Yes, it is possible to add three vectors of equal magnitudes and get zero. This can happen if the resultant of the two vectors are equal and opposite in direction to the third vector.

5 0

4 years ago

P.E

Vladimir79 [104]

Answer:

pagtalon?

Explanation:

because that had to be the answer

5 0

3 years ago

A woman is listening to her radio, which is 174 m from the radio station transmitter. (a) How many wavelengths of the radio wave

vladimir2022 [97]

Explanation:

It is given that,

The distance between the radio and the radio station is 174 m

We need to find how many wavelengths of the radio waves are there between the transmitter and radio receiver if the woman is listening to an AM radio station broadcasting at 1540 kHz.

f = 1540 kHz

Wavelength,

$\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{1540\times 10^3}\\\\\lambda=194.8\ m$

Let there are n wavelengths of the radio waves. So,

$n=\dfrac{d}{\lambda}\\\\n=\dfrac{174}{194.8}\\\\n=0.89\ \text{wavelengths}$

There are 0.89 wavelengths.

7 0

3 years ago

In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed"). One way i

lara [203]

Answer:

Approximately $1.44\times 10^3 \; \rm N \cdot m^{-1}$ assuming that the spring has zero mass.

Explanation:

Without any external force, a piece of mass connected to an ideal spring (like the chair in this question) will undergo simple harmonic oscillation.

On the other hand, the force constant of a spring (i.e., its stiffness) can be found using Hooke's Law. If the spring exerts a restoring force $\mathbf{F}$ when its displacement is $\mathbf{x}$ , then its force constant would be:

$\displaystyle k = -\frac{\mathbf{F}}{\mathbf{x}}$ .

The goal here is to find the expressions for $F$ and for $x$ . By Hooke's Law, the spring constant would be ratio of these two expressions.

Let $T$ represent the time period of this oscillation. With the chair alone, the period of oscillation is $T = 1.00\; \rm s$ .

For a simple harmonic oscillation, the angular frequency $\omega$ can be found from the period:

$\displaystyle \omega = \frac{2\pi}{T}$ .

Let $A$ stands for the amplitude of this oscillation. In a simple harmonic oscillation, both $\mathbf{F}$ and $\mathbf{x}$ are proportional to $A$ . Keep in mind that the spring constant $k$ is simply the opposite of the ratio between $\mathbf{F}$ and $\mathbf{x}$ . Therefore, the exact value of $A$ shouldn't really affect the value of the spring constant.

In a simple harmonic motion (one that starts with maximum displacement and zero velocity,) the displacement (from equilibrium position) at time $t$ would be:

$\displaystyle \mathbf{x}(t) = A \cos(\omega \cdot t)$ .

The restoring velocity at time $t$ would be:

$\displaystyle \mathbf{v}(t) = \mathbf{x}^\prime(t) = -A\, \omega \sin(\omega\cdot t)$ .

The restoring acceleration at time $t$ would be:

$\displaystyle \mathbf{a}(t) = \mathbf{v}^\prime(t) = -A\, \omega^2 \cos(\omega\cdot t)$ .

Assume that the spring has zero mass. By Newton's Second Law of motion, the restoring force at time $t$ would be:

$\begin{aligned}& \mathbf{F}(t) \\ &= m(\text{chair}) \cdot \mathbf{a}(t) \\&= -m(\text{chair}) \, A\, \omega^2 \cos(\omega \cdot t)\end{aligned}$ .

Apply Hooke's Law to find the spring constant, $k$ :

$\begin{aligned} k & = -\frac{\mathbf{F}}{\mathbf{x}} \\ &= -\left(\frac{-m(\text{chair}) \, A\, \omega^2 \cos(\omega \cdot t)}{A\cos(\omega \cdot t)}\right) \\ &= \omega^2 \cdot m(\text{chair}) \end{aligned}$ .

Again, $\omega$ stands for the angular frequency of this oscillation, where

$\displaystyle \omega = \frac{2\pi}{T}$ .

Before proceeding, note how $A$ was eliminated from the ratio (as expected.) Additionally, $t$ is also eliminated from the ratio. In other words, the spring constant is "constant" at all time. That agrees with the assumption that this spring is indeed ideal. Back to $k$ :

$\begin{aligned} k & = -\frac{\mathbf{F}}{\mathbf{x}} \\ &= \cdots \\ &= \omega^2 \cdot m(\text{chair}) \\ &= \left(\frac{2\pi}{T}\right)^2 \cdot m(\text{chair}) \\ &= \left(\frac{2\pi}{1.00\; \rm s}\right)^2 \times 36.4\; \rm kg\end{aligned}$ .

Side note on the unit of $k$ :

$\begin{aligned} & 1\; \rm kg \cdot s^{-2} \\ &= 1\rm \; \left(kg \cdot m \cdot s^{-2}\right) \cdot m^{-1} \\ &= 1\; \rm N \cdot m^{-1}\end{aligned}$ .

6 0

3 years ago

2. How important salad dressings in a salad?​

2. How important salad dressings in a salad?