91Ó°ÊÓ

Understanding Newton's Laws of Motion is fundamental to solving problems related to forces and motion. Newton's First Law, sometimes called the Law of Inertia, states that an object will remain at rest or move with a constant velocity unless acted upon by a net external force. In the problem of the sliding crate, since it moves at a constant speed, the net force acting on it is zero. This means that the forces applied by the workers are perfectly balanced by the kinetic friction force. Newton's Second Law ties force, mass, and acceleration together, expressed by the equation \( F = ma \). In our scenario, since the crate moves at constant speed, the acceleration \( a \) is zero, implying the net force is zero. Lastly, Newton's Third Law tells us that for every action, there is an equal and opposite reaction, which helps us understand how the floor pushes back with a normal force.

The normal force is a key concept in understanding how objects interact with surfaces. It is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this exercise, the crate is resting on a horizontal floor, meaning there are no vertical movements. Because of this, the normal force \( N \) is equal to the gravitational force acting on the crate. This can be calculated by multiplying the mass of the crate \( m \) by the gravitational acceleration \( g \), resulting in \( N = m \times g = 300 \text{ kg} \times 9.8 \text{ m/s}^2 = 2940 \text{ N} \). The normal force plays a crucial role in kinetic friction calculations because it influences the magnitude of the frictional force.

Kinetic friction occurs when two surfaces slide past each other. It resists the motion, and its magnitude can be calculated once you know the normal force and the coefficient of kinetic friction. The force of kinetic friction \( f_k \) is given by \( f_k = \mu_k \times N \), where \( \mu_k \) is the coefficient of kinetic friction. In the problem given, both workers apply a combined force to keep the crate moving at constant speed, balancing the kinetic friction force. To find \( \mu_k \), you divide the total applied force by the normal force, resulting in \( \mu_k = \frac{730 \text{ N}}{2940 \text{ N}} = 0.248 \). This coefficient is a measure of how easily the crate slides over the floor.

Moving at constant speed indicates a balance in forces, meaning the net force on an object is zero. In the practice problem, this balance is achieved between the applied force by the workers and the kinetic frictional force opposing it. Since the speed is constant, the total horizontal force applied equals the kinetic friction force. This concept is vital for understanding the problem because it allows us to equate the total force exerted by the workers to the friction force. By doing so, we can accurately determine the coefficient of kinetic friction, as all forces have reached equilibrium. Recognizing when forces are in balance helps simplify these types of physics problems significantly.