A 65 kg bungee jumper leaps from a bridge. She is tied to a bungee cord that is 11m long when unstretched, and falls a total of 30m .
Part a) Calculate the spring constant of the bungee cord assuming Hooke's law applies.
part b)Calculate the maximum acceleration she experiences.
i got the answer for part a which is 105.8 but i need help with part b
b) While falling freely, her acceleration remains g = 9.8 m/s^2 (positive downward). There is another relative maximum acceleration, in the opposite direction, at maximum stretch, X = 19 m. Acceleration then equals
Fnet/m = (-kX +Mg)/M
If your k is correct, that would be
(-105.8*19 +65*9.8)/65 = -21.1 m/s^2
To calculate the maximum acceleration experienced by the bungee jumper, we need to consider the forces acting on her during the fall.
Let's assume that the bungee cord obeys Hooke's law until it reaches its maximum stretching, and then acts like a freely falling object after that.
1. Calculate the maximum stretching of the bungee cord:
The bungee cord is initially 11m long and falls a total of 30m. So, the maximum stretching is:
Maximum stretching = Total fall distance - Initial length
Maximum stretching = 30m - 11m
Maximum stretching = 19m
2. Calculate the force exerted by the bungee cord when it reaches maximum stretching:
According to Hooke's law, the force (F) exerted by a spring is given by the formula:
F = k * x
where k is the spring constant and x is the displacement from the equilibrium position.
In this case, the maximum stretching (x) is 19m, and the weight (W) of the bungee jumper is given by:
W = m * g
where m is the mass of the bungee jumper (65kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the force exerted by the bungee cord at maximum stretching is:
F = k * x = W
k * x = m * g
k = (m * g) / x
Plugging in the given values:
k = (65kg * 9.8 m/s^2) / 19m
k ≈ 33.364 N/m (rounded to three decimal places)
Now, to calculate the maximum acceleration (a_max) experienced by the bungee jumper, we need to consider the forces acting on her.
3. Forces acting on the bungee jumper at maximum stretching:
- Weight (W) acts downward and is given by: W = m * g
- Force exerted by the bungee cord (F) acts upward and is given by: F = k * x
At maximum stretching, when the bungee cord is fully stretched, the net force acting on the bungee jumper is zero. Therefore, the weight is balanced by the force exerted by the bungee cord:
W = F
m * g = k * x
Now, we can calculate the maximum acceleration (a_max):
a_max = g - (F / m)
a_max = g - (k * x / m)
a_max = 9.8 m/s^2 - (33.364 N/m * 19m) / (65kg)
a_max ≈ -13.404 m/s^2 (rounded to three decimal places)
Note that the negative sign indicates that the maximum acceleration is in the opposite direction of gravity, which means it is upward in this scenario.
Therefore, the maximum acceleration experienced by the bungee jumper is approximately 13.404 m/s^2 upward.
To calculate the maximum acceleration experienced by the bungee jumper, we need to use the equation for acceleration. Since the bungee cord obeys Hooke's law, we can use the spring constant to determine the force acting on the jumper at any given point during the fall.
First, let's consider the forces acting on the jumper at the maximum downward displacement. At this point, the jumper is at the lowest point of the fall, and the bungee cord is fully extended and stretched.
1. Find the force acting on the jumper:
The force acting on the jumper at the maximum displacement can be calculated using Hooke's law: F = -kx, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position.
At the maximum displacement, x = 30 m (the total fall distance) - 11 m (the length of the unstretched bungee cord) = 19 m.
Therefore, the force acting on the jumper at this point is F = -k * 19.
2. Calculate the weight of the jumper:
The weight of the jumper can be calculated using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. In this case, m = 65 kg, and g = 9.8 m/s^2.
3. Set up the equation for acceleration:
The net force acting on the jumper at this point is the sum of the force due to the bungee cord (F) and the force due to gravity (W). Therefore, we have:
F + W = ma,
where F is the force acting on the jumper, W is the weight of the jumper, m is the mass of the jumper, and a is the acceleration.
4. Substitute the values and solve for acceleration:
Substituting the values into the equation, we have:
-F + W = ma,
-k * 19 + (65 kg * 9.8 m/s^2) = 65 kg * a.
Rearranging the equation to solve for a gives us:
a = (-k * 19 + (65 kg * 9.8 m/s^2)) / 65 kg.
By plugging in the given value for the spring constant k and solving the equation, you will be able to find the maximum acceleration experienced by the bungee jumper.