A continuous belt links three cylindrical wheels so that the belt remains taut and…
MATHEMATICS · Multi-part · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics
Problem
A continuous belt links three cylindrical wheels so that the belt remains taut and does not slip at any point of contact. The belt wraps around the wheels as follows:
• 200° around Wheel A (radius 0.315 m),
• 90° around Wheel B (radius 0.150 m),
• 70° around an idler Wheel C (radius 0.200 m).
The segment of belt in contact with Wheel A is found to have a length of 1.10 m.
(a) Wheel A is given an angular displacement of 3.0 rad. Calculate the length of belt that passes a fixed reference mark on the belt during this rotation.
(b) For the same 3.0 rad rotation of Wheel A, determine the corresponding angular displacement of Wheel B.
(c) Calculate the length of belt that is in contact with Wheel C.
(d) Using your results, compute the minimum total belt length required to accommodate all three wrap segments around the wheels, neglecting the straight portions between wheels.