Based on Newton's second law of motion, the net force applied to an object is equal to the product of the mass of the object and the acceleration it experiences. That is,
F = ma
If we are to assume that the net force is constant and that the mass is increased, the acceleration should therefore decrease in order to make constant the value at the right-hand side of the equation.
<span>These Russian nesting dolls are a good analogy for the strongest magnet in the world, because the magnitis were put inside each other. The magnets would be fitted together. Because they are closer together, the coils of magnet would be stronger. They would be able to magnetize better.</span>
Answer:
![\boxed{\sf Mass \ of \ an \ adult \ femur \ bone = 0.00054 \ kg}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Csf%20Mass%20%5C%20of%20%5C%20an%20%5C%20adult%20%5C%20femur%20%5C%20bone%20%3D%200.00054%20%5C%20kg%7D%20)
Given:
Bone density = 2.0 kg/m³
Volume of bone (V) = 0.00027 m³
To Find:
Mass of an adult femur bone (m).
Explanation:
![\sf \implies Density = \frac{Mass (m)}{Volume (V)} \\ \\ \sf \implies \frac{Mass}{Volume} = Density \\ \\ \sf \implies Mass = Density \times Volume \\ \\ \sf \implies Mass = 2.0 \ kg/ \cancel{m^{3}} \times 0.00027 \ \cancel{m^{3}} \\ \\ \sf \implies Mass = 0.00054 \ kg](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20Density%20%3D%20%5Cfrac%7BMass%20%28m%29%7D%7BVolume%20%28V%29%7D%20%5C%5C%20%5C%5C%20%5Csf%20%5Cimplies%20%5Cfrac%7BMass%7D%7BVolume%7D%20%3D%20Density%20%5C%5C%20%5C%5C%20%5Csf%20%5Cimplies%20Mass%20%3D%20Density%20%5Ctimes%20Volume%20%5C%5C%20%5C%5C%20%5Csf%20%5Cimplies%20Mass%20%3D%202.0%20%5C%20kg%2F%20%5Ccancel%7Bm%5E%7B3%7D%7D%20%5Ctimes%200.00027%20%5C%20%5Ccancel%7Bm%5E%7B3%7D%7D%20%5C%5C%20%5C%5C%20%5Csf%20%5Cimplies%20Mass%20%3D%200.00054%20%5C%20kg%20)
Answer:
![a = 0.53 m/s^2](https://tex.z-dn.net/?f=a%20%3D%200.53%20m%2Fs%5E2)
Explanation:
initially the merry go round is at rest
after 6.73 s the merry go round will accelerates to 20 rpm
so final angular speed is given as
![\omega = 2\pi f](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%20f)
![\omega = 2\pi ( \frac{20}{60})](https://tex.z-dn.net/?f=%5Comega%20%3D%202%5Cpi%20%28%20%5Cfrac%7B20%7D%7B60%7D%29)
![\omega = 2.10 rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%202.10%20rad%2Fs)
so final tangential speed is given as
![v = r\omega](https://tex.z-dn.net/?f=v%20%3D%20r%5Comega)
![v = 1.71 (2.10) = 3.58 m/s](https://tex.z-dn.net/?f=v%20%3D%201.71%20%282.10%29%20%3D%203.58%20m%2Fs)
now average acceleration of the girl is given as
![a = \frac{v_f - v_i}{\Delta t}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bv_f%20-%20v_i%7D%7B%5CDelta%20t%7D)
![a = \frac{3.58 - 0}{6.73}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B3.58%20-%200%7D%7B6.73%7D)
![a = 0.53 m/s^2](https://tex.z-dn.net/?f=a%20%3D%200.53%20m%2Fs%5E2)
The angular acceleration of a rotating object is given by
![\alpha = \frac{\omega_f - \omega_i}{\Delta t}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%20%5Cfrac%7B%5Comega_f%20-%20%5Comega_i%7D%7B%5CDelta%20t%7D%20)
where
![\omega_f](https://tex.z-dn.net/?f=%5Comega_f)
is the final angular speed of the object
![\omega_i](https://tex.z-dn.net/?f=%5Comega_i)
is its initial angular speed
![\Delta t](https://tex.z-dn.net/?f=%5CDelta%20t)
is the time taken to accelerate
For the wheel in our problem,
![\omega_f=11.1 rad/s](https://tex.z-dn.net/?f=%5Comega_f%3D11.1%20rad%2Fs)
,
![\omega_i = 0](https://tex.z-dn.net/?f=%5Comega_i%20%3D%200)
and
![\Delta t=2.99 s](https://tex.z-dn.net/?f=%5CDelta%20t%3D2.99%20s)
, so its angular acceleration is