Answer:
![t = 0.85 s](https://tex.z-dn.net/?f=t%20%3D%200.85%20s)
Explanation:
As we know that the block of wood is suspended by spring
Now at equilibrium position we have net force balanced on it
so we have
![mg = kx](https://tex.z-dn.net/?f=mg%20%3D%20kx)
![0.30 \times 9.81 = k(0.02)](https://tex.z-dn.net/?f=0.30%20%5Ctimes%209.81%20%3D%20k%280.02%29)
so we will have
![k = 147.15 N/m](https://tex.z-dn.net/?f=k%20%3D%20147.15%20N%2Fm)
now the time period of the spring block system for one complete oscillation is given 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)
now plug in all values in it
![T = 2\pi \sqrt{\frac{0.30}{147.15}}](https://tex.z-dn.net/?f=T%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7B0.30%7D%7B147.15%7D%7D)
![T = 0.28 s](https://tex.z-dn.net/?f=T%20%3D%200.28%20s)
Now total time to complete 3 cycles is given as
![t = 3T](https://tex.z-dn.net/?f=t%20%3D%203T)
![t = 0.85 s](https://tex.z-dn.net/?f=t%20%3D%200.85%20s)
Answer:
1081.9 J
Explanation:
In order to calculate how much energy is converted into thermal energy due to friction, we have to calculate the difference between the mechanical energy of the child at the top and at the bottom of the slide.
At the top of the slide, he is at rest, so its kinetic energy is zero, and so he only has gravitational potential energy. Therefore:
![E_i = U = mgh = (24)(9.8)(5)=1176 J](https://tex.z-dn.net/?f=E_i%20%3D%20U%20%3D%20mgh%20%3D%20%2824%29%289.8%29%285%29%3D1176%20J)
where
m = 24 kg is the mass of the child
g = 9.8 m/s^2 is the acceleration of gravity
h = 5 m is the height relative to the ground
At the bottom of the slide, the child has only kinetic energy, so its total energy is
![E_f = K = \frac{1}{2}mv^2=\frac{1}{2}(24)(2.8)^2=94.1 J](https://tex.z-dn.net/?f=E_f%20%3D%20K%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%3D%5Cfrac%7B1%7D%7B2%7D%2824%29%282.8%29%5E2%3D94.1%20J)
where
v = 2.8 m/s is the final speed of the child
Therefore, the therma energy generated due to friction is equal to the difference between the initial and final energy:
![\Delta E = 1176 - 94.1=1081.9 J](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%201176%20-%2094.1%3D1081.9%20J)
Answer: the answer is d
Explanation: there are not more than 10 violations within a twelve month period hope this helps
If a bus travels 30 km in 1/2 hr, then in one hr, he can travel twice the distance.
30*2=60 km
Final answer: 60 km per hr
Answer:
Explanation:
Given
radius of Planet is equal to radius of Earth
![r_p=r_e](https://tex.z-dn.net/?f=r_p%3Dr_e)
Weight of body on Planet ![F_p=mg_p](https://tex.z-dn.net/?f=F_p%3Dmg_p)
where m=mass of body
![g_p=acceleration\ due\ to\ gravity\ on\ surface\ of\ Planet](https://tex.z-dn.net/?f=g_p%3Dacceleration%5C%20due%5C%20to%5C%20gravity%5C%20on%5C%20surface%5C%20of%5C%20Planet)
Weight of body on earth ![F_e=mg_e](https://tex.z-dn.net/?f=F_e%3Dmg_e)
![g_e=acceleration\ due\ to\ gravity\ on\ Earth](https://tex.z-dn.net/?f=g_e%3Dacceleration%5C%20due%5C%20to%5C%20gravity%5C%20on%5C%20Earth)
acceleration due to gravity is given by
![g=\frac{GM}{r^2}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7Br%5E2%7D)
where G=gravitational constant
M=mass of Planet
r=radius of planet
for earth ![g_e=\frac{GM_e}{r_e^2}](https://tex.z-dn.net/?f=g_e%3D%5Cfrac%7BGM_e%7D%7Br_e%5E2%7D)
for planet ![g_p=\frac{GM_p}{r_p^2}](https://tex.z-dn.net/?f=g_p%3D%5Cfrac%7BGM_p%7D%7Br_p%5E2%7D)
substituting these values in
and ![F_p](https://tex.z-dn.net/?f=F_p)
![F_p=m\times \frac{GM_p}{r_p^2}---1](https://tex.z-dn.net/?f=F_p%3Dm%5Ctimes%20%5Cfrac%7BGM_p%7D%7Br_p%5E2%7D---1)
![F_e=m\times \frac{GM_e}{r_e^2}---2](https://tex.z-dn.net/?f=F_e%3Dm%5Ctimes%20%5Cfrac%7BGM_e%7D%7Br_e%5E2%7D---2)
divide 1 and 2
![\frac{F_p}{F_e}=\frac{m\times \frac{GM_p}{r_p^2}}{m\times \frac{GM_e}{r_e^2}}](https://tex.z-dn.net/?f=%5Cfrac%7BF_p%7D%7BF_e%7D%3D%5Cfrac%7Bm%5Ctimes%20%5Cfrac%7BGM_p%7D%7Br_p%5E2%7D%7D%7Bm%5Ctimes%20%5Cfrac%7BGM_e%7D%7Br_e%5E2%7D%7D)
![10=\frac{M_p}{M_e}](https://tex.z-dn.net/?f=10%3D%5Cfrac%7BM_p%7D%7BM_e%7D)
![M_p=10M_e](https://tex.z-dn.net/?f=M_p%3D10M_e)