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KengaRu [80]
3 years ago
12

You have a spring with k = 640 N/m connected to a mass with m = 10 kg. You start the system oscillating and measure the velocity

of the mass as it moves through the spring's equilibrium position to be 4 m/s. At what position is the kinetic energy of the system equal to the potential energy?
Physics
1 answer:
sdas [7]3 years ago
4 0

Answer:

X= 0.5 m

Explanation:

Given that

K= 640 N/m

m=10 kg

v= 4 m/s

We know that

kinetic energy of the mass

KE=1/2 m v²

Potential energy

PE=1/2 k X²

Given that kinetic and potential energy are equal

1/2 k X² = 1/2 m v²

k X² =  m v²

Now by putting the values

640  X² = 10 x 4²

X= 0.5 m

So at 0.5 m  kinetic and potential energy will be equal.

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A dielectric-filled parallel-plate capacitor has plate area A = 30.0 cm2 , plate separation d = 9.00 mm and dielectric constant
PIT_PIT [208]

Answer:

9.96\cdot 10^{-10}J

Explanation:

The capacitance of the parallel-plate capacitor is given by

C=\epsilon_0 k \frac{A}{d}

where

ϵ0 = 8.85x10-12 C2/N.m2 is the vacuum permittivity

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A=30.0 cm^2 = 30.0\cdot 10^{-4}m^2 is the area of the plates

d = 9.00 mm = 0.009 m is the separation between the plates

Substituting,

C=(8.85\cdot 10^{-12}F/m)(3.00 ) \frac{30.0\cdot 10^{-4} m^2}{0.009 m}=8.85\cdot 10^{-12} F

Now we can calculate the energy of the capacitor, given by:

U=\frac{1}{2}CV^2

where

C is the capacitance

V = 15.0 V is the potential difference

Substituting,

U=\frac{1}{2}(8.85\cdot 10^{-12}F)(15.0 V)^2=9.96\cdot 10^{-10}J

4 0
3 years ago
One problem with digital data is that it can be vulnerable to hackers.
hoa [83]

Answer: c. A person who gains unauthorized access to digital data

Explanation:

5 0
2 years ago
The old rubber boot has two leaks. The top of the boot is 0.3 m higher than the leaks. What is the velocity of the water coming
Otrada [13]

Answer:

Leak 1 = 3.43 m/s

Leak 2 = 2.42 m/s

Explanation:

Given that the top of the boot is 0.3 m higher than the leaks. 

Let height H = 0.3m and the acceleration due to gravity g = 9.8 m/s^2

From the figure, the angle of the leak 1 will be approximately equal to 45 degrees. While the leak two can be at 90 degrees.

Using the third equation of motion under gravity, we can calculate the velocity of leak 1 and 2

Find the attached files for the solution and figure

7 0
3 years ago
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