What are the 26th - 50th Elements of the Periodic Table

A turntable that spins at a constant 80.0 rpmrpm takes 3.50 ss to reach this angular speed after it is turned on. Find its angul

Veronika [31]

Answer:

The angular acceleration is <u>2.39 rad/s²</u>.

The number of degrees it rotates is <u>841.68 degrees</u>.

Explanation:

Given:

Initial angular speed (ω₀) = 0 rad/s

Final angular speed in rpm (N) = 80.0 rpm

Time taken (t) = 3.50 s

First, let us determine the final angular speed in radians per second.

We know that,

$\omega=\frac{2\pi N}{60}\ rad/s$

Plug in the values and find the final angular speed, 'ω'. This gives,

$\omega=\frac{2\pi\times 80.0}{60}=8.38\ rad/s$

Now, using equation of motion for rotational motion, we have:

$\omega=\omega_0+\alpha t\\\\\alpha\to angular\ acceleration$

Plug in the given values and solve for α. This gives,

$8.38=0+\alpha \times 3.50\\\\\alpha=\frac{8.38}{3.50}=2.39\ rad/s^2$

Therefore, the angular acceleration is 2.39 rad/s².

Now, again using rotational equation of motion relating angular displacement, we have:

$\omega^2=\omega_0^2+2\alpha\theta\\\\\theta=\frac{\omega^2-\omega_0^2}{2\alpha }$

Plug in the given values and solve for 'θ'. This gives,

$\theta=\frac{(8.38)^2-0}{2\times 2.39}\\\\\theta=\frac{70.2244}{4.78}=14.69\ rad$

Convert radians to degrees using the conversion factor. This gives,

π radians = 180°

So, 1 radian =( 180 ÷ π ) degrees

Therefore, $14.69\ rad=14.69\times (\frac{180}{\pi})=841.68^\circ$

So, the number of degrees it rotates is 841.68 degrees.

3 0

3 years ago

(pleases show work)

Feliz [49]

a. 46 m/s east

The jet here is moving with a uniform accelerated motion, so we can use the following suvat equation to find its velocity:

$v=u+at$

where

v is the velocity calculated at time t

u is the initial velocity

a is the acceleration

The jet in the problem has, taking east as positive direction:

u = +16 m/s is the initial velocity

$a=+3 m/s^2$ is the acceleration

Substituting t = 10 s, we find the final velocity of the jet:

$v=16 + (3)(10)=46 m/s$

And since the result is positive, the direction is east.

b. 310 m

The displacement of the jet can be found using another suvat equation

$s=ut+\frac{1}{2}at^2$

where

s is the displacement

u is the initial velocity

a is the acceleration

t is the time

For the jet in this problem,

u = +16 m/s is the initial velocity

$a=+3 m/s^2$ is the acceleration

t = 10 s is the time

Substituting into the equation,

$s=(16)(10)+\frac{1}{2}(3)(10)^2=310 m$

4 0

3 years ago

our friend is constructing a balancing display for an art project. She has one rock on the left (ms=2.25 kgms=2.25 kg) and three

Licemer1 [7]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The torque produced by the pile of rocks is $\tau = 35.63\ N \cdot m$

b

The distance of the single for equilibrium to occur is $r_s =1.62 \ m$

Explanation:

From the question we are told that

The mass of the left rock is $m_s = 2.25 \ kg$

The mass of the rock on the right $m_p = 10.1 kg$

The distance from fulcrum to the center of the pile of rocks is $r_p = 0.360 \ m$

Generally the torque produced by the pile of rock is mathematically represented as

$\tau = m_p * g * r_p$

Substituting values

$\tau = 10.1 * 9.8 * 0.360$

$\tau = 35.63\ N \cdot m$

Generally we can mathematically evaluated the distance of the the single rock that would put the system in equilibrium as follows

The torque due to the single rock is

$\tau = m_s * g * r_s$

At equilibrium the both torque are equal

$35.63 = m_s * r_s * g$

Making $r_s$ the subject of the formula

$r_s = \frac{35.63 }{m_s * g}$

Substituting values

$r_s = \frac{35.63 }{2.25 * 9.8}$

$r_s =1.62 \ m$

6 0

3 years ago

A daredevil is shot out of a cannon at 45.0° to the horizontal with an initial speed of 31.0 m/s. A net is positioned a horizont

hodyreva [135]

Answer:

s = vcos(x)t

50 = 25cos(45)t

cos(45)t = 2

t = 2/cos(45) = 2sqrt(2)

h = vsin(x)t + gt^2/2

h = 25sin(45)*2sqrt(2) - 4.9*8

h = 10.8 metres

Explanation:

5 0

3 years ago

Read 2 more answers

A tiny boat is floating in a metal bucket. If you build a fire under the bucket ,how will most of the heat be transferred from t

Dimas [21]

The molecules will heat up and move faster, some evaporating and turning to gas, the toy boat will heat up if made of conducting materials but otherwise unchanged. The water will also start to boil.

7 0

2 years ago