Concept explainers
An ice cube with a mass of 0.0507 kg is placed at the midpoint of a 1.00-m-long wooden board that is propped up at a 50° angle. The coefficient of kinetic friction between the ice and the wood is 0.133. a. How much time does it take for the ice cube to slide to the lower end of the board? b. If the ice cube is replaced with a 0.0507-kg wooden block, where the coefficient of kinetic friction between the block and the board is 0.275, at what angle should the board be placed so that the block takes the same amount of time to slide to the lower end as the ice cube does? You may find a spreadsheet program helpful in answering this question.
(a)
The time does the ice cube takes to slide to the lower end of the board.
Answer to Problem 25PQ
The time does the ice cube takes to slide to the lower end of the board is
Explanation of Solution
Consider the axis is along the incline.
Free body diagram
Write the expression for the net force acting on the ice cube.
Here,
Write the expression for the normal force.
Write the expression for the net force in terms of Newton’s law.
Here,
Use (II) and (III) to rewrite (I).
Write the expression for the time taken to slide down the lower end.
Here,
Use equation (IV) to rewrite (V).
Conclusion:
Ice slides down from the mid-point of the board of length
Substitute
Therefore, the time does the ice cube takes to slide to the lower end of the board is
(b)
The angle the board be placed so that the block takes the same amount of time to slide to the lower end as the ice cube does.
Answer to Problem 25PQ
The angle the board be placed so that the block takes the same amount of time to slide to the lower end as the ice cube does is
Explanation of Solution
Rewrite the equation (VI) to solve for
Here,
Conclusion:
Substitute
Substitute different values for
Tabular column shows the result for various values of
Result | |
From the above table for the angle
Therefore, the angle the board be placed so that the block takes the same amount of time to slide to the lower end as the ice cube does is
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Chapter 6 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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