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Art [367]
3 years ago
8

A 2-kg object is moving horizontally across a frictionless surface with a speed of 4 m/s. How much force is required to keep the

object moving at this speed and in this direction?​
Physics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

  none

Explanation:

Newton's first law says an object in motion will stay in motion at the same speed and direction unless acted upon by some force.

No force is necessary for the object to keep its speed and direction on a frictionless surface.

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The radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 40 mm?
marin [14]

Using <span>r </span> to represent the radius and <span>t </span> for time, you can write the first rate as:

<span><span><span><span>dr</span><span>dt</span></span>=4<span>mms</span></span> </span>

or

<span><span>r=r<span>(t)</span>=4t</span> </span>

The formula for a solid sphere's volume is:

<span><span>V=V<span>(r)</span>=<span>43</span>π<span>r3</span></span> </span>

When you take the derivative of both sides with respect to time...

<span><span><span><span>dV</span><span>dt</span></span>=<span>43</span>π<span>(3<span>r2</span>)</span><span>(<span><span>dr</span><span>dt</span></span>)</span></span> </span>

...remember the Chain Rule for implicit differentiation. The general format for this is:

<span><span><span><span><span>dV<span>(r)</span></span><span>dt</span></span>=<span><span>dV<span>(r)</span></span><span>dr<span>(t)</span></span></span>⋅<span><span>dr<span>(t)</span></span><span>dt</span></span></span> </span>with <span><span>V=V<span>(r)</span></span> </span> and <span><span>r=r<span>(t)</span></span> </span>.</span>

So, when you take the derivative of the volume, it is with respect to its variable <span>r </span> <span><span>(<span><span>dV<span>(r)</span></span><span>dr<span>(t)</span></span></span>)</span> </span>, but we want to do it with respect to <span>t </span> <span><span>(<span><span>dV<span>(r)</span></span><span>dt</span></span>)</span> </span>. Since <span><span>r=r<span>(t)</span></span> </span> and <span><span>r<span>(t)</span></span> </span> is implicitly a function of <span>t </span>, to make the equality work, you have to multiply by the derivative of the function <span><span>r<span>(t)</span></span> </span> with respect to <span>t </span> <span><span>(<span><span>dr<span>(t)</span></span><span>dt</span></span>)</span> </span>as well. That way, you're taking a derivative along a chain of functions, so to speak (<span><span>V→r→t</span> </span>).

Now what you can do is simply plug in what <span>r </span> is (note you were given diameter) and what <span><span><span>dr</span><span>dt</span></span> </span> is, because <span><span><span>dV</span><span>dt</span></span> </span> describes the rate of change of the volume over time, of a sphere.

<span><span><span><span><span>dV</span><span>dt</span></span>=<span>43</span>π<span>(3<span><span>(20mm)</span>2</span>)</span><span>(4<span>mms</span>)</span></span> </span><span><span>=6400π<span><span>mm3</span>s</span></span> </span></span>

Since time just increases, and the radius increases as a function of time, and the volume increases as a function of a constant times the radius cubed, the volume increases faster than the radius increases, so we can't just say the two rates are the same.

7 0
3 years ago
Why is water not used as a liquid in glass thermometers?
Maslowich

Answer:

Water is not able to be used as a thermometer liquid because of its higher freezing point and lower boiling point than the other liquids in general. If water is used in a thermometer, it will start phase variation at 0∘C and 100∘C. This will not help in measuring temperature, beyond this range.

Explanation:

plzzzzzzz Mark my answer in brainlist

3 0
3 years ago
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How does a vacuum flask keep drinks hot? Explain in terms of conduction, convection and radiation.
Flura [38]
Vacum flask has inner layer of glass and outer body of plastic.the glass has a reflective metal layer..when a hot drink is poured into the flask it prevents conduction.tight lid stops the convection.when radiation tries to leave the hot drink the reflective layer of the glass reflects it back so no heat can escape.
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3 years ago
Why is vehicle systems forensics useful today? Cars are less computerized than before More people own cars Devices like smartpho
kvasek [131]

Answer:

Devices like smartphones can interface with cars and leave evidence

Explanation:

Vehicle system forensic relates to digital data stored in a vehicles system.

Bluetooth connection times can be used to figure out at what time the owner was near his car. e.g. between a smart-watch and car infotainment system

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Which observation BEST supports evidence that two different species share a common ancestor? A) they both prey on the same anima
Anna [14]
The answer is definitely C
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3 years ago
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