Concept explainers
Gear A weighs 1 lb and has a radius of gyration of 1.3 in.; gear B weighs 6 lb and has a radius of gyration of 3 in.; gear C weighs 9 lb and has a radius of gyration of 4.3 in. Knowing a couple M of constant magnitude of 40 lb
i.
The angular acceleration of gear C.
Answer to Problem 16.37P
Angular acceleration of gear C = 129.99 rad/s2
Explanation of Solution
Given:
weight of Gear A, wa = 1 lb radius of gyration of gear A,
radius of gear A = 2 in.
weight of gear B, wb = 6 lb
radius of gyration of gear B,
radius of gear B, r1 = 4 in.; r2 = 2 in.
weight of Gear C, wc = 9 lb
radius of gyration of gear C,
radius of gear C = 6 in.
Magnitude of Couple applied on gear A, M = 40lb-in. = 40/12 lb-ft = 3.333 lb-ft
Concept used:
Mass moment of acceleration is given by-
The tangential force acting on a gear will provide the angular acceleration to the gear. Therefore,
The free body diagram of the three gears is as following-
Calculation:
Mass of gear A =
Mass of gear B =
Mass of gear C =
Mass moment of inertia of gear A =
Mass moment of inertia of gear B =
Mass moment of inertia of gear A =
At the point of contact between A and B
At the point of contact between B and C
For gear A,
For gear B,
For gear C,
Conclusion:
Angular acceleration of gear C = 129.99 rad/s2
ii.
The tangential force that gear B exerts on gear C.
Answer to Problem 16.37P
Force exerted by gear B on gear C = 9.33 lb
Explanation of Solution
Given:
weight of Gear A, wa = 1 lb radius of gyration of gear A,
radius of gear A = 2 in.
weight of gear B, wb = 6 lb
radius of gyration of gear B,
radius of gear B, r1 = 4 in.; r2 = 2 in.
weight of Gear C, wc = 9 lb
radius of gyration of gear C,
radius of gear C = 6 in.
Magnitude of Couple applied on gear A, M = 40lb-in. = 40/12 lb-ft = 3.333 lb-ft
Angular acceleration of gear C = 129.99 rad/s2
Concept used:
Mass moment of acceleration is given by-
The tangential force acting on a gear will provide the angular acceleration to the gear. Therefore,
The free body diagram of the three gears is as following-
Calculation:
Mass of gear A =
Mass of gear B =
Mass of gear C =
Mass moment of inertia of gear A =
Mass moment of inertia of gear B =
Mass moment of inertia of gear A =
At the point of contact between A and B
At the point of contact between B and C
For gear A,
For gear B,
As found in part I,
Angular acceleration of gear C = 129.99 rad/s2
Tangential force of gear B, on gear C-
Conclusion:
Angular acceleration of gear C = 129.99 rad/s2
Force exerted by gear B on gear C = 9.33 lb
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Chapter 16 Solutions
Vector Mechanics For Engineers
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