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3 years ago

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A carver begins work on the following block of granite that weighs 2700 g. The dimensions of the block are 20 cm, 5 cm and 10 cm

. What is the density of the granite in g/cm³?

1 answer:

CaHeK987 [17]3 years ago

6 0

Answer:

$\text { "Density" of the given granite block is } 2.7 \mathrm{g} / \mathrm{cm}^{3} \text { . }$

Explanation:

Density of an object is defined as the mass occupied per unit volume. “Density” is represented by “ρ”. Mathematically, $\rho=\frac{m}{v}$ where, “m" mass of an object and "v" is volume of an object.

Given that,

Dimensions of the block are 20 cm, 5 cm and 10 cm.

$\text { Volume of the block is } l \times b \times h$

$\text { Volume of the block is } 20 \times 5 \times 10$

$\text { Volume of the block is } 1000 \mathrm{cm}^{3} \text { . }$

Mass of the block is 2700 g.

Substitute the given values in $\rho=\frac{m}{v}$ to find density of a block.

$\rho=\frac{2700}{1000}$

$\rho=2.7 \mathrm{g} / \mathrm{cm}^{3}$

$\text { "Density" of the given granite block is } 2.7 \mathrm{g} / \mathrm{cm}^{3}$

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Let's break the question into two parts:

1) The force needed in Ramp scenario.
2) The effort force needed in the lever scenario.

1. Ramp Scenario:
In an incline, the only component of cart's weight(mg) that is in the direction of motion is $mgsin \alpha$ . Therefore the effort force in this case must be equal or greater than $mgsin \alpha$ .

Now we need to find $\alpha$ . $\alpha$ is the angle between the incline of the ramp and the ground.

Since the height is 5m and the length of the ramp is 8m, $sin \alpha$ would be 5/8 or 0.625. Now that you have $sin \alpha$ , mutiple it with mg.

=> m*g* $sin \alpha$ = 20 * 10 * 5 / 8. (Taking g = 10 m/s² for simplicity) = 125N
Therefore, the minimum Effort force you would require in this case is 125N.

2. Lever Scenario:
Just apply "moment action" in this case, which is:
$F_{e} d_{e} = F_{r} d_{r}$

$F_{e}$ = ?

$F_{r}$ = mg = 20 * 10 = 200N
$d_{e}$ = 10m
$d_{r}$ = 1m

Plug-in the values in the above equation:
$F_{e}$ = 200/10= 20N

As 20N << 125N, the best choice is to use lever.

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A positively charged wire with uniform charge density +λ lies along the x-axis and a negatively charged wire with uniform charge

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Answer:

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Explanation:

The electric field created by an infinitely long wire can be found by Gauss' Law.

$\int \vec{E}d\vec{a} = \frac{Q_{enc}}{\epsilon_0}\\E2\pi r h = \frac{\lambda h}{\epsilon_0}\\\vec{E} = \frac{\lambda}{2\pi\epsilon_0 r} \^r$

For the electric field at point (x,y), the superposition of electric fields created by both lines should be calculated. The distance 'r' for the first wire is equal to 'y', and equal to 'x' for the second wire.

$\vec{E} = \vec{E}_1 + \vec{E}_2 = \frac{\lambda}{2\pi\epsilon_0 y}(\^y) + \frac{-\lambda}{2\pi\epsilon_0 x}(\^x)\\\vec{E} = \frac{\lambda}{2\pi\epsilon_0 y}(\^y) - \frac{\lambda}{2\pi\epsilon_0 x}(\^x)\\\vec{E} = \frac{\lambda}{2\pi\epsilon_0}[\frac{1}{y}(\^y) - \frac{1}{x}(\^x)]$

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3 years ago

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Answer:

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Explanation:

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Magnetic field = 0.45 T

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Put the value into the formula

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