Answer:
1) k = 52 N/m
2) E = 1.0 J
3) ω = 8.1 rad/s
4) v = 1.4 m/s
Though asked for a velocity, we can only supply magnitude (speed) because we don't have enough information to determine direction.
If it happens to be the first time it is at y = - 10 cm after release, the velocity is upward.
Explanation:
Assuming the initial setup is after all transients are eliminated.
kx = mg
k = mg/x = 0.8(9.8) / 0.15
k = 52.26666.... ≈ 52 N/m
E = ½kA² = ½(52)(0.20²) = 1.045333... ≈ 1.0 J
ω = √(k/m) = √(52 / 0.8) = 8.0829... ≈ 8.1 rad/s
½mv² = ½kA² - ½kx²
v = √(k(A² - x²)/m) = √(52(0.20² - 0.10²)/0.8) = 1.39999... ≈ 1.4 m/s
The object has a mass of 15 kilograms. Therefore, it weighs 147 newtons on Earth, where gravitational acceleration is 9.8 meters per second per second. To counteract gravity, the acting force needs to be at least 147 newtons, It has to move 3 meters upward. When multiplying force by distance, the product comes to 441 joules, where joules are the standard unit of work.
The magnitude of the centripetal acceleration of the car as it goes round the curve is 4.8 m/s²
<h3>Circular motion</h3>
From the question, we are to determine the magnitude of the centripetal acceleration.
Centripetal acceleration can be calculated by using the formula
![a_{c} =\frac{v^{2} }{r}](https://tex.z-dn.net/?f=a_%7Bc%7D%20%3D%5Cfrac%7Bv%5E%7B2%7D%20%7D%7Br%7D%20)
Where
is the centripetal acceleration
is the velocity
and
is the radius
From the given information
![v = 12 \ m/s](https://tex.z-dn.net/?f=v%20%3D%2012%20%5C%20m%2Fs)
and ![r = 30 \ m](https://tex.z-dn.net/?f=r%20%3D%2030%20%5C%20m)
Therefore,
![a_{c} =\frac{12^{2} }{30}](https://tex.z-dn.net/?f=a_%7Bc%7D%20%3D%5Cfrac%7B12%5E%7B2%7D%20%7D%7B30%7D%20)
![a_{c} =\frac{144 }{30}](https://tex.z-dn.net/?f=a_%7Bc%7D%20%3D%5Cfrac%7B144%20%7D%7B30%7D%20)
![a_{c} = 4.8\ m/s^{2}](https://tex.z-dn.net/?f=a_%7Bc%7D%20%3D%204.8%5C%20m%2Fs%5E%7B2%7D%20)
Hence, the magnitude of the centripetal acceleration of the car as it goes round the curve is 4.8 m/s²
Learn more on circular motion here: brainly.com/question/20905151
I think its true i dont kno for sure
Answer:
2240.92365 m/s
Explanation:
= Mass of electron = ![9.11\times 10^{−31}\ kg](https://tex.z-dn.net/?f=9.11%5Ctimes%2010%5E%7B%E2%88%9231%7D%5C%20kg)
= Speed of electron = ![5.7\times 10^7\ m/s](https://tex.z-dn.net/?f=5.7%5Ctimes%2010%5E7%5C%20m%2Fs)
= Neutrino has a momentum = ![7.3\times 10^{-24}\ kg m/s](https://tex.z-dn.net/?f=7.3%5Ctimes%2010%5E%7B-24%7D%5C%20kg%20m%2Fs)
M = total mass = ![2.34\times 10^{-26}\ kg](https://tex.z-dn.net/?f=2.34%5Ctimes%2010%5E%7B-26%7D%5C%20kg)
In the x axis as the momentum is conserved
![Mv_x=m_1v_1\\\Rightarrow v_x=\dfrac{m_1v_1}{M}\\\Rightarrow v_x=\dfrac{9.11\times 10^{−31}\times 5.7\times 10^7}{2.34\times 10^{-26}}\\\Rightarrow v_x=2219.10256\ m/s](https://tex.z-dn.net/?f=Mv_x%3Dm_1v_1%5C%5C%5CRightarrow%20v_x%3D%5Cdfrac%7Bm_1v_1%7D%7BM%7D%5C%5C%5CRightarrow%20v_x%3D%5Cdfrac%7B9.11%5Ctimes%2010%5E%7B%E2%88%9231%7D%5Ctimes%205.7%5Ctimes%2010%5E7%7D%7B2.34%5Ctimes%2010%5E%7B-26%7D%7D%5C%5C%5CRightarrow%20v_x%3D2219.10256%5C%20m%2Fs)
In the y axis
![Mv_y=p_2\\\Rightarrow v_y=\dfrac{p_2}{M}\\\Rightarrow v_y=\dfrac{7.3\times 10^{-24}}{2.34\times 10^{-26}}\\\Rightarrow v_y=311.96581\ m/s](https://tex.z-dn.net/?f=Mv_y%3Dp_2%5C%5C%5CRightarrow%20v_y%3D%5Cdfrac%7Bp_2%7D%7BM%7D%5C%5C%5CRightarrow%20v_y%3D%5Cdfrac%7B7.3%5Ctimes%2010%5E%7B-24%7D%7D%7B2.34%5Ctimes%2010%5E%7B-26%7D%7D%5C%5C%5CRightarrow%20v_y%3D311.96581%5C%20m%2Fs)
The resultant velocity is
![R=\sqrt{v_x^2+v_y^2}\\\Rightarrow R=\sqrt{2219.10256^2+311.96581^2}\\\Rightarrow R=2240.92365\ m/s](https://tex.z-dn.net/?f=R%3D%5Csqrt%7Bv_x%5E2%2Bv_y%5E2%7D%5C%5C%5CRightarrow%20R%3D%5Csqrt%7B2219.10256%5E2%2B311.96581%5E2%7D%5C%5C%5CRightarrow%20R%3D2240.92365%5C%20m%2Fs)
The recoil speed of the nucleus is 2240.92365 m/s