91Ó°ÊÓ

The normal force is an essential concept when discussing motion on surfaces. It is the force exerted by a surface to support the weight of an object resting on it. In this scenario, the stockroom worker deals with a box on a horizontal surface. As the box rests on this surface, gravity pulls it downward. The surface responds by exerting an upward normal force.

To calculate the normal force, we use the formula:

• \[ N = m \cdot g \]

where \( m \) is the mass of the box (11.2 kg) and \( g \) is the acceleration due to gravity (approximately 9.81 \( \text{m/s}^2 \)). In this case, the normal force equals the weight of the box because there are no other vertical forces acting on it. Thus, the normal force is 109.872 N.

This normal force plays a crucial role in determining the force of kinetic friction. Since kinetic friction depends on both the coefficient of friction and the normal force, understanding this concept helps in solving related motion problems effectively.

In physics, the horizontal force is crucial in understanding how objects move across surfaces. When an object, like the box in the exercise, moves at a constant speed, it implies that the applied horizontal force balances the frictional force. This means that the net force acting on the box is zero.

The worker must apply a force equal to the force of kinetic friction to maintain constant motion. Kinetic friction can be calculated using the formula:

• \[ f_k = \mu_k \cdot N \]

where \( \mu_k \) is the coefficient of friction (0.20), and \( N \) is the normal force (109.872 N).

In this exercise, the horizontal force required is found to be approximately 22 N. This understanding assists in realizing how different forces interact to result in motion and equilibrium on a plane.

When an object in motion experiences a decrease in speed, it is referred to as deceleration, a form of negative acceleration. In our stockroom worker problem, when the applying force is removed, the box will begin to slow down due to the kinetic friction force opposing its motion.

Deceleration is calculated using Newton's second law of motion, where the force of friction is acting against the mass of the object to decelerate it:

• \[ a = \frac{-f_k}{m} \]

With the kinetic force \( f_k \) as 21.9744 N and the box's mass as 11.2 kg, the box experiences a deceleration of \(-1.962 \, \text{m/s}^{2}\).

This concept is vital for calculating the stopping distance or analyzing how quickly a moving object comes to rest under certain forces.

Kinematic equations are essential tools in physics for predicting the motion of objects. They relate the quantities of velocity, acceleration, displacement, and time. When solving the second part of the exercise, these equations become particularly handy to find how far the box slides after the force is removed.

The equation used here is:

• \[ v^2 = u^2 + 2as \]

where \( v \) is the final velocity (0 m/s, since the box stops), \( u \) is the initial velocity (3.5 m/s), \( a \) is the deceleration (-1.962 m/s²), and \( s \) is the distance traveled.

Solving the equation gives a distance \( s \) of approximately 3.12 meters before the box comes to rest. Understanding how to manipulate these equations allows us to unravel more complex problems related to motion.