91Ó°ÊÓ

Imagine you have a spring. When you stretch or compress it, it wants to return to its original shape. Hooke's Law explains this behavior. This law states that the force required to compress or stretch a spring by a distance, which we call displacement, is directly proportional to that distance. Mathematically, it is expressed as:\[ F = kx \]where - \( F \) is the force applied by or on the spring, - \( k \) is the spring constant (a measure of the spring's stiffness), - \( x \) is the displacement of the spring from its natural or rest position. A larger spring constant means a stiffer spring, requiring more force to stretch it. Understanding this law helps in determining how far a spring can stretch under a certain force without causing movement if friction is also involved.

Spring force is the force exerted by a spring when it is compressed or stretched. When dealing with problems involving springs, like the one in our exercise, determining the spring force is crucial. The spring force is always directed towards returning the spring back to its equilibrium or natural position. It acts in the opposite direction of the displacement. This restorative force is what keeps the spring in tension when it is pulled. Let's recall Hooke's Law: - If the spring constant \( k = 59 \, \mathrm{N/m} \)- The displacement \( x \) could be calculated based on the static friction This tells us how the spring force acts against other forces, like friction, in keeping the box from moving until enough force is applied.

Normal force is a basic yet foundational concept in physics. It is the support force exerted by a surface, perpendicular to the object it is in contact with. In our exercise, the normal force is crucial for understanding friction.Consider the box on the table. The normal force, denoted as \( N \), is equal in magnitude and opposite to the gravitational force acting on the box. The equation for the normal force is:\[ N = mg \]where:- \( m \) is the mass of the box, - \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \mathrm{m/s^2} \) on Earth). In our case, calculating the normal force helps us find the maximum static friction force, which keeps the box stationary on the spring-loaded table.

The coefficient of friction is a measure of how much frictional force exists between two surfaces. It is a dimensionless constant denoted by \( \mu \). There are two types: static and kinetic. In our case, we focus on the static coefficient of friction, \( \mu_s \), because we want to know how much force is needed to start moving the box.The frictional force between the box and the table is calculated as:\[ f_s = \mu_s \times N \]where - \( f_s \) is the static friction force,- \( \mu_s \) is the static coefficient of friction, - \( N \) is the normal force. In the context of our problem, the static friction keeps the box from moving until the spring force is strong enough. The high \( \mu_s \) value means more friction, which requires a greater force to overcome, highlighting the importance of properly understanding and calculating this parameter.