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3 years ago

Two vectors A and B have components (0,1) and (-1,3), respectively. What is magnitude of the sum of these two vectors?

1 answer:

4 0

We first add the x and y components of the vector to get the x and y components of the resultant vector:
(0 - 1, 1 + 3)
-1 , 4
magnitude = √(1² + 4²)
magnitude = 4.12
The answer is B

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A flat loop of wire consisting of a single turn of cross-sectional area 8.20 cm2 is perpendicular to a magnetic field that incre

olga nikolaevna [1]

Answer:

The induced current is $I = 6.25*10^{-4} \ A$

Explanation:

From the question we are told that

The number of turns is $N = 1$

The cross-sectional area is $A = 8.20 cm^2 = 8.20 * 10^{-4} \ m^2$

The initial magnetic field is $B_i = 0.500 \ T$

The magnetic field at time = 1.02 s is $B_t = 2.60 \ T$

The resistance is $R = 2.70\ \Omega$

The induced emf is mathematically represented as

$\epsilon = - N * \frac{ d\phi }{dt}$

The negative sign tells us that the induced emf is moving opposite to the change in magnetic flux

Here $d\phi$ is the change in magnetic flux which is mathematically represented as

$d \phi = dB * A$

Where dB is the change in magnetic field which is mathematically represented as

$dB = B_t - B_i$

substituting values

$dB = 2.60 - 0.500$

$dB = 2.1 \ T$

Thus

$d \phi = 2.1 * 8.20 *10^{-4}$

$d \phi = 1.722*10^{-3} \ weber$

$|\epsilon| = 1 * \frac{ 1.722*10^{-3}}{1.02}$

$|\epsilon| = 1.69 *10^{-3} \ V$

The induced current i mathematically represented as

$I = \frac{\epsilon}{ R }$

substituting values

$I = \frac{1.69*10^{-3}}{ 2.70 }$

$I = 6.25*10^{-4} \ A$

7 0

4 years ago

a 45kg boy is holding a 12kg pumpkin while standing on ice skates on a smooth frozen pond. the boy tosses the pumpkin with a hor

irga5000 [103]

Let's split the problem into two parts, and let's solve it by using conservation of momentum.

1) Let's analyze the moment when the boy tosses the pumpkin. Before this moment, the boy is standing with the pumpkin, so with speed v=0 and therefore the total momentum of the system (boy+pumpkin) is zero.
After he tosses the pumpkin, the boy will start to move with speed $v_b$ and the pumpkin starts to move with speed $v_p=2.8 m/s$ . The momentum of the boy is $m_b v_b$ (with $m_b =45 kg$ being the mass of the boy), while the momentum of the pumpkin is $m_p v_p$ (where $m_p=12 kg$ is the mass of the pumpkin). Since the total momentum must be equal to zero (because the total momentum cannot change), then we can write
$m_b v_b + m_p v_p =0$
From which we find
$v_b = - \frac{m_p v_p}{m_b}=- \frac{(12 kg)(2.8 m/s)}{45 kg} =-0.75 m/s$
and this is the speed of the boy, and the negative sign means he's moving in the opposite direction of the pumpkin.

2) Now let's focus on the entire system (boy+pumpkin+girl). Initially, the total momentum of this system is zero, because both the boy (holding the pumpkin) and the girl are still. So, the total momentum after the girl catches the pumpkin must be still zero.
After this moment, the boy has a momentum of $m_b v_b$ , while the girl has momentum $(m_g+m_p)v_g$ where $m_g=37 kg$ is the girl mass $v_g$ is the girl speed. Here we use $m_g+m_p$ because the girl is holding the pumpkin now. Therefore, the conservation of momentum becomes
$m_bv_b + (m_g+m_p)v_g =0$
and so
$v_g = - \frac{m_b v_b}{m_g+m_p} =- \frac{(45 kg)(-0.75 m/s)}{37 kg+12 kg} =0.69 m/s$
and this is the girl's speed, with positive sign so with same direction of the pumpkin initial direction.

6 0

4 years ago

How is oxygen purified?

xxTIMURxx [149]

Oxygen is obtained on a commercial scale through the liquefaction and distillation of ambient air at air separation plants. A secondpurification process may be necessary if ultra-high purity levels are required. High-purity oxygen can also be produced through the electrolysis of water.

3 0

4 years ago

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A man walks 30 m to the west, then 5 m to the east in 45 seconds. What is his average speed?

dsp73

The average speed is 0.55 m/s

<h3>What was his displacement?</h3>

Displacement is defined as the change in position of an object.

Mathematically,

D = Initial value - Final Value

D = 30 - 5 = 25m

Now , We have to find the average velocity,

Average velocity is calculated by the formula V = D/t,

where V equals the average velocity, D equals total displacement and t equals total time.

V = D/t

V = 25 m / 45s

V = 0.55 m/s

So , The average speed is o.55 m/s

learn more about average speed:brainly.com/question/9834403

#SPJ1

5 0

2 years ago

Doctors use the radioactive isotope chromium-51 to label red blood cells in the human body. Chromium-51 gives off relatively ___

dimaraw [331]

harmless, a sheet of paper
Alpha particles do not possess a high amount of energy and are not very ionizing, since they have a high mass. This makes them relatively safer to work with.

6 0

3 years ago

Read 2 more answers