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 m 1 of block 1. (c) What If? What does the result of part (b) predict if m 1 is very much less than 1.30 kg? (d) What docs the result of part (b) predict if m 2 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
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 m 1 of block 1. (c) What If? What does the result of part (b) predict if m 1 is very much less than 1.30 kg? (d) What docs the result of part (b) predict if m 2 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
Solution Summary: The author explains how the acceleration of block 1 can be compared with that of the same block.
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)
Expert Solution
To determine
The way in which the acceleration of block 1 can be compared with the acceleration of block 2.
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.
1cm downward motion of block 2 requires block 1 to move 2cm forward. It means block 1 always has twice the speed of block 2 thus the acceleration of block 1 is twice the of block 2.
Then, the acceleration of block 1 is given as, a1=2a2
Here, a1 is the acceleration of block 1 and a2 is the acceleration of block 2.
Conclusion:
Therefore, the acceleration of block 1 is twice the of block 2.
(b)
Expert Solution
To determine
The acceleration of block 2.
Answer to Problem 5.92AP
The acceleration of block 2 is (12.7N)4m1+(1.30kg).
Explanation of Solution
The mass of block 2 is 1.30kg.
Write the expression for the net force on block 1 in the x-direction
∑Fx=m1a1T=m1a1
Here, ∑Fx is the net force on block 1 in the x-direction, T is the tension in the rope and m1 is the mass of block 1.
Substitute 2a2 for a1 in above expression.
T=m1(2a2) (I)
Write the expression for the net force on block 2 in the x-direction
∑Fy=m2a2T+T−m2g=m2(−a2)
Here, ∑Fy is the net force in the y-direction, g is the acceleration due to gravity and m2 is the mass of block 2.
Therefore, the tension in the cord when m1 approaches infinity is 6.37N.
(f)
Expert Solution
To determine
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 1 approaches zero, the block 2 almost undergoes free fall and hence the acceleration of block 2 is same as that of the gravitational acceleration.
In the case, when the mass of block 1 becomes infinite, the system is almost in equilibrium and hence there is no acceleration. Since there is no acceleration, the weight of the block 1 is balanced by the tensional force along the cord. From this, the tension can be found.
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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