A 55-kg female bungee

jumper fastens one end of
the cord (made of elastic
material) to her ankle and the
other end to a bridge. Then
she jumps off the bridge. As
the cord is stretching, it exerts
an elastic force directed up on
her. Calculate her acceleration
at the instant the cord exerts
an elastic force of 825 N [up]
on her.

force-weight=mass*a

825-55g=55a
solve for acceleration a.

To calculate the acceleration of the bungee jumper at the instant the cord exerts an elastic force of 825 N [up] on her, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = m * a).

Given:
Mass of the bungee jumper (m) = 55 kg
Elastic force exerted by the cord (F) = 825 N [up]

We first need to convert the force from Newtons to a positive value since it is directed upwards. Therefore, we have:

F = 825 N

Since the force exerted by the cord is upward, it opposes the gravitational force on the bungee jumper. So, we need to take the difference of these forces:

Net Force = Force upwards - Force downwards
Net Force = 825 N - (mass * gravitational acceleration)

Gravitational acceleration (g) = 9.8 m/s²

Net Force = 825 N - (55 kg * 9.8 m/s²)

Now, we can find the acceleration using Newton's second law:

Net Force = mass * acceleration

825 N - (55 kg * 9.8 m/s²) = 55 kg * acceleration

Simplifying the equation:

825 N - 539 N = 55 kg * acceleration

286 N = 55 kg * acceleration

To find the acceleration, we can divide both sides of the equation by the mass:

acceleration = 286 N / 55 kg

acceleration ≈ 5.20 m/s²

Therefore, the acceleration of the bungee jumper at the instant the cord exerts an elastic force of 825 N [up] on her is approximately 5.20 m/s².

To calculate the acceleration of the bungee jumper at the instant when the cord exerts an elastic force on her, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration.

Here's the step-by-step process to find the acceleration:

Step 1: Write down the given values:
Mass of the bungee jumper (m) = 55 kg
Elastic force exerted by the cord (F) = 825 N

Step 2: Determine the acceleration using Newton's second law:
Net force (F_net) = m * a
Since the cord exerts an upward force on the jumper, the net force can be written as:
F_net = F - Weight
Weight = m * g (where g is the acceleration due to gravity, approximately 9.8 m/s^2)
So, the equation becomes:
F - m * g = m * a

Step 3: Substitute the given values into the equation:
825 N - (55 kg * 9.8 m/s^2) = 55 kg * a

Step 4: Solve for acceleration (a):
825 N - 539 N = 55 kg * a
286 N = 55 kg * a
a = 286 N / 55 kg
a ≈ 5.2 m/s^2

Therefore, the acceleration of the bungee jumper at the instant the cord exerts an elastic force of 825 N [up] on her is approximately 5.2 m/s^2.