Answer: ![0.43\ rad/s](https://tex.z-dn.net/?f=0.43%5C%20rad%2Fs)
Explanation:
Given
Mass of child ![m=34\ kg](https://tex.z-dn.net/?f=m%3D34%5C%20kg)
speed of child is ![v=2.8\ m/s](https://tex.z-dn.net/?f=v%3D2.8%5C%20m%2Fs)
Moment of inertia of merry go round is ![I=510\ kg.m^2](https://tex.z-dn.net/?f=I%3D510%5C%20kg.m%5E2)
radius ![r=2.31\ m](https://tex.z-dn.net/?f=r%3D2.31%5C%20m)
Conserving the angular momentum
![\Rightarrow mvr=I\omega \\\Rightarrow 34\times 2.8\times 2.31=510\times \omega\\\\\Rightarrow \omega=\dfrac{219.912}{510}\\\Rightarrow \omega=0.43\ rad/s](https://tex.z-dn.net/?f=%5CRightarrow%20mvr%3DI%5Comega%20%5C%5C%5CRightarrow%2034%5Ctimes%202.8%5Ctimes%202.31%3D510%5Ctimes%20%5Comega%5C%5C%5C%5C%5CRightarrow%20%5Comega%3D%5Cdfrac%7B219.912%7D%7B510%7D%5C%5C%5CRightarrow%20%5Comega%3D0.43%5C%20rad%2Fs)
The answers to the problem are as follows:
MA= 5
IMA= input distance/ output distance, 5
<span>AMA= output force/ input force, 5/2
</span>
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Explanation:
According to the law of conservation of energy
,
Potential energy = kinetic energy
I =
mgh =
v = 7.4 m/s
thus, we can conclude that the translational speed of the cylinder when it leaves the incline is 7.4 m/s.
Answer:
25 m/s in the opposite direction with the ship recoil velocity.
Explanation:
Assume the ship recoil velocity and velocity of the cannon ball aligns. By the law of momentum conservation, the momentum is conserved before and after the shooting. Before the shooting, the total momentum is 0 due to system is at rest. Therefore, the total momentum after the shooting must also be 0:
![m_sv_s + m_bv_b = 0](https://tex.z-dn.net/?f=m_sv_s%20%2B%20m_bv_b%20%3D%200)
where
are masses of the ship and ball respectively.
are the velocities of the ship and ball respectively, after the shooting.
![2500*0.25 + 25*v_b = 0](https://tex.z-dn.net/?f=2500%2A0.25%20%2B%2025%2Av_b%20%3D%200)
![25v_b = -2500*0.25](https://tex.z-dn.net/?f=25v_b%20%3D%20-2500%2A0.25)
![v_b = -2500*0.25/25 = -25 m/s](https://tex.z-dn.net/?f=v_b%20%3D%20-2500%2A0.25%2F25%20%3D%20-25%20m%2Fs)
So the cannon ball has a velocity of 25 m/s in the opposite direction with the ship recoil velocity.
Answer:
6.13 s
219 N
Explanation:
Newton's law in the x direction:
∑F = ma
150 cos 30° N − 50 N = (30 kg) a
a = 2.66 m/s²
Δx = v₀ t + ½ at²
(50 m) = (0 m/s) t + ½ (2.66 m/s²) t²
t = 6.13 s
Newton's law in the y direction:
∑F = ma
Fn + 150 sin 30° N − (30 kg) (9.8 m/s²) = 0
Fn = 219 N