Concept explainers
(a)
The magnitude of maximum tension when the cart rolls on a horizontal surface.
(a)
Answer to Problem 158P
The magnitude of maximum tension when the cart rolls on a horizontal surface is
Explanation of Solution
The mass of the cart is
Write the expression to calculate the acceleration of the system.
Here, a is the acceleration of the system.
Rewrite the above equation in terms of a.
Write the equilibrium condition of forces in vertical direction for the system.
Here, N is the normal force and g is the acceleration due to gravity.
Rewrite the above equation in terms of N.
The block is not sliding means the magnitude of frictional force and the force on the block would be equal.
Write the expression to calculate the equilibrium of force in horizontal direction.
Substitute
Substitute equation (I) in the above equation to calculate T.
Conclusion:
Therefore, the magnitude of maximum tension when the cart rolls on a horizontal surface is
(b)
The magnitude of maximum tension when the cart rolls on a ramp of angle
(b)
Answer to Problem 158P
The magnitude of maximum tension when the cart rolls up on a ramp is
Explanation of Solution
Write the expression to calculate the acceleration of the system.
Here, a is the acceleration of the system.
Rewrite the above equation in terms of a.
Write the equilibrium condition of forces in vertical direction for the system.
Here, N is the normal force and g is the acceleration due to gravity.
Rewrite the above equation in terms of N.
The block is not sliding means the magnitude of frictional force and the force on the block would be equal.
Write the expression to calculate the equilibrium of force in horizontal direction.
Substitute equation (IV) and (V) in the above equation to calculate T.
Conclusion:
Therefore, the magnitude of maximum tension when the cart rolls on a horizontal surface is
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