The height of the building Spider-Man (a.k.a. Peter Parker, a.k.a. Tobey McGuire
ID: 1500110 • Letter: T
Question
The height of the building Spider-Man (a.k.a. Peter Parker, a.k.a. Tobey McGuire) starts off on is 6 stories, or 18 meters high (assuming one story is 3 meters).The height of the building he wants to swing to is 1 story, or 3 meters high. The crane onto which he shoots his web is 7 stories, or 21 meters high. Tobey McGuire is 1.75 m tall and approximately 72 kg in mass. (Do not use the equations of motion to solve any part of this problem.) Determine…
a. Spider-Man's speed when his feet touch the roof the second building
b. the maximum tension in Spider-Man's web during this video clip the approximate kinetic energy dissipated when Spider-Man struck the wall
Explanation / Answer
Solution:
Initial height from where the man starts = h1 = 18 m
Final height of the building on to which he jumps = h2 = 3 m
Spider Man's mass = = m = 72 kg
a) Using energy conservation principle, the potential energy + kinetic energy INitially = Final Potential energy + kinetic energy
=> mgh1 + 1/2mv^2 =mgh2 + 1/2 mv2^2
=> g(18) + 0 = g(3) +1/2 v2^2
=> 18 g - 3g = 1/2v2^2
=> v2^ = 2 * 15g
=> v = 17.15 m/s
b) Tension is calculated by assuming a circular orbit ; the velocity v = 17.15 m/s is at the bottom of the swing , where the orbit is of radius R =1 8m
using the force equations, centripetal force Fc = Tension - gravity force
=> T - mg = mv^2 /R
=> T = mg + mv^2 ./ R = 72 ( 9.8 + 17.15^2/18) = 1882 N
c) mgh2 +1/2mv2^2 = 1/2mvf^2
=> change in kinetic energy = mgh2 = 72 * 9.8 * 3 = 2116.8 J
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