Question

A 85.1 kg black bear falls off a branch 6.13 m off the ground. She manages to catch another branch 3.05 m off the ground, which bends a maximum of 46.1 cm. What is the stiffness (spring constant) of the branch

Answer 1

K = 1809 N/m = 1.809 KN/m

Step-by-step explanation:

The spring constant can be given by the following formula:

K = F/ΔL

where,

K = Spring Constant = ?

F = Force Applied

ΔL = Change in Length or the given dimension

Therefore, in this case:

ΔL = 46.1 cm = 0.461 m

and the force will be equal to the weight of the object:

F = W = mg = (85.1 kg)(9.8 m/s²)

F = 833.98 N

Therefore,

K = (833.98 N)/(0.461 m)

K = 1809 N/m = 1.809 KN/m