One degree Celsius indicates the same temperature change as

A mass is oscillating with amplitude A at the end of a spring.

A) $x=\pm \frac{A}{2\sqrt{2}}$

The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):

$E=\frac{1}{2}kA^2$ (1)

where k is the spring constant.

The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:

$E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2$ (2)

where x is the displacement, m the mass, and v the speed.

We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:

$U=\frac{1}{3}K$

Using (2) we can rewrite this as

$U=\frac{1}{3}(E-U)=\frac{1}{3}E-\frac{1}{3}U\\U=\frac{E}{4}$

And using (1), we find

$U=\frac{E}{4}=\frac{\frac{1}{2}kA^2}{4}=\frac{1}{8}kA^2$

Substituting $U=\frac{1}{2}kx^2$ into the last equation, we find the value of x:

$\frac{1}{2}kx^2=\frac{1}{8}kA^2\\x=\pm \frac{A}{2\sqrt{2}}$

B) $x=\pm \frac{3}{\sqrt{10}}A$

In this case, the kinetic energy is 1/10 of the total energy:

$K=\frac{1}{10}E$

Since we have

$K=E-U$

we can write

$E-U=\frac{1}{10}E\\U=\frac{9}{10}E$

And so we find:

$\frac{1}{2}kx^2 = \frac{9}{10}(\frac{1}{2}kA^2)=\frac{9}{20}kA^2\\x^2 = \frac{9}{10}A^2\\x=\pm \frac{3}{\sqrt{10}}A$

3 0

3 years ago

Janetta ran a campaign for student body president, and she really wanted to win. She gave election buttons to everyone and told

SVEN [57.7K]

Answer:

No, because she is hoping that people will vote for her.

Explanation:

Altruism is when you do something for others and have very little expectation of getting something in return. In this case, Janetta expected something in return from her friends. We may not also be sure of the sincerity of Janetta appreciating friendship. From the above definition of altruism, we conclude that Janetta's actions are not altruistic because she hoped that people will vote for her.

3 0

3 years ago

Factor the expression 27x-18y

Eva8 [605]

Answer:

9(3x-2y)

Explanation:

27x-18y, the common factor here is 9

9(3x-2y)

7 0

3 years ago

What was Galileo’s contribution to the study of motion?

babunello [35]

Before giving you the answer straight away, I’d like to make sure you understand each option.

FIRST OPTION

“He developed the three laws of motion."

This option is not only the incorrect answer, but it is an incorrect statement. Galileo did not develop the three laws of motion. Isaac Newton was the one to compiled the three laws of motion.

SECOND OPTION

“He was the first to systematically study force and motion."

This option is a statement is true, and it could also be the correct answer. Galileo Galilei used experiments to search for the cause of motion.

THIRD OPTION

“He was the first to discover gravity."

This option is not only the incorrect answer, but it is an incorrect statement. Galileo was not the person to discover gravity. Sir Isaac Newton was the first to discover gravity.

FINAL OPTION

“He improved on Newton's laws."

This option is not only the incorrect answer, but it is an incorrect statement. Galilei did not improve Sir Isaac Newton’s laws.

Now that we’ve gone through each of the options individually, we can go ahead and determine the correct answer to the question, which is...

B ) He was the first to systematically study force and motion.

- Marlon Nunez

8 0

3 years ago

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Ok I am done waiting for an answer for 5 hours can somebody PLEASE PLEASE PLEASE help me TIMED ASSESMENT HERE!!!! PLEASE

JulsSmile [24]

Answer:

Explanation:

I'm going to assume that all the givens are in m/s. If I am correct, The orange line is speeding up. It is going from 4 m/s to 7 m/s. Its slant is from lower left to upper right. It is increasing in speed.

The green line is slowing down. It is going from 4 to 0 m/s. It's slant is from upper left to lower right.

The blue line is horizontal. It is neither slowing down or speeding up.

3 0

2 years ago

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