What is the maximum force reduction for a 4 m ramp in a warehouse?

In summary, the owner of a warehouse asked an engineer to design a ramp to reduce the force needed to lift boxes to the top of a 1/2 m step. The maximum factor by which the lifting force could be reduced is 8, which is determined by the mechanical advantage of the ramp and the ratio between the force of gravity and the force of the ramp's incline. The calculation for this involves finding the angle of the ramp and comparing it to the angle of gravity, assuming no acceleration and no friction. The formula used is mechanical advantage = load/effort = distance traveled by effort/distance traveled by load.
  • #1
jerryez
20
0
The owner of a warehouse ask an engineer to design a ramp which will reduce the force necessary to lift boxes to the top of a 1/2 m step. If there is only room enough for a 4 m ramp, what is the maximum factor by which the lifting force could be reduced?




I am not sure how to find the maximum factor?? Could anyone help?
 
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  • #2
hi jerryez! :wink:

well, the force to lift it without a ramp, vertically upwards (and with zero acceleration), is mgh …

what is the force needed if you use a 4m ramp? :smile:
 
  • #3
Hello Tiny-tim

Would the force than be equal to mgsintheta?? I don't think this is right but that is my best guess.
 
  • #4
You got it...

Now find theta and compare g to g*sintheta
 
  • #5
So theta = 7.2

g = 9.81 m/s(squared)

g*sintheta = 1.23


I still don't understand what the maximum factor by which the lifting force could be reduced is??
 
  • #6
It is a simple machine.

The mechanical advantage = Load/ effort = Distance traveled by the effort/ Distance traveled by the load. = 4/(1/2)
 
  • #7
hello jerryez! :smile:

(just got up :zzz: …)

The reason for the word "maximum" is because it depends on the angle of the force (and also on the acceleration being zero).

Usually when you push or pull something, your applied force isn't exactly along the slope, and if it's not exact, then you need extra force. :wink:
jerryez said:
Would the force than be equal to mgsintheta?? I don't think this is right but that is my best guess.

hmm … guessing will be no good in the exam :redface:

the method to use, as nearly always, is good ol' Newton's second law …

we're assuming no acceleration along the slope

so (let's call that direction "k") (Ftotal).k = ma.k = 0. :wink:
 
Last edited:
  • #8
Along with the other things Tim mentioned, maximum would also assume there is no friction. This would make a signficant difference in the real world. So I assume your problem also avoids this variable as well as if you did not pull the mass parallel to the plane or accelerate the mass up the plane.

I am sorry for the intervention. The posters question went unanswered for a while. So I just added that g v. sintheta*g gives you the appropriate ratio. If its force it would be mg v. m*sintheta*g, but since m is on both sides I took an irresponsible shortcut. Sorry.
 
  • #9
rl.bhat said:
It is a simple machine.

The mechanical advantage = Load/ effort = Distance traveled by the effort/ Distance traveled by the load. = 4/(1/2)

I think its says the forced reduced by, so using your shortcut I think it would be 1/2 over 4. If it said how much "easier"...
 
  • #10
Thank you everyone for your help! The answer to the problem is 8 I just didnt understand how they got it.

rl.bhat said:
It is a simple machine.

The mechanical advantage = Load/ effort = Distance traveled by the effort/ Distance traveled by the load. = 4/(1/2)

I also see now how the ratio between g and g*sintheta also results in the correct answer.

9.81/1.23 = 7.9
 

Related to What is the maximum force reduction for a 4 m ramp in a warehouse?

1. What is an inclined plane and how does it work?

An inclined plane is a simple machine that is a flat surface that is raised at one end. It allows objects to be moved from a lower height to a higher height with less force than it would take to lift the object directly. The inclined plane works by increasing the distance over which the force is applied, allowing for a smaller force to be used.

2. How does the angle of the inclined plane affect the amount of force needed to move an object?

The steeper the angle of the inclined plane, the more force is required to move an object. This is because the steeper angle increases the height that the object needs to be lifted, requiring more upward force to overcome the force of gravity pulling the object down.

3. What is the relationship between the length of the inclined plane and the force needed to move an object?

The longer the inclined plane, the less force is needed to move an object. This is because a longer inclined plane allows for a smaller angle, reducing the height that the object needs to be lifted and therefore requiring less force to overcome gravity.

4. How does friction affect the movement of an object on an inclined plane?

Friction can affect the movement of an object on an inclined plane by either helping or hindering the motion. If the object is on a smooth surface, such as a ramp covered in ice, there is very little friction and the object will slide easily. However, if the surface is rough, such as a ramp covered in sandpaper, the friction will increase and make it more difficult to move the object.

5. Can an inclined plane be used to lift an object vertically?

Yes, an inclined plane can be used to lift an object vertically. By increasing the length of the inclined plane, it can be extended to a point where it is essentially a straight line, allowing for a vertical lift. However, as the length of the inclined plane increases, the amount of force needed to lift the object also increases.

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