91Ó°ÊÓ

When you compress or stretch a spring, it stores energy in the form of spring potential energy. This energy depends on two key factors: the stiffness of the spring (known as the spring constant, denoted as \( k \)) and how much you compress or stretch it (displacement, denoted as \( x \)).
The energy stored in the spring is calculated using the formula:

• \( E_{sp} = 0.5 \times k \times x^2 \)

Where:

• \( E_{sp} \) is the spring potential energy.
• \( k \) is the spring constant, with units Newton per meter (N/m).
• \( x \) is the displacement of the spring from its equilibrium position.

In our exercise, we found that compressing a spring with a constant of 100 N/m by 0.20 m stores 2 Joules of energy. This stored energy is what propels the block forward once released. Understanding this is key to building a foundation in mechanics as it shows how potential energy can be converted into other forms.

The work-energy principle is a critical concept in physics that explains how energy is transferred or transformed. It states that the work done on an object is equal to the change in its energy.
This principle can be used to solve problems involving motion. When a force does work on an object, it is essentially transforming energy from one form to another.
In the context of our exercise, the spring potential energy of 2.0 Joules transforms into the work done against friction as the block moves and eventually stops. The formula capturing this idea is:

• \( W = F_{fr} \times d \)

Where:

• \( W \) is the work done, in Joules.
• \( F_{fr} \) is the frictional force opposing motion.
• \( d \) is the distance over which the force is applied.

Through the work-energy principle, we understand that all the initial energy provided by the spring is used to overcome friction, allowing us to solve for the coefficient of friction with clarity.

The coefficient of kinetic friction, denoted as \( \mu_{k} \), specifies the degree to which friction resists the movement of two surfaces sliding past each other. It is a dimensionless value that gives us insight into the roughness between the block and the surface.
This coefficient is crucial for calculating the frictional force, which is given by:

• \( F_{fr} = \mu_{k} \times F_{N} \)

Where:

• \( F_{fr} \) is the frictional force.
• \( F_{N} \) is the normal force, often equivalent to the weight of the object if on a horizontal plane.

In our exercise, by applying the work-energy principle and understanding how friction affects motion, we calculated the coefficient of kinetic friction to be 0.41. This value gives us a clear picture of how much frictional force opposed the block's motion, leading to its eventual rest.