Question

An extreme pogo stick utilizes a spring whose uncompressed length is 46 cm and whose force constant is 1.4 x 10⁴ N/m. A 60 kg enthusiast is jumping on the pogo stick, compressing the spring to a length of only 5 cm at the bottom of her jump. Calculate the net upward force on her at the moment the spring reaches its greatest compression.

A. 4900 N
B. 6700 N
C. 4000 N
D. 5200 N

Answer 1

To calculate the net upward force on the enthusiast when the spring reaches its greatest compression, we can use Hooke's Law. The force constant of the spring and the displacement of the spring are given, allowing us to calculate the net upward force.

Step-by-step explanation:

To calculate the net upward force on the enthusiast when the spring reaches its greatest compression, we need to 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 is represented by the equation F = -kx, where F is the force, k is the force constant of the spring, and x is the displacement from the equilibrium.

Given that the force constant of the spring is 1.4 x 10⁴ N/m and the displacement of the spring is 0.46 m (uncompressed length minus the compressed length), we can calculate the net upward force as follows:

1. Calculate the displacement: 0.46 m - 0.05 m = 0.41 m
2. Use Hooke's Law to find the force: F = (-1.4 x 10⁴ N/m) * (0.41 m) = -5740 N
3. The net upward force is the negative of the force calculated: -(-5740 N) = 5740 N

Therefore, the correct answer is 5740 N.