A vector is a quantity which has actually the magnitude of the quantity and also the direction for the finish expression of the amount whereas the units that call for only the magnitude of the amount for its expression, they are called as the scalar quantities.

You are watching: Given the vector a⃗ =4.00i^+7.00j^ , find the magnitude of the vector.

The magnitude of the vector of any quantity denotes the amount of the specific amount hosted by the vector.

The magnitude of a vector is calculated as: …… (1)

Substitute for and also for in equation (1). Thus, the magnitude of the vector is or .

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nlinux.org Details:

Chapter: Vectors and Scalars

Subject: Physics

Keywords: Vectors, magnitude, direction, scalar, require direction, r epresentation, physical quantity, amount of quantity, physical amount, 4i+7j.

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Triss <41>8 months ago
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nlinux.org:

|A| = 8.06

Explanation:

Given that

Vector A, We should uncover the magnitude of the vector. Let the vector is R = ai + bj. The magnitude of this vector is offered by : In this provided question, a = 4 and also b = 7

The magnitude of vector A is given by : |A| = 8.06

So, the magnitude of offered vector is 8.06. Hence, this is the forced solution.

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evablogger <386>

Top part: The question GIVES you the formula to usage, and also all the numbers to fill right into the formula.

The stress and anxiety in the string is the "F" in the formula F = m v² / r .

The "m" is the mass of the rock out at the finish of the string, the "v" is the rate of the rock as it"s going roughly the circle at the finish of the string, and also the "r" is the length of the string ... the radius of the circle.

This question GIVES you the "m", the "v", and also the "r", and it desires you to find the "F". All you need to carry out is create the numbers in area of the letters in the formula, and also "F" will certainly nearly calculate itself and also jump up off the paper at you.

F = m v² / r

F = (1 kg) (4 mtr/s)² / (1 mtr)

F = (1 · 4² / 1) (kg · mtr²) / (s² · mtr)

F = 16 kg·mtr/s²

F = 16 Newtons

= = = = =

Bottom half, spinning one more rock on the end of an additional string, 4 questions:

Same formula: F = m v² / r

The "m" is the mass of the rock out at the finish of the string, the "v" is the rate of the rock as it"s going approximately the circle at the finish of the string, and the "r" is the size of the string ... the radius of the circle. The "F" in the formula is the tension in the string.

Before we start nlinux.orging the questions, let"s discover the stress in the string NOW, before anypoint changes:

F = m v² / r

F = (2 kg) (3 mtr/s)² / (3 mtr)

F = (2 · 9 / 3) Newtons

F = 6 Newtons

Now, All of these 4 questions ask just how the anxiety in the string would certainly change if the mass, the speed, or the length transforms. So there"s another point to perform prior to we jump right into the questions: Look at the formula, and also view what happens to F once m, v, or r changes.

F = m · v² / r

mass -- "m" multiplies everything else on the ideal side of the formula, so if you multiply the mass by any kind of number, then "F" is multiplied by the very same number.

rate (v) -- everything on the right side of the formula is multiplied by the square of v, so if we multiply v by any type of number, then F gets multiplied by the square of that number.

radius (length) -- The length of the string is in the denominator of the formula, so if we multiply r by any type of number, then F gets split by that number.

Now we"re ready to blast through the four inquiries (and also then I guess we"ll drink the wine):

a). Twice the mass ... That renders F twice as huge, so the tension changes from 6N to 12N.

b). Twice the rate ... That provides F (2²) = 4 times as substantial, so the tension alters from 6N to 24N.

c). Twice the size of string (r) ... That divides F by 2, so it transforms from 6N to 3N.

See more: What Is The Purpose Of A Pentad ? What Is The Purpose Of A Pentad In Writing

d). Change everything: Twice the mass --> Double F. Twice the rate --> 4 times F . Twice the length --> 1/2 F.

Puttum all together: (2) · (4) · (1/2) F . That"s 4 x F . So the anxiety alters from 6N to 24N.