7. A perfect cube has a width of 2 cm. What is the cube's volume? Show your work!

If you subtract vector 3.7 cm at 45° North of East from vector 4.5 cm at 57° West of North using a scale drawing, what is the re

Gelneren [198K]

The resultant vector is 5.2 cm at a direction of 12⁰ west of north.

<h3>Resultant of the two vectors</h3>

The resultant of the two vectors is calculated as follows;

R = a² + b² - 2ab cos(θ)

where;

θ is the angle between the two vectors = 45° + (90 - 57) = 78⁰
a is the first vector
b is the second vector

R² = (3.7)² + (4.5)² - (2 x 3.7 x 4.5) cos(78)

R² = 27.02

R = 5.2 cm

<h3>Direction of the vector</h3>

θ = 90 - 78⁰

θ = 12⁰

Thus, the resultant vector is 5.2 cm at a direction of 12⁰ west of north.

Learn more about resultant vector here: brainly.com/question/28047791

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3 0

10 months ago

3. A certain horizontal east-west lined wire has a mass of 0.2kg per meter of length and carries a current I. Impressed on the w

erica [24]

Answer:

i = 4.9 A

Explanation:

The expression for the magnetic force in a wire carrying a current is

F = i L x B

bold letters indicate vectors.

The direction of the cable is towards the East, the direction of the magnetic field is towards the North, so the vector product is in the vertical direction (z-axis) upwards and the weight of the cable is vertical downwards. Let's apply the equilibrium condition

F - W = 0

i L B = m g

They indicate the linear density of the cable λ = 0.2 kg / m

λ = m / L

m = λ L

we substitute

i B = λ g

i = $\frac{ \lambda \ g}{B}$

let's calculate

i = 0.2 9.8 / 0.4

i = 4.9 A

3 0

2 years ago

A railroad car moving at a speed of 3.46 m/s overtakes, collides and couples with two coupled railroad cars moving in the same d

I am Lyosha [343]

Answer:

$2.09\ \text{m/s}$

$22298.4\ \text{J}$

Explanation:

m = Mass of each the cars = $1.6\times 10^4\ \text{kg}$

$u_1$ = Initial velocity of first car = 3.46 m/s

$u_2$ = Initial velocity of the other two cars = 1.4 m/s

v = Velocity of combined mass

As the momentum is conserved in the system we have

$mu_1+2mu_2=3mv\\\Rightarrow v=\dfrac{u_1+2u_2}{3}\\\Rightarrow v=\dfrac{3.46+2\times 1.4}{3}\\\Rightarrow v=2.09\ \text{m/s}$

Speed of the three coupled cars after the collision is $2.09\ \text{m/s}$ .

As energy in the system is conserved we have

$K=\dfrac{1}{2}mu_1^2+\dfrac{1}{2}2mu_2^2-\dfrac{1}{2}3mv^2\\\Rightarrow K=\dfrac{1}{2}\times 1.6\times 10^4\times 3.46^2+\dfrac{1}{2}\times 2\times 1.6\times 10^4\times 1.4^2-\dfrac{1}{2}\times 3\times 1.6\times 10^4\times 2.09^2\\\Rightarrow K=22298.4\ \text{J}$

The kinetic energy lost during the collision is $22298.4\ \text{J}$ .

6 0

2 years ago

What are applications of zeroth law of thermodynamics?

Harrizon [31]

Answer:

Applications of zeroth law of thermodynamics:

1. When we get very hot food, we wait to make it normal. In this case, hot food exchanges heat with surrounding and brings equilibrium.

2. We keep things in the fridge and those things come equilibrium with fridge temperature.

3. Temperature measurement with a thermometer or another device.

4. In the HVAC system, sensors or thermostats are used to indicate temperature. It always comes in a thermal equilibrium with room temperature.

5. If you and the swimming pool you’re in are at the same temperature, no heat is flowing from you to it or from it to you (although the possibility is there). You’re in thermal equilibrium.

6 0

2 years ago

What's the relationship between magnetism and birds?

neonofarm [45]

Answer:

can detect axis of magnetic field

Explanation:

3 0

1 year ago

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