If Sienna is using the gymnasium floor to cool off, which position will lower her skin temperature the quickest?

You slip a wrench over a bolt. Taking the origin at the bolt, the other end of the wrench is at x=18cm, y=5.5cm. You apply a for

mart [117]

Answer:

The torque on the wrench is 4.188 Nm

Explanation:

Let r = xi + yj where is the distance of the applied force to the origin.

Since x = 18 cm = 0.18 cm and y = 5.5 cm = 0.055 cm,

r = 0.18i + 0.055j

The applied force f = 88i - 23j

The torque τ = r × F

So, τ = r × F = (0.18i + 0.055j) × (88i - 23j) = 0.18i × 88i + 0.18i × -23j + 0.055j × 88i + 0.055j × -23j

= (0.18 × 88)i × i + (0.18 × -23)i × j + (0.055 × 88)j × i + (0.055 × -22)j × j

= (0.18 × 88) × 0 + (0.18 × -23) × k + (0.055 × 88) × (-k) + (0.055 × -22) × 0 since i × i = 0, j × j = 0, i × j = k and j × i = -k

= 0 - 4.14k + 0.0484(-k) + 0

= -4.14k - 0.0484k

= -4.1884k Nm

≅ -4.188k Nm

So, the torque on the wrench is 4.188 Nm

8 0

2 years ago

A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is given an initial an

Montano1993 [528]

To solve this problem we will use the kinematic equations of angular motion, starting from the definition of angular velocity in terms of frequency, to verify the angular displacement and its respective derivative, let's start:

$\omega = 2\pi f$

$\omega = 2\pi (2.5)$

$\omega = 5\pi rad/s$

The angular displacement is given as the form:

$\theta (t) = \theta_0 cos(\omega t)$

In the equlibrium we have to $t=0, \theta(t) = \theta_0$ and in the given position we have to

$\theta(t) = \theta_0 cos(5\pi t)$

Derived the expression we will have the equivalent to angular velocity

$\frac{d\theta}{dt} = 2.7rad/s$

Replacing,

$\theta_0(sin(5\pi t))5\pi = 2.7$

Finally

$\theta_0 = \frac{2.7}{5\pi}rad = 9.848\°$

Therefore the maximum angular displacement is 9.848°

6 0

2 years ago

A climatograph for a tropical grassland or savanna would look different from the climatograph shown for a temperate grassland. D

Savatey [412]

Answer:

Savannas have a fairly constant temperature all year; temperate grasslands have a greater seasonal temperature variation.

Explanation:

For example, the African Savanna has an almost constant temperature all year (see the first figure below).

The difference between summer and winter temperatures is only about 5 °C, and the rate of temperature change is quite slow.

The temperature of a temperate grassland (see the second figure below) has a much greater seasonal variation.

The summers are hot, and the winters are cold. The difference between summer and winter temperatures is about 30 °C, with a rapid rate of temperature change from one season to the next.

5 0

2 years ago

A flat uniform circular disk (radius = 2.00 m, mass = 1.00

Ostrovityanka [42]

Answer:

The resulting angular speed of the disk is 0.5 rad/s

Explanation:

Step 1: Data given

Radius of the circular disk = 2.00 meters

Mass of the circular disk = 1.00

Mass op the person = 40.0 kg

Distance from the axis = 1.25 m

tangential speed = 2.00 m/s

Step 2:

There is no external torque acting on the system so we can apply the law of conservation of angular momentum In this case the momentum is conserved.

Angular momentum of the man = Iω

⇒ With I = Inertia of the man about the axis of rotation = M*r²

⇒ I = 40 *1.25² = 62.5

⇒ with ω = Angular velocity of the man

⇒ v = 2m/s

⇒ Circumference of the circle = 2πr = 2 * 3.14 * 1.25 = 7.85m

⇒The time to describe this circle t = 2πr/ v

⇒ in 1 revolution the angle θ = 2π radians

This angle is subtended in time t = 2πr/ v

⇒ The angular speed = ω = θ/t = 2π ( v/ 2πr) = v/r = 2/1.25 = 1.6 rad/s

⇒ The angular momentum of man = I*ω = 62.5 * 1.6 = 100

Since the angular momentum is conserved, before and after the man starts running we have :

Angular momentum of disk = angular momentum of the man

⇒ with Angular momentum of disk = Idisk ωdisk

⇒ Idisk = MdiskR

⇒ with Angular momentum of disk = 100

or I(disk)*ω(disk) = 100

I(disk) = M(disk)*R ²/2 = 100*2*2 / 2 = 200

⇒ with M(disk) = the mass of the disk = 1.00 * 10² kg

⇒ with R = the radius of the disk = 2.00 m

200 ωdisk = 100

ωdisk = 100/200 = 0.5 rad/s

The resulting angular speed of the disk is 0.5 rad/s

(Since the angular speed is positive, the rotation is counterclockwise)

5 0

2 years ago

Calculate the wavelength of a photon having 3.26 x 10^-19 joules of energy

bekas [8.4K]

The energy of a photon is given by:
$E=hf$
where h is the Planck constant and f is the photon frequency.
We know the energy of the photon, $E=3.26 \cdot 10^{-19} J$ , so we can rearrange the equation to calculate the frequency of the photon:
$f= \frac{E}{h}= \frac{3.26 \cdot 10^{-19}J}{6.6 \cdot 10^{-34}Js}=4.94 \cdot 10^{14}Hz$

And now we can use the following relationship between frequency f, wavelength $\lambda$ and speed of light c to find the wavelength of the photon:
$\lambda= \frac{c}{f}= \frac{3 \cdot 10^8 m/s}{4.94 \cdot 10^{14} Hz}=6.07\cdot 10^{-7} m=607 nm$

8 0

2 years ago