Question

a Porter keep standing at a place while holding a suitable of mass 20 kg over his head for five minutes. has he done some work? give reason for your answer

Answer 1

Thanks for the A2A.

The wording of the question is a bit of a challenge. I am not sure I understand what is intended by “upward lifting force relative to him?” If, the question just means how much work does the porter do by carrying the box up the stairs, or how much is the box’s potential energy increased by being carried up the stairs, then the answer is +mgh. This is true because one way to describe work done is as the dot product of force, F and distance, D. The use of the dot product is important here as what matters is the component of the force that is in the direction of the distance moved. In this case, the force is mg, the weight of the box. The distance is the height it is raised, h. That is important and height is, by definition, in the direction opposite to gravity.

Now here is where it is easy to get confused. The force due to gravity is down. However, the work is being done by the porter who is opposing gravity. So the force from the porter is straight up. Hence, the mg that we use here is in the same direction and the distance traveled, h. So, the answer is +mgh.

If the porter were carrying the box down, she would still be exerting that same upward force, but the distance would be -h, so in that case the work done on the box would be -mgh.

I did mention briefly the equivilence of the work and change in potential energy. That is because as long as no energy leaves the system, like in heat due to frictions, etc., that is exactly what is going on. We are storing energy in the box. That energy could be released, or converted to kinetic energy if, upon reaching the top of the stairs, the porter got into an argument about payment and tossed the box out the window. In that case, the stored potential energy, mgh, would be converted into kinetic energy, 1/2mV^2. When the box reached the ground all of the potential energy, relative to what it had when it was at the ground level originally, would be in its speed. That can be found by setting the two energies to be equal:

mgh = 1/2mV^2

gh = 1/2V^2

V^2 = 2gh

V = sqrt (2gh) ;

Answer 2

Hi!!

here is a simple answer which you can write in exam.

☀No, he has not done any work. Work is said to be done only when a force is applied and there is displacement of the object. Here, there is no displacement of the object, i.e. the suitcase therefore we can conclude that no work has been done by him.

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