A block of wood has a length of 4 cm a width of 5 cm and a height of 10 cm what is the volume of the wood?

The function x = (5.2 m) cos[(5πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 5.3 s, what are the (a) di

gulaghasi [49]

Answer:

(a) Displacement = - 3.0576 m

(b) Velocity $=-66.48$ m/s

(c)Acceleration = -753.39 m²/s

(d)The phase motion is 26.7 $\pi$ .

(e)Frequency =2.5 Hz.

(f)Time period =0.4 s

Explanation:

Given function is

$x= (5.2 m)cos[ (5\pi \ rad/s)t+ \frac\pi5]$

(a)

The displacement includes the parameter t, so,at time t=5.3 s

$x|_{t=5.3}= (5.2 m)cos[ (5\pi \ rad/s)5.3+ \frac\pi5]$

$= (5.2 m)cos[ 26.5\pi+ \frac\pi5]$

=(5.2)(-0.588)m

= - 3.0576 m

(b)

$x= (5.2 m)cos[ (5\pi \ rad/s)t+ \frac\pi5]$

To find the velocity of simple harmonic motion, we need to find out the first order derivative of the function.

$v=\frac{dx}{dt}$

$=\frac{d}{dt} (5.2 m)cos[ (5\pi \ rad/s)t+ \frac\pi5]$

$= (5.2 m)(-5\pi)sin[ (5\pi \ rad/s)t+ \frac\pi5]$

$= -26\pi sin[ (5\pi \ rad/s)t+ \frac\pi5]$

Now we can plug our value t=5.3 into the above equation

$v= -26\pi sin[ (5\pi \ rad/s)5.3\ s+ \frac\pi5]$

$=-66.48$ m/s

(c)

To find the acceleration of simple harmonic motion, we need to find out the second order derivative of the function.

$v= -26\pi sin[ (5\pi \ rad/s)t+ \frac\pi5]$

$a=\frac{d^2x}{dt^2}$

$=\frac{dv}{dt}$

$=\frac{d}{dt}( -26\pi sin[ (5\pi \ rad/s)t+ \frac\pi5])$

$= -26\pi (5\pi)cos[ (5\pi \ rad/s)t+ \frac\pi5]$

$= -130\pi^2cos[ (5\pi \ rad/s)t+ \frac\pi5]$

Now we can plug our value t=5.3 into the above equation

$a= -130\pi^2cos[ (5\pi \ rad/s)5.3 \ s+ \frac\pi5]$

= -753.39 m²/s

(d)

The general equation of SHM is

$x=x_mcos(\omega t+\phi)$

$x_m$ is amplitude of the displacement, $(\omega t+\phi)$ is phase of motion, $\phi$ is phase constant.

So,

$(\omega t+\phi)=5\pi t+\frac\pi5$

Now plugging t=5.3s

$(\omega t+\phi)=5\pi \times 5.3+\frac\pi5$

=26.7 $\pi$

The phase motion is 26.7 $\pi$ .

The angular frequency $\omega = 5\pi$

(e)

The relation between angular frequency and frequency is

$\omega =2\pi f$

$\therefore f=\frac{\omega}{2\pi}$

$=\frac{5\pi}{2\pi}$

$=\frac52$

= 2.5 Hz

Frequency =2.5 Hz.

(f)

The relation between frequency and time period is

$T=\frac1 f$

$=\frac1{2.5}$

=0.4 s

Time period =0.4 s

6 0

3 years ago

Which countries were considered the three major Axis Powers?

7nadin3 [17]

B. JAPAN, GERMANY, and ITALY

The main Axis powers were Japan, with Emperor Hirohito as leader; Germany, with Adolf Hitler as leader; and Italy, with Benito Mussolini as leader. They were all dictators.

The Axis powers began to form in 1936

15th October 1936 - Germany and Italy signed a friendship treaty - Rome-German Axis.
25th November 1936 - Germany and Japan signed a treaty against communism - Anti-Comintern Pact

22nd May 1939 - Germany and Italy signed a stronger alliance - Pact of Steel
27th September 1940 - Japan signed the Pact of Steel - It became known as the Tripartite Pact.

8 0

2 years ago

A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N

serg [7]

Answer:

b= 2.14 m

Explanation:

Given that

Weight of the board ,wt = 40 N

Wight of the first children , wt₁=500 N

Weight of the second children ,wt₂ = 350 N

The distance of the 500 N child from center ,a= 1.5 m

lets take distance of the 350 N child from center = b m

Now by taking the moment about the center of the board

We know that moment = Force x Perpendicular distance from the force

wt₁ x a = wt₂ x b

500 x 1.5 = 350 x b

b= 2.14 m

Therefore the distance of the 350 N weight child from the center is 2.14 m.

5 0

2 years ago

An unusual lightning strike has a vertical portion with a current of –400 A downwards. The Earth’s magnetic field at that locati

marusya05 [52]

Answer:

The magnetic force is 0.3 N.

Explanation:

Given that,

Current in an unusual lightning strike, I = -400 A

The Earth’s magnetic field at that location is parallel to the ground and has a magnitude of 30 μT, $B=30\times 10^{-6}\ T$

We need to find the force exerted by the Earth’s magnetic field on the 25 m-long current.

The magnetic force is given by :

$F=ILB\\\\F=400\times 25\times 30\times 10^{-6}\\\\F=0.3\ N$

So, the magnetic force is 0.3 N.

8 0

2 years ago

In 1995 a research group led by Eric Cornell and Carl Wiemann at the University of Colorado successfully cooled Rubidium atoms t

saveliy_v [14]

Answer:

0.00493 m/s

Explanation:

T = Temperature of the isotope = 85 nK

R = Gas constant = 8.341 J/mol K

M = Molar mass of isotope = 86.91 g/mol

Root Mean Square speed is given by

$v_r=\sqrt{\dfrac{3RT}{M}}\\\Rightarrow v_r=\sqrt{\dfrac{3\times 8.314\times 85\times 10^{-9}}{86.91\times 10^{-3}}}\\\Rightarrow v_r=0.00493\ m/s$

The Root Mean Square speed is 0.00493 m/s

6 0

3 years ago