An elevator has mass 600 kg, not including passengers. The elevator is designed to ascend, at co

step 1 Welcome to a new problem. This is an elevator problem. So it starts on the ground floor. And the

An elevator has mass 600 kg, not including passengers. The...

Key Concepts

Gravitational Potential Energy

This concept refers to the energy an object possesses due to its position in a gravitational field. It is calculated as the product of the total mass, the gravitational acceleration, and the height above a reference point. In problems involving elevation changes, such as an elevator moving vertically, the change in gravitational potential energy is directly related to the work that must be done against gravity.

Work and Power in Mechanical Systems

Work is defined as the energy transferred when a force is applied over a distance, and power is the rate at which this work is done, expressed as energy per unit time. In scenarios where a motor drives a mechanical system, understanding the relationship between the work required (such as raising a mass against gravity) and the power output of the motor is essential for determining system limits and performance capabilities.

Unit Conversion (Horsepower to Watts)

In many engineering problems, power is provided in various units, necessitating unit conversion for consistency in calculations. Horsepower, a common unit in mechanical and automotive contexts, must often be converted to watts, the SI unit of power, to make direct comparisons and computations involving energy, time, and work in physics problems.

Mass Addition and Load Constraints

When additional mass is introduced into a system, such as passengers in an elevator, the total energy required to perform a mechanical task increases proportionally. Understanding how to incorporate the additional mass into energy and power calculations is crucial for ensuring that the system operates within its mechanical and power limits. This concept underlies the analysis of maximum allowed loads based on available energy or power constraints.

Transcript

00:01 Welcome to a new problem.

00:03 This is an elevator problem.

00:06 So it starts on the ground floor.

00:09 And the elevator is going to be lifted up a distance of 20 meters.

00:18 That's five floors.

00:20 The mass of the elevator happens to be 600 kilograms.

00:26 And there are going to be people inside the elevator.

00:29 We don't know how many.

00:31 So let's just call them x.

00:33 Stands for the number of people inside the elevator.

00:46 And that's the number we want to find.

00:49 The information given is that it's being powered, the elevator is being powered.

00:56 So by a mortar that has horse power.

01:01 So horse power is a different unit of power.

01:05 If we have large power, so this is 40 horse powers.

01:11 So the question is how many people, how many passengers are going to be inside the elevator? if each one, if each one not weighs, but each one has a mass.

01:28 Remember weight and mass are different.

01:30 Weight is a force.

01:31 Mass is a, weight is a force vector.

01:34 Mass is a scalar.

01:36 So the mass of each passenger, which i'm going to call mp.

01:43 Is 65 kilograms.

01:47 If the elevator has to go all the way up, it means it has to oppose the weight of the people, all the people inside the elevator.

01:59 And so it has to oppose the mass of the elevator and also the mass of the people.

02:08 We have x people.

02:09 Each one of them is mp.

02:11 So the total weight being opposed.

02:13 Is equivalent to this one.

02:18 If the elevator gains height up until 20 meters, then you can recall that the potential energy at any specific height is mgh.

02:31 And so the total potential energy gained by the elevator together with the p -point side is m -e -x -mp.

02:40 Remember m -e stands for the mass of the elevator.

02:44 This one is the mass of the elevator and mv stands or rather mp stands for the mass of each one of the passengers and then times h which happens to be the height that the elevator has to go all the way up we want to know what energy is expanded in moving the people from the ground level of five flows up until a height of 20 meters.

03:19 Remember, power is energy over time.

03:23 So the energy has to be the power times the time.

03:27 And we can use that as a formula.

03:30 So the potential energy expanded to move all these people up happens to be a pt, or the power times the time, which equals to m .e.

03:44 Plus x.

03:45 Mp times h...

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