Concept explainers
The test rig is shown was developed to perform fatigue testing on fitness trampolines. A motor drives the 9-in.-radius flywheel AB, which is pinned at its center point A, in a counterclockwise direction. The flywheel is attached to slider CD by the 18-in. connecting rod BC. Knowing that the a “feet” at D should hit the trampoline twice every second, at the instant when
Fig. P15.59
(a)
The angular velocity of the connecting rod BC
Answer to Problem 15.59P
The angular velocity of connecting rod BC is
Explanation of Solution
Given information:
Radius of flywheel is
The length of connecting rod BC is
The absolute value of point A
The relative velocity of A with respect to B is defined as
Calculation:
The angular velocity of AB
According to the geometry
Therefore
The position vector of B relative to A
Substitute
The position vector of C relative to B
Substitute
The absolute velocity of
The absolute velocity of
But we know that
According to above equations
Substitute
Equate components
Therefore
Conclusion:
The angular velocity of connecting rod BC is
(b)
The velocity of D
Answer to Problem 15.59P
Explanation of Solution
Given information:
Radius of flywheel is
The length of connecting rod BC is
The absolute value of point A
The relative velocity of A with respect to B is defined as
Calculation:
According to sub part a
We have found
And
Equate components
Therefore
We know that
Therefore
Conclusion:
The velocity of point D is
(c)
The velocity of mid-point CB
Answer to Problem 15.59P
The velocity of mid-point of CB is
Explanation of Solution
Given information:
Radius of flywheel is
The length of connecting rod BC is
The absolute value of point E
The relative velocity of E with respect to C is defined as
Calculation:
Assume E as the midpoint of CB
The position vector of E relative to C
Substitute
According to sub part a
The velocity of point E
Substitute
The magnitude of the velocity
The angle
Conclusion:
The velocity of mid-point of CB is
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Chapter 15 Solutions
Vector Mechanics For Engineers
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