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zalisa [80]
3 years ago
6

If you know that the period of a pendulum is 1.87 seconds, what is the length of that pendulum? (Assume that we are on Earth and

that gravity is 9.81 meters/second².) Select one of the options below as your answer: A. 0.87 centimeters B. 2.1 meters C. 1.6 meters D. 0.87 meters E. 8.3 meters
Physics
2 answers:
shepuryov [24]3 years ago
8 0

Period of an ideal simple pendulum  =  2π √(L / G)

                                          1.87 = 2π √ (L / 9.81)

Divide each side by  2π :      (1.87 / 2π) = √ (L / 9.81)

Square each side:                (1.87 / 2π)²  =  L / 9.81

Multiply each side by  9.81 :      L = (9.81) (1.87 / 2π)²  = <em> 0.869 meter</em>

                                              Choice 'D' is the closest one.


mote1985 [20]3 years ago
8 0

Answer : The correct option is, (D) 0.87 meters

Solution :

Formula used :

T=2\pi \times \sqrt{\frac{L}{g}}

where,

T = time period of a pendulum = 1.87 seconds

L = length of the pendulum = ?

g = gravity on earth = 9.8m/s^2

Now put all the given values in the above formula, we get the length of the pendulum.

1.87s=2\times \frac{22}{7}\times \sqrt{\frac{L}{9.8m/s^2}}

0.2975=\sqrt{\frac{L}{9.8m/s^2}}

Now squaring on both the sides, we get

L=0.868m=0.87m

Therefore, the length of the pendulum is, 0.87 meters.

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Luigi twirls a round piece of pizza dough overhead with a frequency of
viva [34]

The linear speed of the pepperoni is 0.628 m/s. Its direction is tangential to the circle.

We know that;

v = rω

r = radius of the piece = 10 cm or 0.1 m

ω = angular velocity

We have to convert 60 revolutions per minute to radians per second

1 rev/min = 0.10472 rad/s

60 revolutions per minute = 60 rev/min × 0.10472 rad/s/1 rev/min

= 6.28 rad/s

v =  0.1 m ×  6.28 rad/s

v = 0.628 m/s

The direction of this velocity is tangential to the circle.

Learn more: brainly.com/question/4612545

5 0
2 years ago
A 4000 kg satellite is placed 2.60 x 10^6 m above the surface of the Earth.
mash [69]

a) The acceleration of gravity is 4.96 m/s^2

b) The critical velocity is 6668 m/s (24,006 km/h)

c) The period of the orbit is 8452 s

d) The satellite completes 10.2 orbits per day

e) The escape velocity of the satellite is 9430 m/s

f) The escape velocity of the rocket is 11,191 m/s

Explanation:

a)

The acceleration of gravity for an object near a planet is given by

g=\frac{GM}{(R+h)^2}

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

h is the height above the surface

In this problem,

M=5.98\cdot 10^{24} kg (mass of the Earth)

R=6.37\cdot 10^6 m (Earth's radius)

h=2.60\cdot 10^6 m (altitude of the satellite)

Substituting,

g=\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)^2}=4.96 m/s^2

b)

The critical velocity for a satellite orbiting around a planet is given by

v=\sqrt{\frac{GM}{R+h}}

where we have again:

M=5.98\cdot 10^{24} kg (mass of the Earth)

R=6.37\cdot 10^6 m (Earth's radius)

h=2.60\cdot 10^6 m (altitude of the satellite)

Substituting,

v=\sqrt{\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)}}=6668 m/s

Converting into km/h,

v=6668 m/s \cdot \frac{3600 s/h}{1000 m/km}=24,006 km/h

c)

The period of the orbit is given by the circumference of the orbit divided by the velocity:

T=\frac{2\pi (R+h)}{v}

where

R=6.37\cdot 10^6 m

h=2.60\cdot 10^6 m

v = 6668 m/s

Substituting,

T=\frac{2\pi (6.37\cdot 10^6 + 2.60\cdot 10^6)}{6668}=8452 s

d)

One day consists of:

t = 24 \frac{hours}{day} \cdot 60 \frac{min}{hours} \cdot 60 \frac{s}{min}=86400 s

While the period of the orbit is

T = 8452 s

So, the number of orbits completed by the satellite in one day is

n=\frac{t}{T}=\frac{86400}{8452}=10.2

e)

The escape velocity for an object in the gravitational field of a planet is given by

v=\sqrt{\frac{2GM}{R+h}}

where here we have:

M=5.98\cdot 10^{24} kg

R=6.37\cdot 10^6 m

h=2.60\cdot 10^6 m

Substituting, we find

v=\sqrt{\frac{2(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)}}=9430 m/s

f)

We can apply again the formula to find the escape velocity for the rocket:

v=\sqrt{\frac{2GM}{R+h}}

Where this time we have:

M=5.98\cdot 10^{24} kg

R=6.37\cdot 10^6 m

h=0, because the rocket is located at the Earth's surface, so its altitude is zero.

And substituting,

v=\sqrt{\frac{2(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6)}}=11,191 m/s

Learn more about gravitational force:

brainly.com/question/1724648

brainly.com/question/12785992

#LearnwithBrainly

6 0
3 years ago
A helicopter has blades of length 4.0 m rotating at 3.0 rev/s in a horizontal plane.If the vertical component of the Earth’s mag
VARVARA [1.3K]

Answer:

Induced emf, \epsilon=9.79\times 10^7\ volts

Explanation:

Given that,

Length of the helicopter, l = 4 m

Angular speed of the helicopter, \omega=3\ rev/s=18.84\ rad/s

The vertical component of the Earth’s magnetic field is, B=6.5\times 10^5\ T

We need to find the induced emf between the tip of a blade and the hub. The induced emf in terms of angular velocity of an rotating object is given by :

\epsilon=\dfrac{1}{2}B\omega l^2

\epsilon=\dfrac{1}{2}\times 6.5\times 10^5\times 18.84\times (4)^2

\epsilon=9.79\times 10^7\ volts

So, the induced emf between the tip of a blade and the hub is \epsilon=9.79\times 10^7\ volts. Hence, this is the required solution.

5 0
3 years ago
What is the change in internal energy of the system (∆U) in a process in which 10 kJ of heat energy is absorbed by the system an
Trava [24]

Answer:

Explanation:

According to first law of thermodynamics:

∆U= q + w

= 10kj+(-70kJ)

-60kJ

, w = + 70 kJ

(work done on the system is positive)

q = -10kJ ( heat is given out, so negative)

∆U = -10 + (+70) = +60 kJ

Thus, the internal energy of the system decreases by 60 kJ.

8 0
3 years ago
In a lab, a block weighing 80 N is attached to a spring scale, and both are pulled to the right on a horizontal surface. Frictio
notka56 [123]
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

There should be an image that should accompanied your question, I was able to chcek it from other sources. the acceleration of the block when the scale reads 32N is <span>4.0 m/s*s</span>
5 0
2 years ago
Read 2 more answers
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