<span>A force of 110 N is applied at an angle of 30</span>°<span> to the horizontal. Because the force does not align directly either vertically or horizontally with the sled, it can be broken down into two components based on sine and cosine.
For the component parallel to the ground:
x = rcos</span>β
<span>x = 110cos30</span>°
<span>x = 95.26
For the component perpendicular to the ground:
y = rsin</span>β
<span>y = 110sin30</span>°
<span>y = 55</span>
<span>A centripetal force maintains an object's circular motion. When the ball is at the highest point, we can assume that the ball's speed v is such that the weight of the ball matches the required centripetal force to keep it moving in a circle. Hence, the string will not become slack.
centripetal force = weight of 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
Thus, the minimum speed for the ball at the top position is 2.62 m/s.</span>
I do not concur with her stance. The concept of planetary motion emerges from a collaborative effort involving Johannes Kepler and Sir Isaac Newton. I believe Tycho Brahe's role was minimal since it was really Kepler who made the significant discoveries.
(this is my original response that was accepted)
