount of heat released or involved in a chemical reaction. Whereas thermometer can only measures temperature or hotness of a substance. It cannot be used to measure the thermal rate or amount of heat energy of a reaction.

Explanation:

Consider two balls in motion at the same time. Joe drops the first ball from rest at height h. Directly below Joe, on the ground, Hayley simultaneously tosses a second ball upward with speed v0.a. If the two balls collide at the moment the second ball is instantaneously at rest, what is the height of the collision?b. What is the relative speed of the balls when they collide?

Answers

Answer:

A. To find height of collision let's find

Speed of collision first

Using

Vf= √2g(h-g)

But for Harvey's ball we have

V²-2gy= 0

y=( v²/2g) so this is height of collision

B.

To find relative speed of the ball

Using V at y to find Vsr

Vs= √2g(h-v²/2g)

= √2gh- v²

Put Newton’s 1st Law in your own words

Answers

Answer:Newton’s law also states that larger bodies with heavier masses exert more gravitational pull, which is why those who walked on the much smaller moon experienced a sense of weightlessness, as it had a smaller gravitational pull. To help explain his theories of gravity and motion, Newton helped create a new, specialized form of mathematics.

Explanation:Here I dont know

A technical machinist is asked to build a cubical steel tank that will hold 310L of water. Calculate in meters the smallest possible inside length of the tank.

Answers

Answer:

0.68 m

Explanation:

Since the volume of water is 310 L, and we know that 1 litre = 1 dm³. So the volume of water is V = 310 dm³. Since this volume of water is the volume of water the cubical steel tank can contain, it equals the volume of the cubical steel tank.

We know that the volume of the cubical steel tank V = L³ where L is the length of side of the cube on the inside.

So the length of side of the cube L = ∛V = ∛310 dm³ = 6.77 dm = 6.77 dm × 1m/10 dm = 0.677 m ≅ 0.68 m

So, the smallest possible inside length of the tank is 0.68 m

Two pounds of water vapor at 30 psia fill the 4-ft3 left chamber of a partitioned system. The right chamber has twice the volume of the left and is initially evacuated. Determine the pressure of the water after the partition has been removed and enough heat has been transferred so that the temperature of the water is 40oF.

Answers

Answer:

3.38atm

Explanation:

Using data from the steam table we have that

Moles of water vapour = 907.19 / 18

= 50.4 moles

So

p1 = 30 psi = 30 x 0.68 = 2.04 atm

v1 = 4ft³= 113.2 L

Then from

PV= nRT

Then to find T we use

T1 = p1 V1 / n R

= 2.04 x 113.2 / 50.4 x 0.0821

= 55.8 K

Then to find volume two

v2 = 2v1 + v1

So

3 v1 = 339.6 K

The pressure two we use

P2 = n R T2 / V2

= 50.4 x 0.0821 x 277.6 / 339.6

So we have

= 3.38 atm =

Assuming it is a van der Waals gas, calculate the critical temperature, pressure and volume for CO2. (a = 3.610 atm L2 mol-2, b = 0.0429 L mol-1)
pc = ___ atm
Tc = ___ K
Vc = ___ L/mol

Answers

Answer

To get critical pressure

We use

Pc = a/(27b²)

So

= 3.610/(27 X 0.0429²)

We have

= 72.7 atm

Critical temperaturewe

We use

Tc = 8a/27Rb

= 8 x 3.610/(27 x 0.0812 x 0.0429)

= 307 K

Critical volume

We use

Vc =3b =

3 x 0.0429

= 0.129L/mol

(7) A 2500 lbm car moving at 25 mi/hr is accelerated at a constant rate of 15 ft/s2 up to a speed of 50 mi/hr. What is the force and total time required?

Answers

Answer:

The  force is  [tex]F =  1164.6\  lbf[/tex]

The time is   [tex]\Delta t =  2.44 \  s[/tex]

Explanation:

From the question we are told that

  The  mass of the car is  [tex]m  =  2500 \ lbm[/tex]

   The  initial velocity of the car is [tex]u  =  25 \ mi/hr[/tex]

   The final  velocity of the car is  [tex]v  =  50 \  mi/hr[/tex]

  The acceleration is  [tex]a =  15 ft/s^2 =  \frac{15 *  3600^2}{ 5280} =  36818.2 \  mi/h^2[/tex]

   

Generally the acceleration is mathematically represented as

      [tex]a =  \frac{v-u}{\Delta t}[/tex]

=>   [tex]36818.2 =  \frac{50 - 25 }{ \Delta t}[/tex]

=>   [tex]t = 0.000679 \  hr[/tex]

converting to seconds

       [tex]\Delta t =  0.0000679 *  3600[/tex]

=>     [tex]\Delta t =  2.44 \  s[/tex]

Generally the force is mathematically represented as

        [tex]F  =  m * a[/tex]

=>      [tex]F  =  2500 *  15[/tex]

=>      [tex]F  =  37500 \ \frac{lbm *  ft}{s^2}[/tex]

Now converting to foot-pound-second we have  

         [tex]F =  \frac{37500}{32.2}[/tex]

=>        [tex]F =  1164.6\  lbf[/tex]

A ball with a mass of 3.7 kg is thrown downward with an initial velocity of 8 m/s from a high building. How fast will it be moving after 3 seconds?

Answers

Answer:

v=37.4 m/s

Explanation:

It is given that,

Mass of a ball, m = 3.7 kg

Initial velocity of the ball is u = 8 m/s

We need to find its velocity after 3 seconds. It is moving downwards. The equation of motion is this case is

v=u+gt

[tex]v=8+9.8\times 3\\\\v=37.4\ m/s[/tex]

So, the velocity of the ball after 3 seconds is 37.4 m/s.

Check Concepts
4.
35. Which of the following do you calculate
when
you
divide the total distance trav-
eled by the total travel time?
A) average speed
B) constant speed
C) variable speed
D) instantaneous speed

Answers

Answer:

I think its A.........

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