Solution to problem 8.4.12 from the collection of Kepe O.E.

8.4.12. Let us assume that gear 3 rotates uniformly with angular acceleration ?3 = 8 rad/s². It is necessary to determine the path traveled by load 1 in a time period t = 3 s, if the radii are R2 = 0.8 m, R3 = 0.6 m, r = 0.4 m. The initial position of load 1 is at rest. (Answer 10.8)

Given: angular acceleration ?3 = 8 rad/s², t = 3 s, R2 = 0.8 m, R3 = 0.6 m, r = 0.4 m. Find: the path traveled by load 1 in time t.

Solution: Angular acceleration ?3 = α3 / R3, therefore, α3 = ?3 * R3 = 4.8 rad/s². The angular acceleration of gear 2 is equal to α2 = r * α3 / R2 = 2.4 rad/s². The angle of rotation of gear 3 during time t is equal to φ3 = 0.5 * ?3 * t² = 36 rad. The angle of rotation of gear 2 during time t is equal to φ2 = r * φ3 / R2 = 18 rad. The angle of rotation of load 1 during time t is equal to φ1 = R1 * φ2 / r = 27 rad. The path traveled by load 1 during time t is equal to L1 = r * φ1 = 10.8 m.

Answer: 10.8.

Solution to problem 8.4.12 from the collection of Kepe O.?.

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Solving the problem includes a sequence of calculations, starting with determining the angular acceleration ?3 and ending with calculating the path traveled by load 1 during time t. The solution describes in detail each stage of the calculations, which makes it easy to understand the material and successfully solve the problem.

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This product is a solution to problem 8.4.12 from the collection of Kepe O.?. The task is to determine the path traveled by load 1 in time t=3 seconds, provided that gear 3 rotates uniformly with angular acceleration ?3=8 rad/s^2, and the radii of the gear, pulley and load are respectively equal to R3= 0.6 m, R2=0.8 m and r=0.4 m. It is required to find a solution to the problem using appropriate formulas and methods and obtain an answer that is equal to 10.8.

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