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wel
2 years ago
7

Show the equation of simple pendulum to be dimensionally consistent

Physics
1 answer:
nataly862011 [7]2 years ago
6 0
T is in seconds (s) 

<span>2pi is dimensionless </span>

<span>L is in meters (m) </span>

<span>g is in meters per second squared (m/s^2) </span>

<span>so you can write the equation for the period of the simple pendulum in its units... </span>

<span>s=sqrt(m/(m/s^2)) </span>

<span>simplify</span>

<span>s=sqrt(m*s^2*1/m) cancelling the m's </span>

<span>s=sqrt(s^2) </span>

<span>s=s </span>

<span>therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.</span>
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Find the radius of the circle formed by the intersection of a sphere of diameter 26 units and a plane that is 5 units away from
horrorfan [7]

Answer:

12 units

Explanation:

This problem can be solved if we take into account the equation for a sphere

x^{2}+y^{2}+z^{2}=r^{2}\\x^{2}+y^{2}+z^{2}=(\frac{26}{2})^{2}=13^{2}

where we took that the radius is 13 units. If we take z=5 and we replace this value in the equation of the sphere we have

x^{2}+y^{2}+(5)^{5}=13^{2}\\x^{2}+y^{2}=144=(12)^{2}

where we have taken x2 +y2 because if the equation of a circunference.

In this case the intersection is made when we take z=5, for this value the sphere and the plane coincides in values.

Hence, the radius is 12 units

I hope this is useful for you

regards

8 0
2 years ago
Which kind of energy transformation occurs during skydiving? A) mechanical to gravitational B) gravitational to kinetic C) kinet
Aleks [24]

B) gravitational to kinetic

Explanation:

The skydiver, when he is located at a certain height h above the ground, possesses gravitational potential energy, equal to:

U=mgh

where m is the mass of the skydiver, g is the gravitational acceleration and h is the height above the ground. As he falls, its height h decreases, while his speed v increases, so part of the gravitational potential energy is converted into kinetic energy, which is given by

K=\frac{1}{2}mv^2

so, we see that as v increases, the kinetic energy increases. Therefore the correct answer is

B) gravitational to kinetic

7 0
3 years ago
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What is stopping distance of a body at 20 m/s is decelerated at 2m/s² to rest?<br>​
AlladinOne [14]

Answer:

s = 100 m

Explanation:

v² = u² + 2as

s = (v² - u²) / 2a

s = (0² - 20²) / 2(-2)

s = 100 m

5 0
3 years ago
Mention two similarities of citizen and aliens​
lesantik [10]

Answer:

The main points of difference between a citizen and alien are: (a) A citizen is a permanent resident of a state, while an alien is a temporary resident, who comes for a specific duration of time as a tourist or on diplomatic assignment. ... Aliens do not possess such rights in the state where they reside temporarily

Explanation:

6 0
3 years ago
A wire of radius 5 x 10⁻⁴ m is needed to prepare a coil of resistance 40 Ω. The resistivity of the material of the wire is 3.14x
SIZIF [17.4K]

Answer:

100 m

Explanation:

From the question,

R = Lρ/A.................... Equation 1

Where R = resistance of the wire, L = length of the wire, ρ = resistivity of the wire, A = cross sectional area of the wire.

But,

A = πr².................... Equation 2

Where r = radius of the wire.

Substitute equation 2 into equation 1

R = Lρ/πr²

Make L the subject of the equation

L = Rπr²/ρ...................... Equation 3

Given: R = 40 Ω, r = 5×10⁻⁴ m, ρ = 3.14×10⁻⁷ Ωm

Constant: π = 3.14

Substitute these values into equation 3

L = [40×3.14×( 5×10⁻⁴)²]/ (3.14×10⁻⁷)

L = 40×3.14×25×10⁻⁸/(3.14×10⁻⁷)

L = 100 m

Hence the length of the wire is 100 m

4 0
2 years ago
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