The micrometer (1 μm) is often called the micron. (a) How many microns make up 3.0 km? (b) How many centimeters equal 3.0 μm? (c
1 answer:
Answer:
3 x 10⁻⁹km
3 x 10⁻⁴cm
2.73 x 10⁶μm
Explanation:
A micron is a subunit of measurement usually for length dimensions.
1μm = 1 x 10⁻⁶m
a. How many microns make up 3km;
Now convert to meter first;
1000m = 1km
So, 3km will be made up of 3000m
So;
1 x 10⁻⁶m = 1μm
3000m = =
= 3 x 10⁻⁹km
b. How many centimeters equal 3.0 μm?
Since;
1μm = 1 x 10⁻⁶m
3μm = 3 x 1 x 10⁻⁶ = 3 x 10⁻⁶m
So;
100cm = 1m;
1m = 100cm
3 x 10⁻⁶m = 3 x 10⁻⁶ x 10² = 3 x 10⁻⁴cm
c. How many microns are in 3.0 yd?
1yd = 0.91m
3yd = 3 x 0.91 = 2.73m
So;
1 x 10⁻⁶m = 1μm
2.73m will give = 2.73 x 10⁶μm
You might be interested in
There is a missing data in the text of the problem (found on internet):
"with force constant<span> k=</span>450N/<span>m"
a) the maximum speed of the glider
The total mechanical energy of the mass-spring system is constant, and it is given by the sum of the potential and kinetic energy:
</span>
<span>where
k is the spring constant
x is the displacement of the glider with respect to the spring equilibrium position
m is the glider mass
v is the speed of the glider at position x
When the glider crosses the equilibrium position, x=0 and the potential energy is zero, so the mechanical energy is just kinetic energy and the speed of the glider is maximum:
</span>
<span>Vice-versa, when the glider is at maximum displacement (x=A, where A is the amplitude of the motion), its speed is zero (v=0), therefore the kinetic energy is zero and the mechanical energy is just potential energy:
</span>
<span>
Since the mechanical energy must be conserved, we can write
</span>
<span>from which we find the maximum speed
</span>
<span>
b) </span><span> the </span>speed<span> of the </span>glider<span> when it is at x= -0.015</span><span>m
We can still use the conservation of energy to solve this part.
The total mechanical energy is:
</span>
<span>
At x=-0.015 m, there are both potential and kinetic energy. The potential energy is
</span>
<span>And since
</span>
<span>we find the kinetic energy when the glider is at this position:
</span>
<span>And then we can find the corresponding velocity:
</span>
<span>
c) </span><span>the magnitude of the maximum acceleration of the glider;
</span>
For a simple harmonic motion, the magnitude of the maximum acceleration is given by
where
is the angular frequency, and A is the amplitude.
The angular frequency is:
and so the maximum acceleration is
d) <span>the </span>acceleration<span> of the </span>glider<span> at x= -0.015</span><span>m
For a simple harmonic motion, the acceleration is given by
</span>
<span>where x(t) is the position of the mass-spring system. If we substitute x(t)=-0.015 m, we find
</span>
<span>
e) </span><span>the total mechanical energy of the glider at any point in its motion. </span><span>
we have already calculated it at point b), and it is given by
</span>
"with force constant<span> k=</span>450N/<span>m"
a) the maximum speed of the glider
The total mechanical energy of the mass-spring system is constant, and it is given by the sum of the potential and kinetic energy:
</span>
<span>where
k is the spring constant
x is the displacement of the glider with respect to the spring equilibrium position
m is the glider mass
v is the speed of the glider at position x
When the glider crosses the equilibrium position, x=0 and the potential energy is zero, so the mechanical energy is just kinetic energy and the speed of the glider is maximum:
</span>
<span>Vice-versa, when the glider is at maximum displacement (x=A, where A is the amplitude of the motion), its speed is zero (v=0), therefore the kinetic energy is zero and the mechanical energy is just potential energy:
</span>
<span>
Since the mechanical energy must be conserved, we can write
</span>
<span>from which we find the maximum speed
</span>
<span>
b) </span><span> the </span>speed<span> of the </span>glider<span> when it is at x= -0.015</span><span>m
We can still use the conservation of energy to solve this part.
The total mechanical energy is:
</span>
<span>
At x=-0.015 m, there are both potential and kinetic energy. The potential energy is
</span>
<span>And since
</span>
<span>we find the kinetic energy when the glider is at this position:
</span>
<span>And then we can find the corresponding velocity:
</span>
<span>
c) </span><span>the magnitude of the maximum acceleration of the glider;
</span>
For a simple harmonic motion, the magnitude of the maximum acceleration is given by
where
The angular frequency is:
and so the maximum acceleration is
d) <span>the </span>acceleration<span> of the </span>glider<span> at x= -0.015</span><span>m
For a simple harmonic motion, the acceleration is given by
</span>
<span>where x(t) is the position of the mass-spring system. If we substitute x(t)=-0.015 m, we find
</span>
<span>
e) </span><span>the total mechanical energy of the glider at any point in its motion. </span><span>
we have already calculated it at point b), and it is given by
</span>