Answer:
2.67 m
Explanation:
k = Spring constant = 1.5 N/m
g = Acceleration due to gravity = 9.81 m/s²
l = Unstretched length
Frequency of SHM motion is given by
![f_s=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}](https://tex.z-dn.net/?f=f_s%3D%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D)
Frequency of pendulum is given by
![f_p=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}](https://tex.z-dn.net/?f=f_p%3D%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bg%7D%7Bl%7D%7D)
Given in the question
![f_p=\dfrac{1}{2}f_s](https://tex.z-dn.net/?f=f_p%3D%5Cdfrac%7B1%7D%7B2%7Df_s)
![\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}=\dfrac{1}{2}\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}\\\Rightarrow \sqrt{\dfrac{g}{l}}=\dfrac{1}{2}\sqrt{\dfrac{k}{m}}\\\Rightarrow \dfrac{g}{l}=\dfrac{1}{4}\dfrac{k}{m}\\\Rightarrow l=\dfrac{4gm}{k}\\\Rightarrow l=\dfrac{4\times 9.81\times \dfrac{1}{9.81}}{1.5}\\\Rightarrow l=2.67\ m](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bg%7D%7Bl%7D%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5C%5C%5CRightarrow%20%5Csqrt%7B%5Cdfrac%7Bg%7D%7Bl%7D%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bg%7D%7Bl%7D%3D%5Cdfrac%7B1%7D%7B4%7D%5Cdfrac%7Bk%7D%7Bm%7D%5C%5C%5CRightarrow%20l%3D%5Cdfrac%7B4gm%7D%7Bk%7D%5C%5C%5CRightarrow%20l%3D%5Cdfrac%7B4%5Ctimes%209.81%5Ctimes%20%5Cdfrac%7B1%7D%7B9.81%7D%7D%7B1.5%7D%5C%5C%5CRightarrow%20l%3D2.67%5C%20m)
The unstretched length of the spring is 2.67 m
Answer:
I think it's strong I'm not to sure I'm sorry if it's wrong
Hi There,
This is False.
Hope this helped!
Answer:
Neither.
Explanation:
When an electron is released from rest, in an uniform electric field, it will accelerate moving in a direction opposite to the field (as the field has the direction that it would take a positive test charge, and the electron carries a negative charge).
It will move towards a point with a higher potential, so its kinetic energy will increase, while its potential energy will decrease:
⇒ ΔK + ΔU = 0 ⇒ ΔK = -ΔU = - (-e*ΔV)
As ΔV>0, we conclude that the electric potential energy decreases while the kinetic energy increases in the same proportion, in order to energy be conserved, in absence of non-conservative forces.
Answer:
Explanation:
To find out the angular velocity of merry-go-round after person jumps on it , we shall apply law of conservation of ANGULAR momentum
I₁ ω₁ + I₂ ω₂ = ( I₁ + I₂ ) ω
I₁ is moment of inertia of disk , I₂ moment of inertia of running person , I is the moment of inertia of disk -man system , ω₁ and ω₂ are angular velocity of disc and man .
I₁ = 1/2 mr²
= .5 x 175 x 2.13²
= 396.97 kgm²
I₂ = m r²
= 55.4 x 2.13²
= 251.34 mgm²
ω₁ = .651 rev /s
= .651 x 2π rad /s
ω₂ = tangential velocity of man / radius of disc
= 3.51 / 2.13
= 1.65 rad/s
I₁ ω₁ + I₂ ω₂ = ( I₁ + I₂ ) ω
396.97 x .651 x 2π + 251.34 x 1.65 = ( 396.97 + 251.34 ) ω
ω = 3.14 rad /s
kinetic energy = 1/2 I ω²
= 3196 J