The minimum height h is 65m so that the car will not fall off the track at the top of the circular part of the loop.
<h3>What is mechanical energy?</h3>
Potential energy plus kinetic energy are combined to form mechanical energy. According to the principle of mechanical energy conservation, mechanical energy is constant in an isolated system when only conservative forces are acting on it. Potential energy increases when an object moves in the opposite direction of a conservative net force. Kinetic energy also changes as an object's speed, not velocity, changes. However, nonconservative forces, such as frictional forces, will always be present in real systems; however, if these forces are of minimal magnitude, mechanical energy changes little, making the idea of its conservation a reasonable approximation.
For completing the vertical circle the minimum speed at the bottom must be 
so conserving mechanical energy
⇒ h= 
h = 65m
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Jennifer runs 5 miles east, then stops to take a break. after her break, she continues running 4 more miles east.
In this the total distance she covers is 9 miles and the total displacement is also the same as the distance that is 9 miles.
<h3>What is the difference between distance and displacement?</h3>
Displacement is the shortest distance between initial and final position, or we can say it is the straight-line distance between initial and final position.
Whereas distance is considered as the total path length covered from initial position till the final position. The Displacement of a body is always less than or equal to the distance.
Displacement can be zero in case the initial and final positions coincide, but distance can never be zero.
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The spiral structure of the milky way can be explained by long lived quasi-static density waves<em>, </em><em>according to the lin-shu hypothesis. </em>Curiously, the waves of higher density gas and stars (seen as spiral arms) appear to remain static as stars move around the galaxy. This explained by assuming that the gravitational disturbances cause by the 'clumping' material in the arms does not affect the gravitational field of the galaxy as whole and is therefore negligible.
source: Astrophysicist
The centripetal force is:
F = mv² / R
Where:
m: mass of the object
v: object speed
R: radius of the curve.
We have to:
m = 2000kg
v = 25 m / s
R = 80 meters.
Then the centripetal force acting on the vehicle is:
F = (2000kg * (25m / s) ²) / 80m
F = 15625 N
