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.