91Ó°ÊÓ

Normal force is a vital concept in physics, describing the force perpendicular to a surface. It is exerted by a surface to support the weight of an object resting upon it. This force is crucial because it balances the object's weight when stable on a surface, preventing it from falling through. In the context of the exercise, the normal force is the force exerted by the floor on the 35 kg crate. To calculate the normal force, we need to consider the weight of the crate. The force due to gravity on the crate is calculated using the formula: \[ F_n = m \cdot g \] where \( m \) is the mass (35 kg) and \( g \) is the acceleration due to gravity (approximately \(9.8\, \text{m/s}^2\)). Plugging in these values, we find that the normal force \( F_n \) equals \(343\, \text{N}\). This normal force plays a pivotal role in determining the frictional forces at work.

Static frictional force is the force that acts to resist the initiation of sliding motion between two surfaces in contact. It is the reason objects do not slide down a sloped surface or remain still when a small force is applied. The formula to determine the static frictional force \(f_{s,\text{max}}\) is: \[ f_{s,\text{max}} = \mu_s \cdot F_n \] where \( \mu_s \) is the coefficient of static friction, and \( F_n \) is the normal force. In our crate exercise, with \( \mu_s = 0.37 \) and \( F_n = 343 \text{ N} \), the maximum static frictional force is found to be \( 126.91 \text{ N} \). This value is the threshold force required to overcome static friction and initiate the crate's movement. When the applied force is less than \(f_{s,\text{max}}\), as it is in this case (\( 110 \text{ N}\)), the static frictional force equals the applied force (\( 110 \text{ N}\)), preventing motion.

Newton's laws of motion form the foundation for understanding mechanics in physics. These laws describe the relationship between a body and the forces acting on it, and how it moves as a result.1. **First Law**: An object will remain at rest or in uniform motion unless acted upon by an external force. In this exercise, the crate does not move because the static frictional force is equal to the applied force, illustrating the first law. 2. **Second Law**: The acceleration of an object depends on the net force acting on it and its mass, expressed as \( F = m \cdot a \). If the net force exceeds the static frictional force, the crate would accelerate. 3. **Third Law**: For every action, there is an equal and opposite reaction. When the worker pushes the crate, the floor pushes back with an equal force of static friction.Understanding these laws empowers us to predict an object's motion or the forces necessary to alter that motion. They are critical for comprehending why the crate remains stationary or what additional forces are needed to induce movement.