To solve this problem we will apply the concepts related to energy conservation. From this conservation we will find the magnitude of the amplitude. Later for the second part, we will need to find the period, from which it will be possible to obtain the speed of the body.
A) Conservation of Energy,
![KE = PE](https://tex.z-dn.net/?f=KE%20%3D%20PE)
![\frac{1}{2} mv ^2 = \frac{1}{2} k A^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20mv%20%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20k%20A%5E2)
Here,
m = Mass
v = Velocity
k = Spring constant
A = Amplitude
Rearranging to find the Amplitude we have,
![A = \sqrt{\frac{mv^2}{k}}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B%5Cfrac%7Bmv%5E2%7D%7Bk%7D%7D)
Replacing,
![A = \sqrt{\frac{(0.750)(31*10^{-2})^2}{13}}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B%5Cfrac%7B%280.750%29%2831%2A10%5E%7B-2%7D%29%5E2%7D%7B13%7D%7D)
![A = 0.0744m](https://tex.z-dn.net/?f=A%20%3D%200.0744m)
(B) For this part we will begin by applying the concept of Period, this in order to find the speed defined in the mass-spring systems.
The Period is defined as
![T = 2\pi \sqrt{\frac{m}{k}}](https://tex.z-dn.net/?f=T%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D)
Replacing,
![T = 2\pi \sqrt{\frac{0.750}{13}}](https://tex.z-dn.net/?f=T%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7B0.750%7D%7B13%7D%7D)
![T= 1.509s](https://tex.z-dn.net/?f=T%3D%201.509s)
Now the velocity is described as,
![v = \frac{2\pi}{T} * \sqrt{A^2-x^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BT%7D%20%2A%20%5Csqrt%7BA%5E2-x%5E2%7D)
![v = \frac{2\pi}{T} * \sqrt{A^2-0.75A^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B2%5Cpi%7D%7BT%7D%20%2A%20%5Csqrt%7BA%5E2-0.75A%5E2%7D)
We have all the values, then replacing,
![v = \frac{2\pi}{1.509}\sqrt{(0.0744)^2-(0.750(0.0744))^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B1.509%7D%5Csqrt%7B%280.0744%29%5E2-%280.750%280.0744%29%29%5E2%7D)
![v = 0.2049m/s](https://tex.z-dn.net/?f=v%20%3D%200.2049m%2Fs)
The force that the book exerts on the table is a normal force, not a weight force. (The book's weight doesn't act on the table, it acts on the book.) It's equal in magnitude to the weight of the book, again, because of the first law.
Answer:
vf = 0
Explanation:
Since the initial height hi = 0, we can rewrite the energy equation as
vf^2 = vi^2 - 2ghf = (10 m/s)^2 - 2(10 m/s^2)(5 m) = 0
Therefore, his final velocity vf is
vf = 0
Answer:
If the density of the object is high its molecular arrangement is compact while if the density is lows its molecular arrangement isnt that compact