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3 years ago

A pendulum

Physics

1 answer:

RSB [31]3 years ago

8 0

Explanation:

The time period rotation of the bob is t and the tension in the thread is T. ... A simple pendulum of length. ... Balancing the forces in Horizontal and vertical direction: ... Circular motion 2.

1 answer

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What is the mass defect of lithium? Assume the following: Atomic number of lithium = 3 Atomic mass of lithium = 7.0144 atomic ma

Mice21 [21]

3 protons x 1.0073amu = 3.022 
4 neutrons x 1.0087amu = 4.035 

mass = 7.0567amu 
mass defect = 7.0567 - 7.0144 = 0.0423amu.....B with your mass of Li

6 0

3 years ago

What force is required so that a particle of mass m has the position function r(t) = t3 i + 7t2 j + t3 k?

Rasek [7]

Answer:

$F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k\\F(t)=\,(6\,m\,t,14\,m,6\,m\,t)$

Explanation:

Recall that force is defined as mass times acceleration, and acceleration is the second derivative with respect to time of the position. Since the position comes in terms of time, and with separate functions for each component in the three dimensional space, we first calculate the velocity (with the first derivative, and then the acceleration as the second derivative:

$r(t)=t^3\,\hat i+7\,t^2\,\hat j+t^3\,\hat k\\v(t)=3\,t^2\,\hat i+14\,t\,\hat j+3\,t^2\,\hat k\\a(t)=6\,t\,\hat i+14\,\hat j+6\,t\,\hat k$

Therefore, the force will be given by the product of this acceleration times the mass "m":

$F(t)=m\,\,a(t)=6\,m\,t\,\hat i+14\,m\,\hat j+6\,m\,t\,\hat k$

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3 years ago

What part of the geocentric model was incorporated in the heliocentric model?

PilotLPTM [1.2K]

Astronomer Cladius Ptolemy believed that the earth was the center of the solar system and all other planets rotated around it.

Approximately 500 years ago, another astronomer, Nicolaus Copernicus theorized that the planets’ orbits should be plotted with respect to the Sun.

Hence, the role of Earth changed to a planet status, however, all planets were proven to revolve around a fixed point being the Sun.

5 0

3 years ago

How to prove formula for volume of a sphere ?

atroni [7]

Answer:

The volume of radius is $\frac{4}{3}$ × π × radius³ Proved

Explanation:

Given as :

We know that volume of sphere is v = $\frac{4}{3}$ × π × radius³

Or, v = $\frac{4}{3}$ × π × r³

Let prove the volume of sphere

So, From the figure of sphere

At the height of z , there is shaded disk with radius x

Let Find the area of triangle with side x , z , r

From Pythagorean theorem

x² + z² = r²

Or, x² = r² - z²

Or, x = $\sqrt{r^{2}-z^{2} }$

Now, Area of shaded disk = Area = π × x²

Where x is the radius of disk

Or, Area of shaded disk = π × ( $\sqrt{r^{2}-z^{2} }$ ) ²

∴ Area of shaded disk = π × (r² - z²)

Again

If we calculate the area of all horizontal disk, we can get the volume of sphere

So, we simply integrate the area of all disk from - r to + r

i.e volume = $\int_{-r}^{r} \Pi(r^{2}-z^{2} )dz$

Or, v = $\int_{-r}^{r} \Pi r^{2}dz$ - $\int_{-r}^{r} \Pi z^{2}dz$

Or, v = π r² (r + r) - π $\frac{r^{3} -(-r)^{3})}{3}$

Or, v = π r² (r + r) - π $\frac{2r^{3}}{3}$

Or, v = 2πr³ - π $\frac{2r^{3}}{3}$

Or, v = 2πr³ ( $\frac{3-1}{3}$ )

Or, v = 2πr³ × $\frac{2}{3}$

∴ v = $\frac{4}{3}$ × π × r³

Hence, The volume of radius is $\frac{4}{3}$ × π × radius³ Proved . Answer

5 0

3 years ago

A sprinter begins from rest and accelerates at the rate of 2 m/s^2 for .12 mi, what is the sprinters velocity?

Lena [83]

Given:

Initial velocity = 0 m/s

Acceleration = 2 $\frac{m}{s^{2} }$

Time = 12 minutes = 12 × 60 = 720 second

To find:

Final velocity = ?

Formula used:

v = u + at

v = final velocity

u = initial velocity

a = acceleration

t = time

Solution:

According to first equation of motion,

v = u + at

v = final velocity

u = initial velocity

a = acceleration

t = time

v = 0 + 2(720)

v = 1440 $\frac{m}{s}$

The sprinters velocity is 1440 $\frac{m}{s}$

8 0

3 years ago

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