a 62.0kg bungee jumper jumps from a bridge. she is tied to a bungee cord whose unstretched length is 12.0 m and falls a total of 31m a) calculate the spring constant k of the bungee cord and b) calculate the maximum acceleration she experiences.
To calculate the spring constant (k) of the bungee cord, you can use Hooke's Law, which states that the force exerted by an ideal spring is directly proportional to the displacement of the spring from its equilibrium position. The equation can be written as:
F = -kx
Where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
a) To find the spring constant (k), we need to calculate the force (F) exerted by the bungee cord. The jumper is falling a total distance of 31m, so the displacement (x) will be 31m - 12m = 19m. Since the force exerted by the spring is equal to the weight of the jumper, we can calculate it using:
F = mg
Where m is the mass of the jumper (62.0kg) and g is the acceleration due to gravity (9.8 m/s²).
F = (62.0kg)(9.8 m/s²) = 607.6 N
Now, we can find the spring constant (k) using Hooke's Law:
F = -kx
607.6N = -k(19m)
k = -607.6N / 19m
k ≈ -31.98 N/m (Note that the negative sign indicates that the spring is stretched and exerts an upward force)
So, the spring constant (k) of the bungee cord is approximately 31.98 N/m.
b) To calculate the maximum acceleration experienced by the bungee jumper, we can use the equation of motion:
F = ma
Where F is the net force acting on the jumper and a is the acceleration.
In this case, the net force acting on the bungee jumper is the force exerted by the bungee cord, which is equal to the weight of the jumper (607.6 N). So we have:
ma = 607.6 N
Now, we can substitute the mass (m) of the jumper:
(62.0kg)a = 607.6 N
a ≈ 9.80 m/s²
Therefore, the maximum acceleration experienced by the bungee jumper is approximately 9.80 m/s².