<span>A centripetal force is a force which keeps an object moving in a circle. When the ball is at the top position, let's assume that the speed v is such that the gravitational force is precisely equal to the required centripetal force to keep the ball moving around in a circle. Then the string will not go slack.
centripetal force = force of gravity on the ball
m v^2 / r = m g
v^2 / r = g
v^2 = g r
v = sqrt { g r }
v = sqrt { (9.80~m/s^2) (0.7 m) }
v = 2.62 m/s
The minimum speed of the ball at the top position is 2.62 m/s</span>
Acceleration is the change of velocity, and velocity is the change of distance. The opposite of finding change, or differentiation, is integration.
Acceleration = 1.3 m/s²
Velocity: ∫ 1.3 dx = 1.3x + c m/s
Distance: ∫ 1.3x dx = 1.3x²/2 + c m
Distance run: 1.3*3²/2 = 5.85 m
<em>What</em><em> </em><em>bad</em><em> </em><em>thing</em><em> </em><em>happened</em><em>?</em>
How dense the medium is in the compression part of the wave and how rare the medium is in the rarefaction part of the wave is a measure of the longitudinal wave's amplitude.