What is the importance of measurement?

A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block

MariettaO [177]

Answer:

v₀ = 0.5058 m/s

Explanation:

From the question, for the block to hit the bottle, the elastic potential energy of the spring at the bottle (x = 0.08 m) should be equal to the sum of the elastic potential energy of the spring at x = 0.05 m and the kinetic energy of block at x = 0.05 m

Now, the potential energy of the block at x = 0.08 m is ½kx²

where;

k is the spring constant given by; k = ω²m

ω is the angular velocity of the oscillation

m is the mass of the block.

Thus, potential energy of the spring at the bottle(x = 0.08 m) is;

U = ½ω²m(0.08m)²

Also, potential energy of the spring at the bottle(x = 0.05 m) is;

U = ½ω²m(0.05m)²

and the kinetic energy of the block at x = 0.05 m is;

K = ½mv₀²

Thus;

½ω²m(0.08)² = ½ω²m(0.05)² + ½mv₀²

Inspecting this, ½m will cancel out to give;

ω²(0.08)² = ω²(0.05)² + v₀²

Making v₀ the subject, we have;

v₀ = ω√((0.08)² - (0.05)²)

So,

v₀ = 8.1√((0.08)² - (0.05)²)

v₀ = 0.5058 m/s

7 0

3 years ago

One atom has 14 neutrons. Another has 13 neutrons. Both have 13 protons. These atoms are...

agasfer [191]

Hello!

These atoms are isotopes

Isotopes are atoms with the same number of protons (which determine the atomic number) and a different number of neutrons. These two atoms have the same number of protons (13), but a different number of neutrons, so they are isotopes.

According to their number of protons, these are Aluminum isotopes: ²⁷Al (stable), and ²⁶Al (radioactive), respectively.

Have a nice day!

7 0

3 years ago

An opera singer breaks a crystal glass with her voice. Which best explains why this occurs? The pitch of her voice matches the p

aalyn [17]

The frequency at which the body vibrates breaks is natural frequency. The glass with her voice because the frequency of her voice matches the natural frequency of the glass.

<h3>What is the natural frequency?</h3>

When there is no external force acting on the body unless the body vibrates is known as the natural frequency of vibration.it is denoted by $\rm w_n$ .