Answer:
The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
Explanation:
Given that,
Mass = 2.15 kg
Distance = 0.0895 m
Amplitude = 0.0235 m
We need to calculate the spring constant
Using newton's second law

Where, f = restoring force


Put the value into the formula


We need to calculate the kinetic energy of the mass
Using formula of kinetic energy

Here, 

Here, 


Put the value into the formula


Hence, The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
Good afternoon.
We have:

The function of velocity:

For
t = 5 s:
Answer:
The coefficient of static friction is 0.29
Explanation:
Given that,
Radius of the merry-go-round, r = 4.4 m
The operator turns on the ride and brings it up to its proper turning rate of one complete rotation every 7.7 s.
We need to find the least coefficient of static friction between the cat and the merry-go-round that will allow the cat to stay in place, without sliding. For this the centripetal force is balanced by the frictional force.

v is the speed of cat, 

So, the least coefficient of static friction between the cat and the merry-go-round is 0.29.
Answer:
1) f= 8.6 GHz
2) t= 0.2 ms
Explanation:
1)
- Since microwaves are electromagnetic waves, they move at the same speed as the light in vacuum, i.e. 3*10⁸ m/s.
- There exists a fixed relationship between the frequency (f) , the wavelength (λ) and the propagation speed in any wave, as follows:

- Replacing by the givens, and solving for f, we get:

⇒ f = 8.6 Ghz (with two significative figures)
2)
- Assuming that the microwaves travel at a constant speed in a straight line (behaving like rays) , we can apply the definition of average velocity, as follows:
where v= c= speed of light in vacuum = 3*10⁸ m/s
d= distance between mountaintops = 52 km = 52*10³ m

⇒ t = 0.2 ms (with two significative figures)
The EM spectrum has no limits. Any frequency you can imagine
is the frequency of some electromagnetic radiation somewhere.