Question

In which direction is the unbalanced force acting during the part of the trip where the elevator is traveling at \(6 \mathrm{~m} / \mathrm{s}\) ? (A) downward (B) upward (C) toward the entrance of the elevator (D) There is no unbalanced force.

Short answer

(D) There is no unbalanced force.

Step-by-step solution

Recognize the key concept involved

The key concept to grasp in this exercise is Newton's First Law of Motion, which states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Identify the velocity and acceleration of the elevator

We are given that the elevator is traveling at 6 m/s. Since we are not given any information about a change in the elevator's velocity, we can assume that the elevator is moving at a constant speed. Consequently, its acceleration is 0 m/s².

Determine the unbalanced force acting on the elevator

Since the acceleration of the elevator is 0 m/s², this means that there are no unbalanced forces acting on the elevator. If there were any unbalanced forces, the elevator would be accelerating, contrary to the information provided.

Select the correct answer choice

Based on our analysis, we concluded that there is no unbalanced force acting on the elevator while it is traveling at a constant speed of 6 m/s. Therefore, the correct answer choice is: (D) There is no unbalanced force.

Key concepts

Unbalanced Force

When discussing motion, the concept of an unbalanced force is fundamental. This term refers to a force that is not countered by another force of equal magnitude but in the opposite direction. According to Newton's First Law of Motion, also known as the law of inertia, an object continues to remain at rest or move at a constant velocity unless an unbalanced force acts upon it.

Applied to the exercise about the elevator, an unbalanced force would result in a change in the elevator's motion - either speeding it up, slowing it down, or changing its direction. Since we learned that the elevator travels at a constant speed and in a fixed direction, and there is no indication of acceleration, we deduce that the forces acting upon the elevator are balanced. Therefore, in this scenario, the absence of acceleration confirms that no unbalanced force is acting on the elevator while it moves at 6 m/s.

Understanding the relationship between forces and motion is essential for students to comprehend how objects behave. An improvement in exercises could involve visual or interactive elements that depict the effects of unbalanced forces, to reinforce the concept that only an unbalanced force can change an object's state of motion.

Constant Velocity

The term constant velocity implies that an object is moving in a straight line at a steady speed. Velocity is a vector quantity which means it has both magnitude (speed) and direction. Thus, when we say an object maintains a constant velocity, we are saying that neither its speed nor its direction is changing over time.

From the exercise context concerning the elevator, the constant velocity indicates that the elevator had no acceleration or deceleration while traveling at 6 m/s, suggesting no net forces were acting on it. This adheres to Newton's First Law of Motion, signifying that in the absence of an unbalanced force, the velocity of the elevator remains unchanged. An enhancement to student understanding might be to present scenarios where they need to compare situations of constant velocity to those involving varying speeds, to emphasize the impact of balanced and unbalanced forces on an object's motion.

Acceleration

The concept of acceleration entails a change in the velocity of an object over time. This can mean an increase in speed, a decrease in speed (often referred to as deceleration), or a change in direction. Mathematically, acceleration is calculated as the change in velocity divided by the time over which the change occurs.

In the elevator example, if it were accelerating, we would observe a change from the initial velocity of 6 m/s. Since the elevator maintains this velocity throughout, it experiences zero acceleration. To convey this more effectively to students, exercises could include comparing the elevator's motion with other motion scenarios involving known accelerations, reinforcing the idea that acceleration describes how quickly velocity changes. Students would benefit from hands-on activities, perhaps using simulations, where they can actively change variables to see the direct effect on acceleration, deepening their understanding of the concept.