Suppose you watch a leaf bobbing up and down as ripples pass it by in a pond. You notice that it does two full up and down bobs
1 answer:
Answer:
The frequency of the ripples is 2Hz, and their period is 0.5 seconds.
Explanation:
Since the ripples on the pond are making the leaf oscillate up and down at a rate of two times per second, we can calculate the period T and the frequency f of the ripples on the pond.
The frequency, by definition, is the number of waves per unit of time. In this case, we have two waves per second, so the frequency is 2s⁻¹, or 2Hz.
The period is the inverse of the frequency, so
Then, the period is equal to 0.5 seconds.
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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>
Answer:
c.) 25 N
Explanation:
We find the volume of the brick, knowing that the volume of a cube is given by the formula:
being l the side of the cube, which in this case is 10 cm or 0,1 m. Now we find the mass of the object, knowing the density and the Volume of the cube:
We find the weight by multiplying the mass of the object with the gravity constant.