A block is sitting on a platform 20 m high. It weighs 50 kg. How much potential energy does it contain?

At t1 = 2.00 s, the acceleration of a particle in counterclockwise circular motion is 6.00 i + 4.00 j m/s2 . It moves at constan

Jet001 [13]

The particle moves with constant speed in a circular path, so its acceleration vector always points toward the circle's center.

At time $t_1$ , the acceleration vector has direction $\theta_1$ such that

$\tan\theta_1=\dfrac{4.00}{6.00}\implies\theta_1=33.7^\circ$

which indicates the particle is situated at a point on the lower left half of the circle, while at time $t_2$ the acceleration has direction $\theta_2$ such that

$\tan\theta_2=\dfrac{-6.00}{4.00}\implies\theta_2=-56.3^\circ$

which indicates the particle lies on the upper left half of the circle.

Notice that $\theta_1-\theta_2=90^\circ$ . That is, the measure of the major arc between the particle's positions at $t_1$ and $t_2$ is 270 degrees, which means that $t_2-t_1$ is the time it takes for the particle to traverse 3/4 of the circular path, or 3/4 its period.

Recall that

$\|\vec a_{\rm rad}\|=\dfrac{4\pi^2R}{T^2}$

where $R$ is the radius of the circle and $T$ is the period. We have

$t_2-t_1=(5.00-2.00)\,\mathrm s=3.00\,\mathrm s\implies T=\dfrac{3.00\,\rm s}{\frac34}=4.00\,\mathrm s$

and the magnitude of the particle's acceleration toward the center of the circle is

$\|\vec a_{\rm rad}\|=\sqrt{\left(6.00\dfrac{\rm m}{\mathrm s^2}\right)^2+\left(4.00\dfrac{\rm m}{\mathrm s^2}\right)^2}=7.21\dfrac{\rm m}{\mathrm s^2}$

So we find that the path has a radius $R$ of

$7.21\dfrac{\rm m}{\mathrm s^2}=\dfrac{4\pi^2R}{(4.00\,\mathrm s)^2}\implies\boxed{R=2.92\,\mathrm m}$

8 0

3 years ago

The mass of a moving object increases, but its speed stays the same. What happens to the kinetic energy of the object as a resul

Ronch [10]

Answer:

kinetic energy increases because of speed and motion overall

Explanation:

dont know if i helped you but you can give me a thumbs down if you hate the answer or it is not the answer you are looking for

8 0

3 years ago

Can someone help me with this free body diagram problem?

zavuch27 [327]

Lol I just finished this

5 0

3 years ago

The tallest building in the world, according to some architectural standards, is the Taipei 101 in Taiwan, at a height of 1671 f

Andrej [43]

Answer:

35.14°C

Explanation:

The equation for linear thermal expansion is $\Delta L = \alpha L_0\Delta T$ , which means that a bar of length $L_0$ with a thermal expansion coefficient $\alpha$ under a temperature variation $\Delta T$ will experiment a length variation $\Delta L$ .

We have then $\Delta L$ = 0.481 foot, $L_0$ = 1671 feet and $\alpha$ = 0.000013 per centigrade degree (this is just the linear thermal expansion of steel that you must find in a table), which means from the equation for linear thermal expansion that we have a $\Delta T =\frac{\Delta L }{\alpha L_0}$ = 22.14°. As said before, these degrees are centigrades (Celsius or Kelvin, it does not matter since it is only a variation), and the foot units cancel on the equation, showing no further conversion was needed.

Since our temperature on a cool spring day was 13.0°C, our new temperature must be $T_f=T_0+\Delta T$ = 35.14°C

3 0

4 years ago

Q30. When working near some large air cored inductors you misplace a socket and as you cannot find it you

Andre45 [30]

When the piece of metal blundered into the air-core coil, it changed the inductance of the coil.

4 0

3 years ago