Mess up my notes please part 1

A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal

Gemiola [76]

Answer:

Time taken, $T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Explanation:

It is given that, a small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone as shown in attached figure.

From the figure,

The sum of forces in y direction is :

$T\ cos\theta-mg=0$

$T=\dfrac{mg}{cos\theta}$

Sum of forces in x direction,

$T\ sin\theta=\dfrac{mv^2}{r}$

$mg\ tan\theta=\dfrac{mv^2}{r}$ .............(1)

Also, $r=l\ sin\theta$

Equation (1) becomes :

$mg\ tan\theta=\dfrac{mv^2}{l\ sin\theta}$

$v=\sqrt{gl\ tan\theta.sin\theta}$ ...............(2)

Let t is the time taken for the ball to rotate once around the axis. It is given by :

$T=\dfrac{2\pi r}{v}$

Put the value of T from equation (2) to the above expression:

$T=\dfrac{2\pi r}{\sqrt{gl\ tan\theta.sin\theta}}$

$T=\dfrac{2\pi l\ sin\theta}{\sqrt{gl\ tan\theta.sin\theta}}$

On solving above equation :

$T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Hence, this is the required solution.

4 0

3 years ago

What is the acceleration of the the object during the first 4 seconds?

AVprozaik [17]

Answer:

Velocity (m/s) over time (s) graph

We could write out our average acceleration as:

a = Δv/ Δta=Δv/Δta, equals, Δ, v, slash, Δ, t

a = (15 m/s - 0 m/s) / 0.2 seconds

a = 15 m/s / 0.2 seconds

a = 75 m/s / second

Explanation:

What this formula is telling us is that if we know the acceleration of an object, and the ... we can plug in our acceleration of 12.5 m/s2 for a, and 4 seconds for t.

Velocity (m/s) over time (s) graph

We could write out our average acceleration as:

a = Δv/ Δta=Δv/Δta, equals, Δ, v, slash, Δ, t

a = (15 m/s - 0 m/s) / 0.2 seconds

a = 15 m/s / 0.2 seconds

a = 75 m/s / second

6 0

3 years ago

The size of a balloon increases when the pressure inside it increases. The balloon gets bigger when it is left in the heat from

Masteriza [31]

Explanation:

This happens because the gas inside tend to expand because its temperature gets higher.

This is why the balloon that is put in a freezer for too long tend to gets smaller, because the gas temperature that is inside the balloon decreases.

(you can try it at home)

It is related to the temperature of the gas.

5 0

3 years ago

A student is using a frequency generator set to 440 Hz. Another student has an identical generator playing an unknown frequency.

Anna71 [15]

Answer:

The unknown frequency is either 438 Hz or 442 Hz.

Explanation:

The frequency of a beat heard when two sounds with frequencies f₁ and f₂, are played simultaneously, is simply the difference between two frequencies.

b = |f₁ - f₂|

b = 2 Hz

f₁ = 440 Hz

f₂ = ?

440 - f₂ = 2 or 440 - f₂ = -2

f₂ = 438 Hz or 442 Hz

The unknown frequency is either 438 Hz or 442 Hz.

Hope this Helps!!!

5 0

3 years ago

The hanging mass is released and allowed to fall. When it has traveled a distance h (that is, the moment just before it hits the

abruzzese [7]

Answer:

Gravitational potential energy to kinetic energy

Explanation:

In this case you have a case about conservation of energy.

When the mass is released and allowed to fall, its energy is completely gravitational potential energy with a value of U = mgh. m is the mass, g is the gravitational constant and h is the height to the floor from the mass.

While the mass is falling down part of its potential energy converts to kinetic energy of value K=1/2mv^2, because the mass has been acquiring more and more velocity.

Thus, the kinetic energy is increasing while the potential energy is decreasing.

When the mass is just above the floor (the moment just before the mass hits the floor) all its potential energy has been converted to kinetic energy.

Then, you have that the kinetic energy of the mass when the mass is just above the floor, is equal to the potential energy when the mass is at height of h. That is:

$mgh=\frac{1}{2}mv^2$

This is how the law of conservation of energy is fulfilled.

5 0

3 years ago