Find the dimension of volume

A 280-g mass is mounted on a spring of constant k = 3.3 N/m. The damping constant for this damped system is b = 8.4 x 10^-3 kg/s

yulyashka [42]

Answer:

The number of oscillation is 36.

Explanation:

Given that

Mass = 280 g

Spring constant = 3.3 N/m

Damping constant $b=8.4\times10^{-3}\ Kg/s$

We need to check the system is under-damped, critical damped and over damped by comparing b with $2m\omega_{0}$

$2m\omega_{0}=2m\sqrt{\dfrac{k}{m}}$

$2\sqrt{km}=2\times\sqrt{3.3\times280\times10^{-3}}=1.92kg/s$

Here, b<< $2m\omega_{0}$

So, the motion is under-damped and will oscillate

$\omega=\sqrt{\omega_{0}^2-\dfrac{b^2}{4m^2}}$

The number of oscillation before the amplitude decays to $\dfrac{1}{e}$ of its original value

$A exp(\dfrac{-b}{2m}t)=A exp(-1)$

$\dfrac{b}{2m}t=1$

$t = \dfrac{2m}{b}$

$t=\dfrac{2\times280\times10^{-3}}{8.4\times10^{-3}}$

$t=66.67\ s$

We need to calculate the time period of one oscillation

$T=\dfrac{2\pi}{\omega}$

$T=\dfrac{2\times3.14}{\sqrt{\omega_{0}^2-\dfrac{b^2}{4m^2}}}$

$T=\dfrac{2\times3.14}{\sqrt{\dfrac{k}{m}-\dfrac{b^2}{4m^2}}}$

$T=\dfrac{2\times3.14}{\sqrt{\dfrac{3.3}{280\times10^{-3}}-\dfrac{(8.4\times10^{-3})^2}{4\times(280\times10^{-3})^2}}}$

$T=1.83\ sec$

The number of oscillation is

$n=\dfrac{t}{T}$

$n=\dfrac{66.67}{1.83}$

$n=36$

Hence, The number of oscillation is 36.

8 0

3 years ago

Suppose you are asked to find 91,321,972×0.007004. Doing a quick estimate by rounding the numbers in scientific notation, what v

slamgirl [31]

Answer:

Product, $P=9.1321972\times 10^7\times 7.004\times 10^{-3}$

P = 639619.091888

Explanation:

In this case, we need to find the product of two numbers. These are as follows :

$N_1=91321972=9.13\times 10^7$

$N_2=0.007004=7.004\times 10^{-3}$

On doing calculation, we get the product of two numbers as :

$P=N_1\times N_2$

$P=9.1321972\times 10^7\times 7.004\times 10^{-3}$

P = 639619.091888

In scientific notation the product of two number is given by :

$P=63\times 10^4$

Hence, this is the required solution.

3 0

2 years ago

Identify what gives an object the greatest and the least kinetic energy

antoniya [11.8K]

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.

5 0

3 years ago

Two skiers start at the same place at the top of the hill, and finish at the same place at the bottom. Skier A takes a straight,

Rus_ich [418]

Answer:A

Explanation:

Given

Skier A takes straight, smooth route while Skier B takes curvy, bumpy route to finish.

We know gravity is conservative in nature i.e. work done against it is independent of path followed

So work done by gravity for A and B is same

According to Work energy Theorem Change in the kinetic Energy is equal to work done by all the forces.

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

$W_g=mgh$

where h=vertical height of hill

thus $v=\sqrt{2gh}$

which is same for both A and B

6 0

2 years ago

What was the Law of Triads? A. Elements were arranged into three rows. B. Elements were arranged in groups of three. C. Elements

shtirl [24]

Answer:

its B

Explanation: i searched it up...

8 0

3 years ago

Find the dimension of volume​

Find the dimension of volume