Tom Sawyer wanders out to the barn one fine summer’s day. He notices that a haystack has recently been built just outside the barn. The barn has a second story door into which the hay will be hauled into the barn by a crane. Tom decides it would be a neat idea to jump out of the second story door onto the haystack. But he knows from sad experience that if he jumps out of the second story door onto the ground, he is likely to break his leg. Knowing lots of physics, Tom decides

The complete question and the solution is given in the explanation box below.

Explanation:

Knowing lots of physics, Tom decides to estimate whether the haystack is good enough to break his fall.

He estimates the height of the haystack to be 1 meter. He presses down on top of the stack and discovers that to compress the stack by 25 cm, he has to exert a force of about 50 N. The barn door is 6 meters above the ground. Solve the problem by breaking it into pieces as follows:

A) Model the haystack by a spring. What is its spring constant?

B) Is the haystack tall enough to bring his speed to zero? (Estimate using conservation of energy)

C) If he does come to a stop before he hits the ground, what will the average force exerted on him be?

a.) -Kx = F { K is spring constant, x is displacement , F is force

K = F/x

= 50 /0.25 = 200 N/m

B.)

velocity of Tom before impact

vf^2 = vi^2 - 2*a*s

= 0 - 2*9.81*6

v= 10.849

K.E of Tom = 0.5 * m*v^2

now,{ K.E of Tom = P.E of HAy }

-0.5 K x^2 = 0.5 mv^2

x^2=(m*v^2)/K

if x>1 then the haystack is not tall enough to bring his speed zero else it will bring down its speed zero.

c.) avergae force would -kx

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