Answer:
the vertical acceleration of the case is 1.46 m/s
Explanation:
Given;
mass of the clarinet case, m = 3.07 kg
upward force applied by the man, F = 25.60 N
Apply Newton's second law of motion;
the upward force on the clarinet case = its weight acting downwards + downward force due to its downward accelaration
F = mg + m(-a)
the acceleration is negative due to downward motion from the top of the piano.
F = mg - ma
ma = mg - F
![a = \frac{mg - F}{m} \\\\a = \frac{(3.07 \times 9.8) \ - \ 25.6}{3.07} \\\\a = 1.46 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bmg%20-%20F%7D%7Bm%7D%20%5C%5C%5C%5Ca%20%3D%20%5Cfrac%7B%283.07%20%5Ctimes%209.8%29%20%5C%20-%20%5C%2025.6%7D%7B3.07%7D%20%5C%5C%5C%5Ca%20%3D%201.46%20%5C%20m%2Fs%5E2)
Therefore, the vertical acceleration of the case is 1.46 m/s²
That's false. Mechanical waves (like sound and ocean waves) do
need a medium to travel in, but electromagnetic waves (like radio
and light) don't.
Explanation:
It is given that,
Speed, v₁ = 7.7 m/s
We need to find the velocity after it has risen 1 meter above the lowest point. Let it is given by v₂. Using the conservation of energy as :
![\dfrac{1}{2}mv_1^2=\dfrac{1}{2}mv_2^2+mgh](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7Dmv_1%5E2%3D%5Cdfrac%7B1%7D%7B2%7Dmv_2%5E2%2Bmgh)
![v_2^2=v_1^2-2gh](https://tex.z-dn.net/?f=v_2%5E2%3Dv_1%5E2-2gh)
![v_2^2=(7.7)^2-2\times 10\times 1](https://tex.z-dn.net/?f=v_2%5E2%3D%287.7%29%5E2-2%5Ctimes%2010%5Ctimes%201)
![v_2=6.26\ m/s](https://tex.z-dn.net/?f=v_2%3D6.26%5C%20m%2Fs)
So, the velocity after it has risen 1 meter above the lowest point is 6.26 m/s. Hence, this is the required solution.
Answer:
d.none
Explanation:
because shape size and physical actually do are dependant
Answer:
h=2.86m
Explanation:
In order to give a quick response to this exercise we will use the equations of conservation of kinetic and potential energy, the equation is given by,
![\Delta PE_i + \Delta KE_i = \Delta PE_f +\Delta KE_f](https://tex.z-dn.net/?f=%5CDelta%20PE_i%20%2B%20%5CDelta%20KE_i%20%3D%20%5CDelta%20PE_f%20%2B%5CDelta%20KE_f)
There is no kinetic energy in the initial state, nor potential energy in the end,
![mgh+0=0+KE_f](https://tex.z-dn.net/?f=mgh%2B0%3D0%2BKE_f)
In the final kinetic energy, the energy contributed by the Inertia must be considered, as well,
![mgh = (\frac{1}{2}mv^2+\frac{1}{2}I\omega^2)](https://tex.z-dn.net/?f=mgh%20%3D%20%28%5Cfrac%7B1%7D%7B2%7Dmv%5E2%2B%5Cfrac%7B1%7D%7B2%7DI%5Comega%5E2%29)
The inertia of the bodies is given by the equation,
![I=\frac{m(R_1^2+R^2_2)}{2}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7Bm%28R_1%5E2%2BR%5E2_2%29%7D%7B2%7D)
![I=\frac{2(0.2^2+0.1^2)}{2}](https://tex.z-dn.net/?f=I%3D%5Cfrac%7B2%280.2%5E2%2B0.1%5E2%29%7D%7B2%7D)
![I=0.05Kgm^2](https://tex.z-dn.net/?f=I%3D0.05Kgm%5E2)
On the other hand the angular velocity is given by
![\omega =\frac{v}{R_2}=\frac{4}{1/5} = 2rad/s](https://tex.z-dn.net/?f=%5Comega%20%3D%5Cfrac%7Bv%7D%7BR_2%7D%3D%5Cfrac%7B4%7D%7B1%2F5%7D%20%3D%202rad%2Fs)
Replacing these values in the equation,
![(0.5)(9.8)(h) =\frac{1}{2}*0.5*4^2+\frac{1}{2}*0.05*20^2](https://tex.z-dn.net/?f=%280.5%29%289.8%29%28h%29%20%3D%5Cfrac%7B1%7D%7B2%7D%2A0.5%2A4%5E2%2B%5Cfrac%7B1%7D%7B2%7D%2A0.05%2A20%5E2)
Solving for h,
![h=2.86m](https://tex.z-dn.net/?f=h%3D2.86m)