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garri49 [273]
3 years ago
12

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. The acceleration of gravity is 9.8 m/s 2 . How long does it take for the ball to rotate once around the axis?
Physics
1 answer:
Gemiola [76]3 years ago
4 0

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.

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A car of mass 500kg travelling at 60m/s has it speed reduced to 40m/s by a constant breaking force over a distance of 200m. find
uranmaximum [27]

Answer:

Ek1 = 900000 [J]

Ek1 = 400000 [J]

Explanation:

In order to solve this problem we must remember that kinetic energy is defined as the product of mass by velocity squared by a medium. Therefore using the following equation we have:

E_{k1}=\frac{1}{2}*m*v1^{2}

where:

m = mass = 500 [kg]

v1 = 60 [m/s]

So we have:

Ek1 = 0.5*500*(60^2)

Ek1 = 900000 [J]

and:

Ek2 = 0.5*500*(40^2)

Ek2 = 400000 [J]

6 0
3 years ago
Suppose that the sound level of a conversation is initially at an angry 71 dB and then drops to a soothing 54 dB. Assuming that
Goryan [66]

Answer:

Explanation:

In the decibel scale , intensity of sound changes logarithmically as follows

10log\frac{I}{I_0} = Value in decibel scale , the value of I₀ = 10⁻¹² W /m².

Putting the values

10log\frac{I}{10^{-12}} = 71

log\frac{I}{10^{-12}} = 7.1

\frac{I}{10^{-12}} = 10^{7.1}

I= 10^{-4.9} W/m²

Similarly for 54 dB sound intensity can be given as follows

I = 10⁻¹² x 10^{5.4}

I= 10^{-6.6 } W / m²

For intensity of sound the relation is as follows

I = 2π²υ²A²ρc where υ is frequency , A is amplitude , ρ is density of air and c is velocity of sound .

Putting the given values for 71 dB

I= 10^{-4.9}  = 2π² x 504²xA²x 1.21 x  346

A² = 60.03 x 10⁻¹⁶

A = 7.74 x 10⁻⁸ m

For 54 dB sound

10^{-6.6} = 2π² x 504²xA²x 1.21 x  346

A² = 1.1978 x 10⁻¹⁶

A = 1.1 x 10⁻⁸ m

6 0
3 years ago
All endothermic reactions absorb heat and make the surroundings warm
svet-max [94.6K]

Answer:

b: false

Explanation:

It's true that endothermic reactions absorb heat from their surrounding.  But this makes the surroundings cooler, not warmer.

6 0
3 years ago
A small sphere has a harge of 9uC and other small sphere has a charge of 4uC.
Helga [31]

Answer:

Electrical force, F = 90 N

Explanation:

It is given that,

Charge on sphere 1, q_1=9\ \mu C=9\times 10^{-6}\ C

Charge on sphere 2, q_1=4\ \mu C=4\times 10^{-6}\ C

Distance between two spheres, d = 6 cm = 0.06 m

Let F is the electrical force between them. It is given by the formula of electric force which is directly proportional to the product of charges and inversely proportional to the square of distance between them such that,

F=k\dfrac{q_1q_2}{d^2}

F=9\times 10^9\times \dfrac{9\times 10^{-6}\times 4\times 10^{-6}}{(0.06)^2}

F = 90 N

So, the electrical force between them is 90 N. Hence, this is the required solution.

7 0
3 years ago
When a container decreases in size, what will happen to an amount of gas in the container??
alexgriva [62]
The gas would also decrease in size since the container lost gas to decrease the size of the container.
7 0
3 years ago
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