Ask question

Ask question

All categories

2 years ago

10

A vector is expressed in polar notation as A⃗ = ( 35.0 N, 37 ∘) Calculate the components of the vector, and enter them (separat

ed by a comma) in the answer box to express the vector in rectangular notation.

1 answer:

Aleks04 [339]2 years ago

7 0

Answer:

A = (27.95 N, 21 N)

Explanation:

The polar co-ordinates are given as:

(r,θ) = (35 N, 37°)

Now, to convert this into polar co-ordinates (x, y), we will use following relations:

r² = x² + y²

(35)² = x² + y²

1225 = x² + y² ----------- equation (1)

and

tan θ = y/x

tan 37° = y/x

y = 0.753 x ------------------- equation (2)

Substituting this value in equation (1):

1225 = x² + (0.753 x)²

1225 = 1.567 x²

x² = 1225/1.567

x = √781.32

x = 27.95 N

using this value in equation (2)

y = (0.753)(27.95 N)

y = 21 N

Therefore, the vector can be represented in polar co-ordinates as:

<u>A = (27.95 N, 21 N)</u>

You might be interested in

A horizontal force of 92.7 N is applied to a 40.5 kg crate on a rough, level surface. If the crate accelerates at 1.13 m/s2, wha

lord [1]

Answer:

The value is $F_f = 46.935 \ N$

Explanation:

From the question we are told that

The magnitude of the horizontal force is $F = 92.7 \ N$

The mass of the crate is $m = 40.5 \ kg$

The acceleration of the crate is $a = 1.13 \ m/s$

Generally the net force acting on the crate is mathematically represented as

$F_{net} = F - F_f = ma$

Here $F_f$ is force of kinetic friction (in N) acting on the crate

So

$92.7 - F_f = 40.5 * 1.13$

=> $F_f = 46.935 \ N$

5 0

2 years ago

A train starts at rest in a station and accelerates at a constant 0.987 m/s2 for 182 seconds. Then the train decelerates at a co

algol [13]

Answer:

$\displaystyle X_T=66.6\ km$

Explanation:

<u>Accelerated Motion </u>

When a body changes its speed at a constant rate, i.e. same changes take same times, then it has a constant acceleration. The acceleration can be positive or negative. In the first case, the speed increases, and in the second time, the speed lowers until it eventually stops. The equation for the speed vf at any time t is given by

$\displaystyle V_f=V_o+a\ t$

where a is the acceleration, and vo is the initial speed .

The train has two different types of motion. It first starts from rest and has a constant acceleration of $0.987 m/s^2$ for 182 seconds. Then it brakes with a constant acceleration of $-0.321 m/s^2$ until it comes to a stop. We need to find the total distance traveled.

The equation for the distance is

$\displaystyle X=V_o\ t+\frac{a\ t^2}{2}$

Our data is

$\displaystyle V_o=0,a=0.987m/s^2,\ t=182\ sec$

Let's compute the first distance X1

$\displaystyle X_1=0+\frac{0.987\times 182^2}{2}$

$\displaystyle X_1=16,346.7\ m$

Now, we find the speed at the end of the first period of time

$\displaystyle V_{f1}=0+0.987\times 182$

$\displaystyle V_{f1}=179.6\ m/s$

That is the speed the train is at the moment it starts to brake. We need to compute the time needed to stop the train, that is, to make vf=0

$\displaystyle V_o=179.6,a=-0.321\ m/s^2\ ,V_f=0$

$\displaystyle t=\frac{v_f-v_o}{a}=\frac{0-179.6}{-0.321}$

$\displaystyle t=559.5\ sec$

Computing the second distance

$\displaystyle X_2=179.6\times559.5\ \frac{-0.321\times 559.5^2}{2}$

$\displaystyle X_2=50,243.2\ m$

The total distance is

$\displaystyle X_t=x_1+x_2=16,346.7+50,243.2$

$\displaystyle X_t=66,589.9\ m$

$\displaystyle \boxed{X_T=66.6\ km}$

8 0

3 years ago

Find the ratio of intensities in 4 different sets of red to violet spectral satellites in Raman scattering spectra of CCl4 molec

Vlad1618 [11]

Complete Question

Find the ratio of intensities in 4 different sets of red to violet spectral satellites in Raman scattering spectra of CCl4 molecules at T=27C temperature if corresponding resonant infrared frequencies (equivalent to frequencies of nuclei vibrations) of CCl4 molecule are 217, 315, 457 and 774 cm-1 . (Note: Wavenumber N in cm-1 is defined as $N=1/\lambda\ cm^{-1}$ )

Answer:

The ratio of intensities is $I_1 : I_2 : I_3 : I_4 = 217 : 315 : 457 : 774$

Explanation:

From the question we are told that

The number of sets of satellite is $n = 4$

The temperature is $T = 27 ^oC$

The resonant infrared frequencies are $f_1 = 217 cm^{-1}$

$f_2 = 315 cm^{-1}$

$f_3 = 457 cm^{-1}$

$f_4 = 774 cm^{-1}$

From the question we see that the wave number also has a unit of $cm^{-1}$ hence the value of the wave numbers of the molecule are

$N_1 = 217 cm^{-1}$

$N_2 = 315 cm^{-1}$

$N_3 = 457 cm^{-1}$

$N_4 = 774 cm^{-1}$

Generally intensity is mathematically represented as

$I = \frac{nhc}{A \lambda }$

Here we see that I varies inversely with wavelength i,.e

$I \ \ \alpha \ \ \frac{1}{\lambda }$

From the question we are told that the wave number is mathematically represented as

$N = \frac{1}{\lambda }$

Therefore

$I \ \ \alpha \ \ N$

This implies that the ratio of intensity in first set to that of second set to that of third set to that of fourth set is equal to the ratio of the wavenumber in the first set to that of the second set to that of third set to that of fourth

This is mathematically represented as

$I_1 : I_2 : I_3 : I_4 = N_1 : N_2 : N_3 : N_4$

Substituting values

$I_1 : I_2 : I_3 : I_4 = 217 : 315 : 457 : 774$

5 0

3 years ago

How much force is required to hold an empty carton of volume 1.5 L beneath the surface in a sink of water? Assume the carton is

Gwar [14]

Answer:

It will require 14.715 N of force to hold the cartoon beneath the water.

Explanation:

Given the the volume of cartoon is 1.5 liters.

We need to find the force required to hold this cartoon beneath the water.

As we know from the Archimedes principle that the net force is equal to the volume of liquid displaced.

Given volume of the cartoon is 1.5 liters. So, 1.5 liters of water will be displaced.

And we know the density of the water is $1000\ kg/m^3$ . That is $1\ kg/L$

And $g=9.81\ m/s^2$

$F_N=\rho Vg\\F_N=1\times 1.5\times 9.81\\F_N=14.715\ N$

So, it will require 14.715 N of force to hold 1.5 liter volume of cartoon beneath the water.

6 0

2 years ago

What would lack of calcium do to bones

timurjin [86]

It would weaken the bones and thy would not be as strong or tough

4 0

3 years ago

Read 2 more answers