typed answers please. Question 6 The Drop Tower is a ride at a proposed amusemen

Question

typed answers please.

Question 6 The Drop Tower is a ride at a proposed amusement park that releases a capsule to drop in free-fall (without any external forces applied to it). At 4.0 x 101 meters above the ground, a clamp engages and applies a constant force to slow the capsule so that it stops when re engaging the clamp, the capsule falls with a . The design weight of the capsule at maximum capacity is 45 kN. it reaches the ground. speed of 25 m/s. (a) Determine the work of the clamping force that is required to stop the capsule at its design weight. (b) Using your answer from part (a). calculate the constant clamping force required to stop the capsule (c) A spring, with spring constant k, is now used to stop the capsule in the same distance as specified in the problem statement. Determine the required spring constant.

Explanation / Answer

a)

KE of the capsule just before engaging the force = 0.5*(45*10^3/9.8)*25^2

= 1.435*10^6 J

So, PE of the capsule at this moment = mgh = (45*10^3/9.8)*9.8*40

= 1.8*10^6 J

So, total work done to stop the capsule = -(KE + PE)

= -(1.435 + 1.8)*10^6

= -3.24*10^6 J

b)

v^2 = u^2 + 2as

So, 0^2 = 25^2 + 2*a*40

So, a = 7.81 m/s2

So, F = m*a = (45*10^3/9.8)*7.81 = 3.59*10^4 N

c)

Work done = enegy stored in the spring

= 0.5*k*x^2

So, 3.23*10^6 = 0.5*k*40^2

So, k = 4037.5 N/m

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