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.

loss of potential energy = m g (31)

= 62 * 9.81 * 31
= 18,855 Joules

gain in potential energy of spring = (1/2) k x^2
=.5 * k (31-12)^2
= 180.5 k
so
k = 18855/180.5 = 104 N/m

F = m a

force down = m g = 62*9.81 = 608 Newtons
force up = kx
when x = 31-12 = 19
F up maximum = 104*19 = 1976 Newtons
net force up at max of spring = 1976-608
= 1368 Newtons up max
a = F/m = 1368/62 = 22 m/s^2 up

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!

a) To calculate the spring constant (k) of the bungee cord, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation is written as:

F = -kx

Where F is the force exerted by the spring (in this case, the weight of the jumper), k is the spring constant, and x is the displacement.

Let's calculate the force (F) exerted by the jumper's weight. The weight force is given by the equation:

F = m * g

Where m is the mass of the jumper (62.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

F = 62.0 kg * 9.8 m/s^2
F = 607.6 N

Now, we can calculate the displacement (x) of the bungee cord using the total fall distance:

x = total fall distance - unstretched length
x = 31 m - 12 m
x = 19 m

Now, we can rearrange Hooke's Law equation to solve for k:

k = -F / x

Substituting the known values:

k = -607.6 N / 19 m
k ≈ -31.98 N/m

Therefore, the spring constant of the bungee cord (k) is approximately 31.98 N/m.

b) The maximum acceleration experienced by the jumper can be calculated using the equation:

a = (k/m) * x

Substituting the known values:

a = (-31.98 N/m) / 62.0 kg * 19 m^2
a ≈ -5.11 m/s^2

Therefore, the maximum acceleration experienced by the jumper is approximately 5.11 m/s^2 (directed upward).

To calculate the spring constant (k) of the bungee cord, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law equation: F = -kx

Where:
F is the force applied by the spring (in Newtons, N)
k is the spring constant (in Newtons per meter, N/m)
x is the displacement from the equilibrium position (in meters, m)

In this case, the displacement is the change in length of the bungee cord, which is the difference between the unstretched length (12.0 m) and the total fall distance (31 m):

x = 31 m - 12 m
x = 19 m

Now, we need to find the force (F) that the bungee cord exerts on the jumper. The force exerted by the bungee cord is equal to the force of gravity acting on the jumper's mass.

Force of gravity equation: F = mg

Where:
m is the mass of the jumper (62.0 kg)
g is the acceleration due to gravity (9.8 m/s²)

Substituting the values, we get:

Force of gravity (F) = (62.0 kg) × (9.8 m/s²)
F = 607.6 N

Now, we can use Hooke's Law to find the spring constant (k):

607.6 N = -k × 19 m

Rearranging the equation to solve for k:

k = -607.6 N / 19 m
k ≈ 32.03 N/m

Therefore, the spring constant (k) of the bungee cord is approximately 32.03 N/m.

Now, let's calculate the maximum acceleration (a) the jumper experiences. The maximum acceleration occurs when the bungee cord is fully stretched and is about to start pulling the jumper upwards.

Using the formula for acceleration (a) from Newton's second law:

Force (F) = mass (m) × acceleration (a)

We can rearrange the equation to solve for a:

a = F / m

Substituting the values:

a = 607.6 N / 62.0 kg
a ≈ 9.80 m/s²

Therefore, the maximum acceleration (a) experienced by the jumper is approximately 9.80 m/s².