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2 years ago

A standard 1 kilogram weight is a cylinder 51.0 mm in height and 42.0 mm in diameter. Determine the density of the material

Physics

1 answer:

worty [1.4K]2 years ago

3 0

Answer:

14160 kg/m^3

Explanation:

First of all, we need to find the volume of the cylinder.

The volume of the cylinder is given by:

$V=\pi r^2 h$

where:

$r=\frac{d}{2}=\frac{42.0 mm}{2}=21.0 mm=0.021 m$ is the radius

$h=51.0 mm=0.051 m$ is the height

Substituting, we find

$V=\pi (0.021 m)^2 (0.051 m)=7.1 \cdot 10^{-5} m^3$

And the density is given by

$d=\frac{m}{V}$

where m = 1 kg is the mass. Substituting, we find

$d=\frac{1 kg}{7.1\cdot 10^{-5} m^3}=14,160 kg/m^3$

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2 years ago

A jogger runs 10.0 blocks do east, 5.0 blocks due South, and another two. Zero blocks do east. Assume all blocks are equal size,

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d1 = 10 blocks East

d2 = 5 blocks South

d3 = 2 blocks East

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1 year ago

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2 years ago

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. O

alexira [117]

Answer:

v_wind = 101.46 km / h , θ = 61.8

Explanation:

This is a velocity composition exercise.

Let's do the problem in parts. Let's start by knowing the speed of the plane without air.

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v = 750 / 3.14

v = 238.85 km / h

This is the speed of the plane relative to the Earth and it does not change.

In the second part, when there is wind, the travel time is greater than when there is no wind, therefore the wind delays the plane. To be more general, suppose that the wind has two components vₓ and $v_{y}$

Let's use trigonometry to find the components of the plane's speed

cos θ = v_N / v

sin θ = v_W / v

v_N = v cos θ

v_W = v sin θ

let's calculate

V _N = 238.85 cos 22 = 221.46 km / h

v_W = -238.85 sin 22 = -89.47

the negative sign is because the plane is going west and the positive sign is the east direction.

As it indicates that the destination of the avine is towards the north, the x component of the wind must be

vₓ - v_W = 0

vₓ = v-w

vₓ = 89.47 km / h

in the direction to the East.

Now let's analyze the component of the wind in the Nort-South direction,

Indicate the travel time, let's calculate the speed that the component must have the speed of the plane

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v_total = 173.61 km / h

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v_total = v_n - vy

vy = v_n - v_total

vy = 221.46 - 173.61

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Let's use the Pythagorean Theorem, to find the magnitude

v_wind² = vₓ² + vy²

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v_wind = 101.46 km / h

the address will then be found using trigonometry

θ = Vy / vx

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90- θtea = 90- 28.2

θ = 61.8

East of South

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1 year ago