While an elevator of mass 2530 kg moves upward, the force exerted by the cable is 33.6 kN . (a)

step 1 Here we have the mass of the elevator, 2 ,530 kilograms. And we have the tension force in the ca

While an elevator of mass 2530 kg moves upward, the force...

While an elevator of mass $2530 \mathrm{kg}$ moves upward, the force exerted by the cable is $33.6 \mathrm{kN} .$ (a) What is the acceleration of the elevator? (b) If at some point in the motion the velocity of the elevator is $1.20 \mathrm{m} / \mathrm{s}$ upward, what is the elevator's velocity 4.00 s later?

Key Concepts

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to the product of its mass and its acceleration (F = ma). This principle is fundamental in solving problems involving motion, such as calculating the acceleration of an elevator by considering the forces acting on it, including the upward cable force and the downward gravitational force.

Free-Body Analysis

Free-body analysis involves drawing a diagram that represents all the forces acting on an object. For the elevator, the diagram would include the upward tension force from the cable and the downward gravitational force. Analyzing these forces allows us to set up the correct equation for net force and subsequently determine the acceleration.

Gravitational Force

Gravitational force is the force exerted by the Earth on any object with mass, calculated by the expression mg, where m represents the mass of the object and g is the acceleration due to gravity. In the elevator problem, this force acts downward and is essential in determining the net force acting on the elevator.

Kinematics with Constant Acceleration

Kinematics with constant acceleration involves using equations that relate displacement, initial velocity, time, acceleration, and final velocity. Once the acceleration of the elevator is determined, these equations can be applied to find how the elevator's velocity changes over a given time interval.

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