You are visiting a friend\'s farm one fine summer\'s day and wander out to the b
ID: 1422353 • Letter: Y
Question
You are visiting a friend's farm one fine summer's day and wander out to the bam. You notice that a haystack has recently been built just outside the bam. The bam has a second story door into which the hay will be hauled into the bam by a crane. You decide it would be a neat idea to jump out of the second story door onto the haystack. But you know that if you jump out of the second story door onto the ground, that you are likely to break a leg. Knowing lots of physics, you decide to estimate whether the haystack is good enough to break your fall. You estimate the height of the haystack to be 1 meter. You press down on top of the stack and discover that to compress the stack by 25 cm, you have to exert a force of about 50 N. The bam door is 6 meters above the ground. Solve the problem by breaking it into pieces as follows:Explanation / Answer
1) We can use Hooke's law for this i.e F = K.x (x is the compression in haystack) , given F = 50 N and x =.25 m (in SI Units) we get K = 200 N/m.
2) Now we can estimate whether after jumping from 6 metres above the haystack or 7 m (6m +1m ) above the ground level we will break our leg or not by using energy conservation. Lets assume mass of the boy is m kg. There are two kind of energy that will be used in our problem, one is potential energy and other is potential energy stored in haystack after it reaches its maximum compressibility.
Suppose m is such that it can be stopped by haystack to touch the ground. initially the potential energy is m.g.6 which was before jumping. Another potential energy adds up when boy lands on the haystack and compresses it by distance x. So total energy is gravitational potential energy and potential energy due to compression.
Total PE = mg.6 + mg.x. To get stopped this should be balanced by haystacks potential energy which is (1/2).k.x2
mg(6+x) = 100 x2. . So, it will depend on our mass whether we will hit the ground or not. we can calculate x for given mass m.
3) Force exerted by us will be given again by Hooke's law. i.e. F = K.x where x is the compression found in the part 2) of the question.
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