November 2018

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

Problem
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

Problem
A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

1. Assume that the distance of the chord from the center of the circle is uniformly distributed.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

2. Assume that the midpoint of the chord is evenly distributed over the circle.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

Problem
A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?