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. Step 1: Identify the formula for the force exerted by a spring, which is given by Hooke's Law: $F=kx$, where $F$ is the force, $k$ is the spring constant, and $x$ is the displacement of the spring from its equilibrium position.
2. Step 2: Convert the displacement from centimeters to meters, as SI units are required for calculations. Since 1 cm = 0.01 m, the displacement $x$ is $5.0\mathrm{cm}=0.050m$.
3. Step 3: Substitute the given values into Hooke's Law. The spring constant $k$ is $750N/m$, and the displacement $x$ is $0.050m$. The formula becomes: $F=750N/m0.050m$.
4. Step 4: Perform the multiplication to find the force. Multiply the spring constant $750$ by the displacement $0.050$. This will give the magnitude of the force exerted by the spring.
5. Step 5: Interpret the result. The force calculated represents how hard the athlete is pushing against the spring to compress it by 5.0 cm. Ensure the units of the final answer are in Newtons (N), as force is measured in Newtons in the SI system.

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 essential for understanding how the spring responds to 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 compress or stretch, which is crucial for calculating the force exerted by the athlete in this scenario.

Force Calculation

To determine how hard the athlete is pushing against the spring, one must calculate the force using Hooke's Law. By substituting the 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), we can find the force exerted by the athlete, which directly correlates to the compression of the spring.