When fully stretched X = 19 m beyond the unstretched length, the stored potential energy (k/2)*19^2 in the cord equals the gravitational potential energy loss, (M*g*30 m). Therefore,
k/2 = M*g*30/(19)^2 = 52.9
k = 105.8 N/m
Part a) Calculate the spring constant of the bungee cord assuming Hooke's law applies.
part b)Calculate the maximum acceleration she experiences.
k/2 = M*g*30/(19)^2 = 52.9
k = 105.8 N/m
Hooke's law can be written as:
F = k * x
Where:
F is the force exerted by the spring,
k is the spring constant,
and x is the displacement of the spring.
In this case, as the bungee cord falls 30m, the displacement of the cord can be calculated as:
x = (30m - 11m) = 19m
The force exerted by the bungee cord can be calculated as:
F = m * g
where m is the mass of the jumper (65 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F = (65 kg) * (9.8 m/s^2)
F = 637 N
Now we can calculate the spring constant:
F = k * x
k = F / x
k = (637 N) / (19m)
k ≈ 33.5 N/m
Therefore, the spring constant of the bungee cord is approximately 33.5 N/m.
To calculate the maximum acceleration the jumper experiences, we need to use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.
The net force acting on the jumper can be calculated as:
Net force = Force of gravity - Force exerted by the bungee cord
Force of gravity = m * g
Force of gravity = (65 kg) * (9.8 m/s^2)
Force of gravity = 637 N
Force exerted by the bungee cord can be calculated using Hooke's law:
Force exerted by the bungee cord = k * x
Force exerted by the bungee cord = (33.5 N/m) * (19m)
Force exerted by the bungee cord ≈ 637 N
Net force = Force of gravity - Force exerted by the bungee cord
Net force = 637 N - 637 N
Net force = 0 N
Since the net force is 0 N, the maximum acceleration the jumper experiences is 0 m/s^2. This occurs momentarily when the bungee cord reaches its maximum length and the force exerted by the cord matches the force of gravity acting on the jumper.