an astronaut on the Moon could experience zero gravity, and would see stars and Earth.
Answer:
graph A
Explanation:
the slope of the distance-time graph is speed, speed is a scalar (with magnitudes but no direction)
but the slope for the velocity time graph is acceleration, acceleration is vector quantity ( has magnitude and direction)
Answer:
Part a)
Mass of m2 is given as
![m_2 = \frac{20}{3} kg](https://tex.z-dn.net/?f=m_2%20%3D%20%5Cfrac%7B20%7D%7B3%7D%20kg)
Part b)
Angular acceleration is given as
![\alpha = 1.96 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D%201.96%20rad%2Fs%5E2)
Part c)
Tension in the rope is given as
![T = 176.6 N](https://tex.z-dn.net/?f=T%20%3D%20176.6%20N)
Explanation:
Part a)
When m1 and m2 both connected to the cylinder then the system is at rest
so we can use torque balance here
![m_1g r_1 = m_2 g r_2](https://tex.z-dn.net/?f=m_1g%20r_1%20%3D%20m_2%20g%20r_2)
![20 g(0.5) = m_2 g(1.5)](https://tex.z-dn.net/?f=20%20g%280.5%29%20%3D%20m_2%20g%281.5%29)
![10 = 1.5 m_2](https://tex.z-dn.net/?f=10%20%3D%201.5%20m_2)
![m_2 = \frac{20}{3} kg](https://tex.z-dn.net/?f=m_2%20%3D%20%5Cfrac%7B20%7D%7B3%7D%20kg)
Part b)
When block m_2 is removed then system becomes unstable
so force equation of mass m1
![m_1g - T = m_1 a](https://tex.z-dn.net/?f=m_1g%20-%20T%20%3D%20m_1%20a)
also we have
![T r_1 = I\alpha](https://tex.z-dn.net/?f=T%20r_1%20%3D%20I%5Calpha)
now we have
![m_1g = \frac{I a}{r_1^2} + m_1 a](https://tex.z-dn.net/?f=m_1g%20%3D%20%5Cfrac%7BI%20a%7D%7Br_1%5E2%7D%20%2B%20m_1%20a)
![a = \frac{m_1g}{\frac{I}{r_1^2} + m_1}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bm_1g%7D%7B%5Cfrac%7BI%7D%7Br_1%5E2%7D%20%2B%20m_1%7D)
![a = \frac{20 (9.81)}{\frac{45}{0.5^2} + 20}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B20%20%289.81%29%7D%7B%5Cfrac%7B45%7D%7B0.5%5E2%7D%20%2B%2020%7D)
![a = 0.981 m/s^2](https://tex.z-dn.net/?f=a%20%3D%200.981%20m%2Fs%5E2)
so angular acceleration is given as
![\alpha = \frac{a}{r_1}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7Ba%7D%7Br_1%7D)
![\alpha = \frac{0.981}{0.5}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B0.981%7D%7B0.5%7D)
![\alpha = 1.96 rad/s^2](https://tex.z-dn.net/?f=%5Calpha%20%3D%201.96%20rad%2Fs%5E2)
Part c)
Tension in the rope is given as
![T = \frac{I\alpha}{r_1}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7BI%5Calpha%7D%7Br_1%7D)
![T = \frac{45 (1.96)}{0.5}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B45%20%281.96%29%7D%7B0.5%7D)
![T = 176.6 N](https://tex.z-dn.net/?f=T%20%3D%20176.6%20N)
If you are asking for a proof on having at least 3 dimensions in space, you can find the physical proof anywhere in your daily life activities. Just the fact that solids have volumes is a proof already that we live in a three-dimensional space. We can move forwards, backwards, sidewards and in all other directions possible.
When you go right into detail, the fundamental laws governing these proofs are very technical. They have differential equations to show as proof. It is too detailed to discuss here. The important things is that, these fundamental laws are what explains the science in our basic activities and natural phenomena:
*Gravitation and planetary motion
* Translation, rotation, magnetic field, forces
* Integrals of equations:
Answer:
Safety
Explanation:
Expressways are banked to resist centifugal action