If a weight hanging on a string of length 5 feet swings through 5^\circ on either side of the vertical, how long is the arc through which the weight moves from one high point to the next high point?

First we can find the circumference of the whole circle with a radius of 5 feet. circumference = 2 pi radius circumference = (2 pi) (5 feet) circumference = (10 pi) feet From one high point to the other high point, the string moves through an angle of 10 degrees. Since a full circle is 360 degrees, this angle is 1/36 of a full circle. Therefore, the arc length is 1/36 of the whole circumference. arc length = (1/36) (circumference) arc length = (1/36) (10 pi) feet arc length = 0.873 feet

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.