How Quickly Can a Rock Be Hoisted with Limited String Strength?

AI Thread Summary
To determine the minimum time to hoist a 1.00-kg rock 10.0 meters with a string that has a breaking strength of 10.8 N, the acceleration must be calculated using the formula a = F/m, where F is the net force. The net force is the difference between the tension in the string and the weight of the rock (10 N). After establishing the correct acceleration, the time can be derived from the kinematic equation, resulting in a minimum time of approximately 4.5 seconds. For a string that is 50% stronger, the increased tension allows for greater acceleration, which reduces the minimum hoisting time significantly. Understanding the forces acting on the rock is crucial for accurate calculations.
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a) What is the minimum time in which one can hoist a 1.00-kg rock height of 10.0m if the string used to pull the rock up has a breaking strength of 10.8 N? Assume the rock to be initially at rest.


b) If the string is replaced by one that is 50% stronger, by what percentage will the minimum time for the hoist be reduced.


a)

i just used a= 2(x-xo)/t^2 and then i got 2(10)/t^2 = 10.8/1
so i got 10.8=20/t^2 and so t would be root 10.8 but the answer is 4.5seconds... how?



b) i need to get a) to solve this...
 
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Hint 1: Draw a free body diagram for the rock.
Hint 2: There is some provided info in the problem you haven't used yet.
 

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