The wind blows a jay bird south with a force of 300 Newtons. The

In an amusement park rocket ride, cars are suspended from 3.40-m cables attached to rotating arms at a distance of 5.90 m from t

ValentinkaMS [3465]

Answer:

The rotational angular speed is measured at 1.34 rad/s.

Explanation:

Considering the following parameters,

Length = 3.40 m

Distance = 5.90 m

Angle = 45.0°

We are tasked with finding the angular speed of rotation

Using the balance equation

Horizontal component

$T\cos\theta=mg$

$T=\dfrac{mg}{\cos\theta}$

Vertical component

$T\sin\theta=m\omega^2 r$

Substituting the tension value

$mg\tan\theta=m\omega^2(d+L\sin\theta)$

$\omega=\sqrt{\dfrac{g\tan\theta}{(d+L\sin\theta)}}$

Substituting the value into the equation

$\omega=\sqrt{\dfrac{9.8\tan45.0}{5.90+3.40\sin45.0}}$

$\omega=1.34\ rad/s$

Thus, the angular speed of rotation computes to 1.34 rad/s.

7 0

3 months ago

The spring in a retractable ballpoint pen is 1.8 cm long, with a 300 N/m spring constant. When the pen is retracted, the spring

Sav [3153]

Answer:

The pen requires 7.2 mJ of energy to extend.

Explanation:

Provided:

Length = 1.8 cm

Spring constant = 300 N/m

Initial compression = 1.0 mm

Additional compression = 6.0 mm

Total compression = 1.0 + 6.0 = 7.0 mm

We need to determine the energy needed

This energy is equivalent to the variation in spring potential energy

$E=PE_{2}-PE_{1}$

$E=\dfrac{1}{2}kx_{2}^2-\dfrac{1}{2}kx_{1}^2$

Substitute the values into the formula

$E=\dfrac{1}{2}\times300\times(7.0\times10^{-3})^2-\dfrac{1}{2}\times300\times(1.0\times10^{-3})^2$

$E=0.0072\ J$

$E=7.2\ mJ$

Therefore, a total of 7.2 mJ is needed to extend the pen.

7 0

3 months ago

Read 2 more answers

Taylor places a nail on a bar magnet. The nail sticks to the magnet when lifted up off the table. She touches a paperclip to the

ValentinkaMS [3465]

Initially, the magnetic domains within the nail were oriented in various directions before coming into contact with the bar magnet. Upon Taylor touching the nail to the bar magnet, the magnetic fields of those domains became aligned, thus transforming the nail into a temporary magnet.

5 0

2 months ago

Read 2 more answers

Because of your knowledge of physics, you have been hired as a consultant for a new James Bond movie, "Oldfinger". In one scene,

Softa [3030]

Answer:

v = [√(g/2h)]L

Explanation:

Let v represent the initial horizontal speed, and t denote the duration James Bond takes to leap off the ledge of length, L.

Thus, we derive vt = L, which leads to t = L/v

Additionally, considering that Bond begins with no horizontal velocity, he descends freely over the height, h; thus the equation y - y' = ut - 1/2gt² is applicable, where y = 0 (top of the cliff) and y' = -h, u = 0 (initial vertical speed), g = acceleration due to gravity = 9.8 m/s², and t = the time required to leap from the cliff = L/v.

By substituting these parameters into the equation, we obtain

y' - y = ut - 1/2gt²

-h - 0 = 0 × t - 1/2g(L/v)²

-h = - 1/2gL²/v²

v² = gL²/2h

taking the square root of both sides gives us

v = [√(g/2h)]L

Therefore, James Bond's required minimum horizontal velocity is v = [√(g/2h)]L

8 0

2 months ago