How much force must the bear apply to keep the jumper from moving?

Calculating the Force Applied by the Bear

• Mass of the bungee jumper (m): 80 kg
• Spring constant (k): 20 N/m
• Extension of the bungee cords (x): 50 m

First, let's calculate the weight of the jumper using the formula:

Weight (W) = mass (m) * acceleration due to gravity (g)

Calculating,

W = 80 kg * 9.8 m/s^2

W = 784 N

Next, calculate the returning force of the bungee cords using Hooke's Law:

Force (F) = spring constant (k) * extension (x)

Calculating,

F = 20 N/m * 50 m

F = 1000 N

Finally, the force to be applied by the bear can be found by subtracting the weight of the jumper from the force of the bungee cords:

Force by Bear (Fb) = Force (F) - Weight (W)

Calculating,

Fb = 1000 N - 784 N

Fb = 216 N

Therefore, the bear must apply a force of 216 N to keep the jumper from moving when caught.