In Figure P5.46, the pulleys and pulleys the cord are light, all surfaces are frictionless, and the cord does not stretch. (a) How does the acceleration of block 1 compare with the acceleration of block 2? Explain your reasoning. (b) The mass of block 2 is 1.30 kg. Find its acceleration as it depends on the mass m1 of block 1. (c) What If? What does the result of part (b) predict if m1 is very much less than 1.30 kg? (d) What docs the result of part (b) predict if m2 approaches infinity? (e) In this last case, what is the tension in the cord? (f) Could you anticipate the answers to parts (c), (d), and (e) without first doing part (b)? Explain.
Figure P5.46
(a)
The way in which the acceleration of block
Explanation of Solution
The acceleration of any object is defined as the rate of change of the velocity on an object with respect to time.
Then, the acceleration of block
Here,
Conclusion:
Therefore, the acceleration of block
(b)
The acceleration of block
Answer to Problem 5.92AP
The acceleration of block
Explanation of Solution
The mass of block
Write the expression for the net force on block
Here,
Substitute
Write the expression for the net force on block
Here,
Rearrange the above expression
Solve the equation (I) and equation (II).
Substitute
Conclusion:
Therefore, the acceleration of block
(c)
The result of part (b) if
Answer to Problem 5.92AP
The acceleration of block
Explanation of Solution
When mass
Rewrite equation (III)
Neglect
Conclusion:
Substitute
Therefore, the acceleration for
(d)
The result of part (b) when
Answer to Problem 5.92AP
The acceleration for
Explanation of Solution
When the
Conclusion:
Therefore, the acceleration for
(e)
The tension in the cord when
Answer to Problem 5.92AP
The tension in the cord when
Explanation of Solution
Recall the equation (II).
Rearrange for
Conclusion:
Substitute
Therefore, the tension in the cord when
(f)
The possibility of predicting the answer to (c), part (d) and part (e) without doing part (b).
Explanation of Solution
As the mass of the bock
In the case, when the mass of block
Conclusion:
Therefore, Yes the answers to the part (c), part (d) and part (e) can be predicted without first doing part (b).
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Chapter 5 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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