A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?

Verified step by step guidance

1. Identify the given values: spring constant (k) = 750 N/m, compression distance (x) = 5.0 cm. Convert the compression distance from cm to meters for consistency in units, so x = 0.05 m.
2. Recall Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The formula is F = -kx.
3. Substitute the given values into Hooke's Law. Here, F = -750 N/m * 0.05 m.
4. Calculate the magnitude of the force, ignoring the negative sign which indicates direction (towards the equilibrium position).
5. The magnitude of the force calculated will tell you how hard the athlete is pushing on the spring.

Key Concepts

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, provided the elastic limit is not exceeded. Mathematically, it is expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement. This principle is fundamental in understanding how springs behave under compression or extension.

Spring Constant

The spring constant, denoted as k, is a measure of a spring's stiffness. It is defined as the force required to compress or extend the spring by a unit distance. A higher spring constant indicates a stiffer spring that requires more force to achieve the same displacement compared to a spring with a lower spring constant.

Force Calculation

To determine the force exerted by the athlete on the spring, one can apply Hooke's Law. By substituting the known values of the spring constant and the displacement into the formula F = kx, where k is 750 N/m and x is 0.05 m (5.0 cm), the force can be calculated. This calculation provides insight into the athlete's effort in compressing the spring.