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3 years ago

What is the energy equivalent of an object with a mass of 25 kg?

Physics

1 answer:

Amanda [17]3 years ago

3 0

Answer:

$2.25\cdot 10^{18} J$

Explanation:

The energy equivalent of the mass of an object can be calculated by using the Einstein's equation:

$E=mc^2$

where

E is the energy

m is the rest mass of the object

$c=3\cdot 10^8 m/s$ is the speed of light

For this object

m = 25 kg

So its equivalent energy is:

$E=(25)(3\cdot 10^8)^2=2.25\cdot 10^{18} J$

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The circumference of a sphere was measured to be

professor190 [17]

To solve this problem we will apply the concepts related to the calculation of the surface, volume and error through the differentiation of the formulas given for the calculation of these values in a circle. Our values given at the beginning are

$\phi = 76cm$

$Error (dr) = 0.5cm$

The radius then would be

$\phi = 2\pi r \\76cm = 2\pi r\\r = \frac{38}{\pi} cm$

And

$\frac{d\phi}{dr} = 2\pi \\d\phi = 2\pi dr \\0.5 = 2\pi dr$

PART A ) For the Surface Area we have that,

$A = 4\pi r^2 \\A = 4\pi (\frac{38}{\pi})^2\\A = \frac{5776}{\pi}$

Deriving we have that the change in the Area is equivalent to the maximum error, therefore

$\frac{dA}{dr} = 4\pi (2r) \\dA = 4r (2\pi dr)$

Maximum error:

$dA = 4(\frac{38}{\pi})(0.5)$

$dA = \frac{76}{\pi}cm^2$

The relative error is that between the value of the Area and the maximum error, therefore:

$\frac{dA}{A} = \frac{\frac{76}{\pi}}{\frac{5776}{\pi}}$

$\frac{dA}{A} = 0.01315 = 1.31\%$

PART B) For the volume we repeat the same process but now with the formula for the calculation of the volume in a sphere, so

$V = \frac{4}{3} \pi r^3$

$V = \frac{4}{3} \pi (\frac{38}{\pi})^3$

$V = \frac{219488}{3\pi^2}$

Therefore the Maximum Error would be,

$\frac{dV}{dr} = \frac{4}{3} 3\pi r^2$

$dV = 2r^2 (2\pi dr)$

$dV = 4r^2 (\pi dr)$

Replacing the value for the radius

$dV = 4(\frac{38}{\pi})^2(0.5)$

$dV = \frac{2888}{\pi^2} cm^3$

And the relative Error

$\frac{dV}{V} = \frac{ \frac{2888}{\pi^2}}{ \frac{219488}{3\pi^2} }$

$\frac{dV}{V} = 0.03947$

$\frac{dV}{V} = 3.947\%$

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3 years ago

if you dig a hole through the earth, from one hemisphere to the other, and drop a tennis ball into it, would it get stuck at the

tia_tia [17]

Answer:

Depending on which hemisphere it is, like western to eastern, It would most likely get stuck at the center. You would also have to put more things into thought like acceleration, velocity, and speed.

BUT since the question asked "would it pop out the other side?", I'm assuming it's talking about northern to southern hemisphere. so in that case it would pop out the other side since gravity makes things go downwards.

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3 years ago

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10. How much total work do you do when you lift a 50 kg microwave 1.0 m off the ground and then push it 1.0 m

Mariulka [41]

Work formula:

$W = Fd\cos(\theta)$

F = 50N, d = 1.0 m

When you lift something straight up, the angle of the force is 90º

cos(90º) is 0, so there's no work done when you lift the microwave off the ground

$W = (50N)(1.0)(0) = 0$

F = 50N, d = 1.0 m

When you push the microwave, the angle is 0º and cos(0º) is 1. So there is work done here:

$W = (50 N)(1.0m)(1)$

$W = 50$

total work = 50 joules

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3 years ago

Why is a shadow formed

a_sh-v [17]

Answer:

Shadows are made by blocking light. Light rays travel from a source in straight lines. If an opaque (solid) object gets in the way, it stops light rays from traveling through it. The size and shape of a shadow depend on the position and size of the light source compared to the object.

Explanation:

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3 years ago

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A bat can detect small objects such as an insect whose size is approximately equal to the wavelength of the sound the bat makes.

slamgirl [31]

Answer:

size of insect = wavelength = 16.1 mm

Explanation:

Since the bat can detect the size of small insects which are of size equal to the wavelength of sound in air

So here we can say that the wavelength of sound is the ratio of speed of sound and its frequency

here we know that