Resolving power on an inclined slope

In summary, the question involves a tractor of 6000kg approaching a slope at an angle of arcsin(0.05) to the horizontal with a non-gravitational resistance of 2000N. The tractor accelerates from 3m/s to 3.25m/s over a distance of 100m while climbing the slope. The time taken to travel this distance is 32 seconds. The average power required over this time period is 15.6KW, calculated by adding the work done against gravity and the resistive force and dividing it by the time taken.
  • #1
ZeuZ
25
0
This one the last questions on my mechanics paper, its hard to visualize without drawing a diagram i found, but i still can't solve it
1.
A tractor of 6000kg approaches a slope at arcsin(0.05) to the horizontal. The non-gravitational resistance to motion on this slope is 2000N. The tractor accellorates uniformly from 3m/s to 3.25m/s over a distance of 100m while climbing the slope

1. Calculate the time taken to travel this distance of 100m, and the average power required over this time period.


Homework Equations



p = Fv
p= F/t
f = ma
Work Done = 0.5mv^2

The Attempt at a Solution



i got as far as using s = (u+v)/2 x t, which gives the time as 32 seconds. I'm just not sure how to find the average power because i don't know where to put the 2000N resistance in the equation, plus the angle of the slope confuses the issue somewhat
 
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  • #2
Find the work done in traversing that distance against (1) gravity, and (2) the resistive force of 2000 N. Add them up and use that total to find the average power.
 
  • #3
cheers i never thought of using GPE. height is 5m so

WD is 0.5 x 6000 x (3.25^2 - 3^2)

+ 6000 x 9.8 x 100 x 0.05

+2000 * 100 = 498687.5 W


i presume that that's the total power from that total?, and the average power will be 498687.5 / 32 which is 15.6 KW?
 
  • #4
Sounds good to me.
 

1. What is resolving power on an inclined slope?

Resolving power on an inclined slope refers to the ability of an object or surface to distinguish between two closely spaced objects or features when viewed from an inclined angle. It is commonly used in scientific studies and engineering applications to measure the accuracy and precision of a measurement system.

2. How is resolving power on an inclined slope calculated?

The resolving power on an inclined slope is calculated by dividing the smallest distance between two objects that can be distinguished by the tangent of the angle of inclination. This calculation takes into account the angle of observation and the precision of the measurement equipment being used.

3. What factors affect the resolving power on an inclined slope?

The resolving power on an inclined slope can be affected by several factors, including the angle of inclination, the distance between the two objects being observed, the precision of the measurement equipment, and the surface properties of the objects being viewed. Other factors such as lighting and environmental conditions can also impact the resolving power.

4. Why is resolving power on an inclined slope important in scientific research?

Resolving power on an inclined slope is important in scientific research because it allows for more accurate and precise measurements of objects and features. This is especially crucial when studying small or closely spaced objects, as it can help researchers gather more detailed and reliable data for their experiments and analyses.

5. How can the resolving power on an inclined slope be improved?

The resolving power on an inclined slope can be improved by using more precise measurement equipment, controlling environmental factors, and optimizing the angle of inclination for the specific objects being observed. Additionally, using advanced imaging techniques and software can also enhance the resolving power and provide more detailed information about the objects being studied.

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