Mechanics- Inclined plane

In summary, the conversation involved a stagehand discussing their job of running crates on wheels up a ramp to the loading bay. They wanted to make a physics equation out of it to determine the amount of work they did. Through calculations and equations, they determined the force of gravity on the crate and the force needed to push it up the slope. They also discussed using energy to calculate the work done on the crate.
  • #1
mstine87
1
0
I am a stagehand and I was just doing a job yesterday involving running crates on wheels up a ramp to the loading bay. I thought it would be interesting if I could make a physics equation out of it and determine the amount of work I did.

Homework Statement


If I want to determine how much mechanical work (J) is done by accelerating a crate on wheels with a mass (m) of 90kg, and pushing it at a constant velocity (v) of 2m/s up a plane inclined at 15 degrees (It's on wheels, so effectively frictionless plane). The ramp is 30 m in distance, and total vertical displacement (h) would be approximately 10.26 m.

I determined that I was reaching the top of the ramp in about 15 seconds, which is how I determined that my average velocity was 2m/s.[/b]



Homework Equations


1. v=Δd/Δt
2. a=Δv/Δt
3. f=m*a
4. w=f*d
5. g=9.8m/s^2

Derivative equation
6. a=g*sin(theta)
7.f=m*g*cos(theta)

The Attempt at a Solution



The Force of gravity on the 90 kg mass is given by (eq3), or f=90 kg*9.8m/s^2. f(g)=882N

I figured that I could determine the force of the mass pushing down the slope against me by determining its rate of acceleration down the slope if I weren't there
(eq6) a=9.8*sin(15 degrees), a=2.5 m/s^2
The force down the slope is then (eq3)f=90kg*2.5m/s^2=225N.
I think this means that I would have to apply a force of 225N to keep the crate still on the plane- precisely opposing the force of gravity pulling it down.

The normal force is given by (eq7). m*g was calculated earlier as 882N, and 882*cos(15 degrees) is 851.94N.

Here is my problem. I can't figure out what I need to do next. I want to know how much work was done to get the mass to the top of the slope. So I would need to know how much force I needed to push the crate at a constant velocity of 2m/s, and I have no idea how to get there. Once I know the total force I applied to overcome the force of gravity, I can add in the force it would take to accelerate the mass to 2m/s and keep it there. Can anybody help me?

I would like to add that this is not homework or school related. I am interested in applying what I learned when I was in school to my job for leisure.
 
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  • #2
Neglecting all kinds of friction, you need the same force to push the crate uphill with constant velocity as to keep it in rest: mgsin(theta).
When you accelerate the cart, you need an additional force ma.

You can solve the problem in this way, multiplying force with displacement, but it is easier to use energy: Your work increases both the kinetic and potential energy of the crate. Calculate the energy of the crate at the top of the slope: That is your work done on it while it is accelerated and pushed to the top of the slope.

ehild
 

1. What is an inclined plane?

An inclined plane is a flat surface that is slanted at an angle, allowing objects to move up or down with less effort than if they were moving on a flat surface.

2. How does an inclined plane work?

An inclined plane works by reducing the amount of force needed to move an object to a higher or lower position. The length of the plane and the angle of incline determine the amount of force required.

3. What are the advantages of using an inclined plane?

The main advantage of using an inclined plane is that it reduces the amount of force needed to lift or lower an object. This makes it easier and more efficient to move heavy objects, such as in construction or transportation.

4. How is the mechanical advantage of an inclined plane calculated?

The mechanical advantage of an inclined plane is calculated by dividing the length of the inclined plane by the height of the plane. This ratio represents the amount of force that is saved by using the inclined plane.

5. What are some real-life uses of inclined planes?

Inclined planes are commonly used in everyday life, such as in ramps for wheelchairs or strollers, as well as in construction for loading heavy materials onto trucks. They are also used in machinery, such as conveyor belts and escalators.

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