91Ó°ÊÓ

The normal force is a crucial concept in physics, especially when dealing with objects on flat surfaces. It is the force exerted by a surface to support the weight of an object resting on it. In this exercise, the normal force is calculated first because it helps determine the frictional force. Since the crate is on a level floor, the normal force is equal to the gravitational force acting on the crate. This can be calculated using the formula: \( N = mg \) . Here, \( m \) represents the mass of the crate (55 kg), and \( g \) is the acceleration due to gravity (9.8 m/s²). Substituting these values, we find that the normal force is \( N = 55 \, kg \, \times 9.8 \, m/s^2 = 539 \, N \). This force acts perpendicular to the surface and is essential for calculating the frictional force.

Frictional force is the resistive force that opposes the motion of an object. In this problem, we focus on kinetic friction, which occurs when the crate is moving. The frictional force can be calculated using the coefficient of kinetic friction \( \text{μ_k} \) and the normal force \( N \). The formula is: \( f_k = μ_k \times N \). For this crate, \( μ_k \) is given as 0.35. By substituting the values, we get \[ f_k = 0.35 \times 539 \, N = 188.65 \, N \]. This means the frictional force acting against the crate’s movement is 188.65 N. Understanding this concept helps explain why objects don't slide infinitely when an initial force is applied.

Newton's Second Law is fundamental for understanding how forces impact the motion of objects. It states that \( F = ma \), where \( F \) is the net force acting on an object, \( m \) is the mass, and \( a \) is the acceleration. In this exercise, we need to find the crate's acceleration using the net force. The net force is the applied force minus the frictional force: \( F_{net} = 220 \, N - 188.65 \, N = 31.35 \, N \). This remaining force causes the crate to accelerate. Rearranging Newton's second law to solve for acceleration, we get \( a = \frac{F_{net}}{m} \). Substituting the known values: \( a = \frac{31.35 \, N}{55 \, kg} = 0.57 \, m/s^2 \). This means the crate accelerates at a rate of 0.57 meters per second squared.

Calculating acceleration is the final step in this problem. Once we have the net force, we can easily find the acceleration using the formula derived from Newton's second law: \( a = \frac{F_{net}}{m} \). With the net force calculated as 31.35 N and the mass of the crate as 55 kg, we substitute these values into the equation: \[ a = \frac{31.35 \, N}{55 \, kg} = 0.57 \, m/s^2 \]. This result tells us how quickly the crate speeds up as it is pushed across the floor. Accurate acceleration calculations are critical in various real-world applications, from vehicle dynamics to space shuttle launches. Understanding each component, such as mass, net force, and acceleration, provides a more comprehensive grasp of how forces influence motion.