A 1000 kg elevator accelerates upward at 1.0 m/s² for 10 m, starting from rest. How much work does the tension in the elevator cable do on the elevator?

Question

Accepted Answer

Hi everyone. In this practice problem, we're being asked to calculate the work done by a crane lifting a container. We will have a crane lifting uh 850 kg container at a constant acceleration of 1.2 m per second squared for 3.5 m. Assuming that the container was initially at rest, we want to actually calculate the work done by the crane in lifting the container. The options given are a 2.6 times 10 to the power of four S B 3.6 stamps 10 to the power of three Joles C 2.9 times 10 to the power of four Joles and D 3. times 10 to the power of four Joles. So the work done is actually going to be the force multiplied by the displacement. So we will equals to F multiplied by D. And in this case, we're not given the applied force. So we will need to actually draw the free body diagram for all the forces acting on the container. So let's imagine this uh sphere is going to be our uh container and there will be an F lifting the container up. And also there will be the weight of the container acting downwards. The acceleration is going to be pointing upwards because that is going to be the movement that is happening here, which is the crane lifting the container, the plus Y axis is going to be pointing upwards as well. And let's make that our convention. So F is going to be the force from the crane and M G is just going to be the gravitational gravitational force or the weight. So we wanna use Newton's second law in order to determine F, we are using a coordinate system where the positive Y axis is pointing upwards. So according to Newton's second law, Sigma F Y, it goes to M multiplied by A and that will then be F minus M G equals to M multiplied by a rearranging. This F will then equals to MA plus M G and we can pull the M out so that F will equals to M multiplied by open parenthesis. A plus G close parenthesis just like that. So we can actually calculate the force because we know what the mass is, which is given in the problem statement, we know what the acceler the constant acceleration is and we know what the gravitational acceleration is. So F will then equals to M which is 850 kg multiplied that by open parenthesis. A which is 1.20 m per second squared plus G which is 9.81 m per second squared, close parentheses. And they will give us a force value of Newton just like. So, so the container is moving upward because that is what's stated from the problem statement. And therefore F and D are in the same direction. So we don't have to take an account of any sort of angle because F and D are moving in the same direction. So work will just be F multiplied by D. And in that case, then F is going to be 9350 Newton and D is going to then B 3.5 m that will give us a work of 32,725 Jews or simplifying that work will then equals to 3.3 times to the power of four jules. And that will essentially be the answer to this particular practice problem. So the work done by the crane is going to be 3.3 times 10 to the power of four jules which will correspond to option D in our answer choices. So option D is going to be the answer for this practice problem. And if you guys still have any sort of confusion, please make sure to check out our adolescent videos on similar topics and that will be it for this one. Thank you.

A 1000 kg elevator accelerates upward at 1.0 m/s² for 10 m, starting from rest. How much work does the tension in the elevator cable do on the elevator?

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Key Concepts

Newton's Second Law of Motion

Work-Energy Principle

Gravitational Force