Answer:
ω₂ = 5.578 rads⁻¹
Explanation:
The moment of inertia of,
turn table = ![\frac{1}{2}mr^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmr%5E%7B2%7D)
block = ![mr^{2}](https://tex.z-dn.net/?f=mr%5E%7B2%7D)
By the law of conservation of angular momentum, as no external torque acts on system the total angular momentum of the system when block sits at center and when block at the outer edge must be same.
Also to find ω, ω = 2πf where f is rpm
= 2π×63/60 = 6.597
So
I₁ω₁ = I₂ω₂
(
+
)×6.597 = (
+
)×ω₂
ω₂ = 5.578 rads⁻¹
Answer:
1.15 m/s
Explanation:
Part of the question is missing. Found the missing part on google:
"1. A hanging mass of 1500 grams compresses a spring 2.0 cm. Find the spring constant in N/m."
Solution:
First of all, we need to find the spring constant. We can use Hooke's law:
![F=kx](https://tex.z-dn.net/?f=F%3Dkx)
where
is the force applied to the spring (the weight of the hanging mass)
x = 2.0 cm = 0.02 m is the compression of the spring
Solving for k, we find the spring constant:
![k=\frac{F}{x}=\frac{14.7}{0.02}=735 N/m](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BF%7D%7Bx%7D%3D%5Cfrac%7B14.7%7D%7B0.02%7D%3D735%20N%2Fm)
In the second part of the problem, the spring is compressed by
x = 3.0 cm = 0.03 m
So the elastic potential energy of the spring is
![U=\frac{1}{2}kx^2=\frac{1}{2}(735)(0.03)^2=0.33 J](https://tex.z-dn.net/?f=U%3D%5Cfrac%7B1%7D%7B2%7Dkx%5E2%3D%5Cfrac%7B1%7D%7B2%7D%28735%29%280.03%29%5E2%3D0.33%20J)
This energy is entirely converted into kinetic energy of the cart, which is:
![U=K=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=U%3DK%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
where
m = 500 g = 0.5 kg is the mass of the cart
v is its speed
Solving for v,
![v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(0.33)}{0.5}}=1.15 m/s](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7B2K%7D%7Bm%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%280.33%29%7D%7B0.5%7D%7D%3D1.15%20m%2Fs)
The momentum of the red cart before the collision is 0.2 kgm/s and the blue cart is 0.
The momentum of the red cart after the collision is 0.05 kgm/s and the blue cart is 0.15 kgm/s.
The change in momentum of the system of the carts is 0.
<h3>
Initial momentum of the carts before collision</h3>
The momentum of the carts before the collision is calculated as follows;
P(red) = 0.5 kg x 0.4 m/s = 0.2 kgm/s
P(blue) = 1.5 x 0 = 0
<h3>Momentum of the carts after collision</h3>
The momentum of the carts after the collision is calculated as follows;
P(red) = 0.5 x 0.1 = 0.05 kgm/s
P(blue) = 1.5 0.1 = 0.15 kgm/s
<h3>Change in momentum of the carts</h3>
![\Delta P = P_f - P_i](https://tex.z-dn.net/?f=%5CDelta%20P%20%3D%20P_f%20-%20P_i)
ΔP = (0.05 + 0.15) - (0.2)
ΔP = 0
Learn more about momentum here: brainly.com/question/7538238
Answer:
Magnetic fields point from the north pole to the south pole of a magnet.
An example of the Biot-Savart law is the effect of the earth's maghytic field on the electron rays coming from the sun.
The north pole of a magnet will be attracted to the south pole of the earth.
If a bar magnet is cut in half two magnets with like poles will be created
Explanation:
The magnetic field of Earth is due to the presence of iron in the core of the Earth.
The metal emits the magnetic waves from it and the North and South pole of the planet.
Both the poles emit the magnetic rays which create magnetic sheet around it.
The Earth acts like a magnet bar if which is cut into two half, the planet will act like two magnets. Also, Biot Savarts's law states that the magnetic field does not affect the electron rays coming from the Sun.
Thus, the selected options are correct.
Equals variation in position over variation in time, here’s the formula hope it helps :)