How can I solve this Work Energy Theorem problem for finding height?

[TheRedDevil18]

Homework Statement

I do not know how to find the height. I am thinking of using mgh=delta k but I am not getting the correct answer. I know the answer is 6.28m because my teacher gave it to me.
Below is the picture and question:

Homework Equations

mgh = delta k

The Attempt at a Solution

ep=ek
mgh=785000
98000h=785000
h = 8.01m

 

[Doc Al]

I do not know how to find the height. I am thinking of using mgh=delta k but I am not getting the correct answer.

Since the truck moves at constant speed, ΔKE = 0. So that won't work.

Instead, consider the work done by the engine and where that work goes.

 

[sankalpmittal]

Take truck as the system. What force acts during its ascension ? How many are non conservative ? What is work done by non conservative force ?

Negative work done by non conservative force= Change in truck's total mechanical energy.

 

[TheRedDevil18]

Take truck as the system. What force acts during its ascension ? How many are non conservative ? What is work done by non conservative force ?

Negative work done by non conservative force= Change in truck's total mechanical energy.

The non conservative force will be the friction right? so if I set up the equation it will be like this
-85000=k1+u1

 

[sankalpmittal]

The non conservative force will be the friction right? so if I set up the equation it will be like this
-85000=k1+u1

I should have told you to take truck+earth as the system to account for external forces.

Yes. Now total change in mechanical energy is change in kinetic energy plus change in potential energy. As change in kinetic energy is zero, so what is the change in potential energy? It will be better to account for minus sign to gravity.

 

[TheRedDevil18]

mgh, Cant work it out, need the height.

 

[sankalpmittal]

mgh, Cant work it out, need the height.

W_friction = M.E_f-M.E_i

M.E. is mechanical energy..

W_friction = ΔK.E + ΔP.E.

As ΔK.E=0 , so

ΔPE=mgh

Now you know, W_friction= -85000 J.. Can you work it out from here ?

 

[Doc Al]

mgh, Cant work it out, need the height.

The height is what you are supposed to find! Just call it h and you will solve for it.

 

[TheRedDevil18]

Okay I think I got the answer:
Fapp-Ffric=mgh
7*10^5-8.5*10^4=10000*9.8*h
h = 6.28m

Correct?

 

[Doc Al]

Okay I think I got the answer:
Fapp-Ffric=mgh
7*10^5-8.5*10^4=10000*9.8*h
h = 6.28m

Correct?

Yes, correct. (Where Fapp is the work done by the applied force, the engine in this case. Better to call it Wapp, right? And the work done against friction would be Wfric.)

 

[TheRedDevil18]

Yeah, sorry its work not force. Anyway,for 3.2 what do they mean by the instantaneous power delivered by the truck. I know P=w/t and I got the time to be 4.14s using t=d/s but what should I use for work, must I subtract Wapp-Wfrict and put it into the equation?

 

[Doc Al]

Anyway,for 3.2 what do they mean by the instantaneous power delivered by the truck. I know P=w/t and I got the time to be 4.14s using t=d/s

Good.

but what should I use for work, must I subtract Wapp-Wfrict and put it into the equation?

To find the power delivered by the engine, just use the work done by the engine.

 

[TheRedDevil18]

Okay so,
p=w/t
= 7*10^5/4.14
= 169082.13 W

Correct?

 

[Doc Al]

Okay so,
p=w/t
= 7*10^5/4.14
= 169082.13 W

Correct?

Good. (I suggest rounding off your final answer and using exponential notation.)

 

[TheRedDevil18]

Will do, and thanks for your help