Answer:
Spring constant required=8910 N/m. Maximum distance compressed=0.99m
Explanation:
The first step here is to consider the Newton's Second Law which states that a force <em>F</em> applied to a body of mass <em>m</em> produces an acceleration <em>a</em>. Our body has a mass of 300 kg and the maximum allowable acceleration is 3.00 g. Considering gravity g=9.81m/s^2, <em>a</em>=3.00*9.81m/s^=29.43m/s^2. Hence,
F=300kg*29.43 m/s^2=8829 N
The force that a spring gives is the multiplication of its force constant <em>K </em>and the distance compressed<em> X.</em> . So the force F sholud be equal to <em>K*
. </em>
<em>F=K*.</em>
Then, when the spring is fully compressed all the kinetic energy of the cart (T) is transferred to the spring as potential elastic energy (U). <em> </em>
<em>
Eq.1</em>
We do not know but we do know that it is equal to F/<em>K. </em>Thus,
Eq.2
Operating in Eq.2 
Finally, putting the valus of <em>K </em>in Eq.1 and solving, <em>=0.99m</em>
The amplitude of vibration for the sphere will be 29.48 nm.
<h3 /><h3>What is amplitude?</h3>
The distance between from the crest of a wave to the next crest is known as the amplitude.
The amplitude of the sphere is;
![\rm A= \frac{\delta_0}{[1-(\frac{\omega}{\omega_n}^2]} \\\\](https://tex.z-dn.net/?f=%5Crm%20A%3D%20%5Cfrac%7B%5Cdelta_0%7D%7B%5B1-%28%5Cfrac%7B%5Comega%7D%7B%5Comega_n%7D%5E2%5D%7D%20%5C%5C%5C%5C)
The stiffness of the load is;
The natural frequency is;
Put the obtained values in the amplitude formula;
![\rm A= \frac{0.015}{[1-(\frac{4 \pi}{17.93}^2]} \\\\ A= 0.02948 \\\\ A= 29.48 \ nm](https://tex.z-dn.net/?f=%5Crm%20A%3D%20%5Cfrac%7B0.015%7D%7B%5B1-%28%5Cfrac%7B4%20%5Cpi%7D%7B17.93%7D%5E2%5D%7D%20%5C%5C%5C%5C%20A%3D%200.02948%20%5C%5C%5C%5C%20A%3D%2029.48%20%5C%20nm)
Hence,the amplitude of vibration for the sphere will be 29.48 nm.
To learn more about the amplitude, refer:
brainly.com/question/8662436
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The action-reaction pairs in the given situation are:
- the backpack and the bench
- the and and the wall
<h3>What are action-reaction pairs?</h3>
Action-reaction pairs are two forces which are equal but oppositely directed in their line of action.
Action-reaction pairs are according to Newton's third law of motion.
The action-reaction pairs in the given situation are:
- the backpack and the bench
- the and and the wall
Learn more about action-reaction pairs at: brainly.com/question/12800382
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Answer:
Coefficient of friction is the ratio of friction force to normal force.
μ = F/N
Answer:
Surface tension
Explanation:
When liquid rises against gravity in a capillary tube, the energy comes from surface tension.
This is because surface tension is the energy that's needed to increase the liquid surface area.
As a result of hydrogen bonding present in Water, it usually has high surface tension which makes it to possess a tough skin that can make it not to break despite high forces applied to it.
The liquid will be in contact with the capillary tube and as such experiences surface tension which in turn makes the capillary tube to experience an upward force that makes the liquid begin to rise up.
The more the liquid keeps rising, the more it gets to the point where the surface tension becomes balanced from the weight of the liquid.
