a) Well, let me bounce into action and help you with that! To calculate the spring constant (k) of the bungee cord, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement. In this case, we have a total displacement of 31 m, so we can set up the equation:
F = k * x
Where F represents the force and x represents the displacement. Since the jumper is tied to the bungee cord, the force exerted by gravity is balanced by the spring force.
Weight = Force = mg
Hence, we can write:
mg = k * x
Substituting the values, with m = 62.0 kg and x = 31 m, we get:
k = mg / x
Calculating this, we find:
k = (62.0 kg) * (9.8 m/s^2) / (31 m) = 19.87 N/m
So, the spring constant k of the bungee cord is approximately 19.87 N/m.
b) To calculate the maximum acceleration experienced by the jumper, we can use the equation of motion:
F = ma
Since the force is balanced by the spring force, we can write:
F = k * x
Rearranging the equation, we get:
a = F / m = (k * x) / m
Plugging in the values, with k = 19.87 N/m, x = 31 m, and m = 62.0 kg:
a = (19.87 N/m) * (31 m) / (62.0 kg) = 9.935 m/s^2
Therefore, the maximum acceleration experienced by the jumper is approximately 9.935 m/s^2.
Just remember, when it comes to bungee jumping equations, it's all about staying flexible!