a 2.5 kg rock is dropped off a 32 m cliff and hits a spring, compressing it 57cm. what is the spring constant
2 answers:
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Answer: The force constant k is 10600 kg/s^2
Step by step:
Use the law of energy conservation. When the elevator hits the spring, it has a certain kinetic and a potential energy. When the elevator reaches the point of still stand the kinetic and potential energies have been transformed to work performed by the elevator in the form of friction (brake clamp) and loading the spring.
Let us define the vertical height axis as having two points: h=2m at the point of elevator hitting the spring, and h=0m at the point of stopping.
The total energy at the point h=2m is:
The total energy at the point h=0m is:
The two Energy values are to be equal (by law of energy conservation), which allows us to determine the only unknown, namely the force constant k:
Answer:
20 m/s westward
Explanation:
Taking eastward as positive direction, we have:
is the velocity of Bill with respect to Amy (which is stationary)
is the velocity of Carlos with respect to Amy
Bill is moving 5 m/s eastward compared to Amy at rest, so the velocity of Bill's reference frame is
Therefore, Carlos velocity in Bill's reference frame will be
and the direction will be westward (negative sign).
Answer:
We can retain the original diffraction pattern if we change the slit width to d) 2d.
Explanation:
The diffraction pattern of a single slit has a bright central maximum and dimmer maxima on either side. We will retain the original diffraction pattern on a screen if the relative spacing of the minimum or maximum of intensity remains the same when changing the wavelength and the slit width simultaneously.
Using the following parameters: <em>y</em> for the distance from the center of the bright maximum to a place of minimum intensity, <em>m</em> for the order of the minimum, <em>λ </em>for the wavelength, <em>D </em>for the distance from the slit to the screen where we see the pattern and <em>d </em>for the slit width. The distance from the center to a minimum of intensity can be calculated with:
From the above expression we see that if we replace the blue light of wavelength λ by red light of wavelength 2λ in order to retain the original diffraction pattern we need to change the slit width to 2d:
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