You are building a display for a children's science museum in which a uniform, solid sphere of radius 0.114 m starts at rest at the top of a "hill" and rolls, without slipping, down a track and around a loop-the-loop of radius R = 1.27 m. You have already determined that the ball has to be moving at a speed no less than 3.37 m/s at the top of the loop in order to make it around the loop without falling. Note: You should consider whether the ball will be above or below the track at the top of the loop.What is the minimum height of the "hill" in order to ensure that this happens?

Problem 2: A tal, cylindrical chimney is toppling over as its base has ruptured. Let us say that the height H of the chimney is significantly larger than its thickness, so we may treat the chimney as a thin, rigid rod of length H. At the instant when the chimney is at angle 0o with respect to the vertical, what is the: (a) angular speed w of the top of the chimney? (b) radial component a, of the acceleration of the top? (c) tangential component aț of the acceleration of the top? (d) the specific value of 60 at which aț is equal to g?

A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…