Concept explainers
Three belts move over tow pulleys without slipping in the speed reduction system shown. At the instant shown, the velocity of point A on the input belt is 2 ft/s to the right, decreasing at the rate of 6 ft/s2. Determine, at the instant, (a) the velocity and acceleration of point C on the output belt, (b) the acceleration of point B on the output pulley.
(a)
The velocity and acceleration of point C.
Answer to Problem 15.23P
The velocity of point C is
The acceleration of point C is
Explanation of Solution
Given Information:
The velocity of point A on the input belt is
Write the expression for the angular velocity of the left side pulley.
Here, the velocity of point A is
Write the expression for the angular acceleration of the left side pulley.
Here, the tangential acceleration of point A is
Write the expression for the velocity of belt.
Here, the inner diameter of the left side pulley is
Write the expression for acceleration of intermediate belt.
Write the expression for the angular velocity of right side pulley.
Here, the outer diameter of the right-side pulley is
Write the expression to calculate the angular acceleration of the right side pulley.
Write the expression to calculate the velocity of point C.
Here, the inner diameter of the right-side pulley is
Write the expression to calculate the acceleration of point C.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The velocity of point C is
The acceleration of point C is
(b)
The acceleration of point B.
Answer to Problem 15.23P
The acceleration of point B is
Explanation of Solution
Write the expression for the normal acceleration of point B.
Write the expression for tangential acceleration of point B.
Write the expression for the resultant acceleration.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The acceleration of point B is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
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