An elevator filled with passengers has a mass of 1.70 ×10^3 kg . (a) The elevator accelerates up

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An elevator filled with passengers has a mass of 1.70 ×10^3...

An elevator filled with passengers has a mass of $1.70 \times 10^{3} \mathrm{kg} .$ (a) The elevator accelerates upward from rest at a rate of $1.20 \mathrm{m} / \mathrm{s}^{2}$ for $1.50 \mathrm{s}$. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of $0.600 \mathrm{m} / \mathrm{s}^{2}$ for $3.00 \mathrm{s}$. What is the tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?

An elevator filled with passengers has a mass of $1.70 \times 10^{3} \mathrm{kg} .$ (a) The elevator accelerates upward from rest at a rate of $1.20 \mathrm{m} / \mathrm{s}^{2}$ for $1.50 \mathrm{s}$. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of $0.600 \mathrm{m} / \mathrm{s}^{2}$ for $3.00 \mathrm{s}$. What is the
tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?

Key Concepts

Equilibrium and Constant Velocity

When an object moves at a constant velocity, there is no net acceleration, implying that all forces acting on the object are balanced. For an elevator moving at a constant speed, this means that the upward tension in the cable exactly balances the downward gravitational force. Understanding this equilibrium condition is important for determining the forces acting in systems undergoing uniform motion.

Kinematics of Constant Acceleration

Kinematics deals with the motion of objects without considering the forces behind the motion. When acceleration is constant, a set of equations can be used to determine changes in velocity and displacement over time. This concept is crucial for calculating quantities such as final velocity and displacement during periods of acceleration or deceleration, as commonly encountered in problems involving moving elevators.

Newton's Second Law

This principle states that the overall or net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = ma). It is used to relate forces acting on a system, such as gravitational force and tension, to the resulting acceleration, making it a foundational concept for analyzing the motion of objects in mechanics.

Tension in a Cable

Tension refers to the pulling force transmitted along a cable, rope, or string when it is used to support or move a mass. In problems involving elevators or similar systems, tension must counteract both the gravitational force acting downward and any additional force needed to accelerate or decelerate the mass, making it essential for understanding the support and motion of the system.

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