Question

Let's investigate the motion of a uniform cylinder (think of a checker piece rolling along its circular edge) with radius released from a height h so that it makes it through a circular loop. It rolls down the hill, enters the loop of radius T_loop as shown, and never loses contact with the circular track. (Figure 1) We will assume the cylinder rolls without slipping. The cylinder's radius T_cyl is much smaller than the loop's radius T_loop Suppose we compare to something that simply slides with zero friction (but doesn't roll at all). Should our rolling cylinder be released from the same height, or from a larger height, or from a smaller height if we would like our cylinder to (barely) completely make it through the circle? Our (rolling) object should be released from a higher height. Our (rolling) object should be released from a lower height. Our (rolling) object should be released from precisely the same height. This question can't be answered unless we know the specific moment of inertia of the object we are rolling. Find the smallest possible starting height h that will allow a solid, uniform cylinder of given mass m and radius to make it through the circular loop with radius r_loop.

Answer 1

Item 6 Part A Let's investigate the motion of a uniform cylinder (think of a checker piece rolling along its circular edge) with radius rcyl released from a height h so that it makes it through a circular loop. It rolls down the hill, enters the loop of radius rloop as shown, and never loses contact with the circular track. (Fiqure 1) Suppose we compare to something that simply slides with zero friction (but doesn't rol a. Should our rolling cylinder be released from the same height, or from a larger height or from a smaller height if we would like our cylinder to (barely) completely make it through the circle? Our (rolling) object should be released from a higher height Our (rolling) object should be released from a lower height Our (rolling) object should be released from precisely the same height This question can't be answered unless we know the specific moment of inertia of the object we are rolling We will assume the cylinder rolls without slipping. The cylinder's radius Tcyl is much smaller than the loops radius Tloop Submit Hints My Answers Give Up Review Part Part B Find the smallest possible starting height h that will allow a solid uniform cylinder of given mass m and radius Tayl to make it through the circular loop with radius r Please give your result for h in terms of just the radius Tloop of the loop Figure 1 ▼of1 Submit Hints My Answers Give Up Review Part ide edbac Continue (A loop If friction is zero then cylinder will alide and do not roll so potential energy at the highest point will be converted nto translational kinetic energy and rotational kinetic energy is zero so less potential energy will be needed Less potential energy needed in sliding object and more potential energy is needed for rolling object so rolling object should release from higher height Option A is correct 2 and at the highest point of the loop its velocity V should be equal to sqrt(gr) because at the highest point centripetal force is equal to its weight 2. 4 3