Two part Question:
A load of 1500N is to be at Height of 3m above the ground. The available Incline planes are 10 degrees and 40 Degrees to the horizontal. Find out the Work Done by effort on the 10 degrees and 40 Degrees ramps. Assume the coefficient of friction is 0.8. Which Incline planes would a weak person use?
I've already calculated the distance, distance for 10 degrees is 17.28 and distance for 40 degrees is 4.68
the only thing i'm missing is the correct force used for both inclined planes as well as show my working out for getting the force
To find out the work done by effort on the inclined planes, we need to use the formula:
Work (W) = Force (F) x Distance (d) x Cosine (θ)
where:
- W is the work done
- F is the force applied
- d is the distance over which the force is applied
- θ is the angle between the direction of force and the direction of motion
The first step is to calculate the force required to lift the load of 1500N to a height of 3m. This force is equal to the weight of the load, which can be calculated using the formula:
Force = Mass x Gravity
where:
- Mass is the weight of the load divided by the acceleration due to gravity (9.8 m/s²)
Calculating the force:
Force = 1500N
Next, we can calculate the distances over which the force will be applied on the two incline planes. To find the distances, we can use the trigonometric relationships of right triangles.
For the 10 degrees inclined plane:
Distance (d) = Height (h) / Sine (θ)
Calculating the distance:
θ = 10 degrees
h = 3m
Using trigonometry:
Distance = 3m / Sine(10 degrees)
For the 40 degrees inclined plane:
Distance (d) = Height (h) / Sine (θ)
Calculating the distance:
θ = 40 degrees
h = 3m
Using trigonometry:
Distance = 3m / Sine(40 degrees)
Now, we can calculate the work done on each inclined plane using the formula mentioned above.
For the 10 degrees inclined plane:
Work = Force x Distance x Cosine (θ)
Calculating the work:
Force = 1500N (as mentioned earlier)
Distance = calculated distance for 10 degrees inclined plane
θ = 10 degrees
Work_10_degrees = 1500N x Distance_10_degrees x Cosine(10 degrees)
For the 40 degrees inclined plane:
Work = Force x Distance x Cosine (θ)
Calculating the work:
Force = 1500N (as mentioned earlier)
Distance = calculated distance for 40 degrees inclined plane
θ = 40 degrees
Work_40_degrees = 1500N x Distance_40_degrees x Cosine(40 degrees)
Now, let's compare the work done on the two inclined planes:
Work_10_degrees = calculated value using the formula
Work_40_degrees = calculated value using the formula
Finally, we need to consider the coefficient of friction to determine which inclined plane a weak person would use. A higher coefficient of friction means more resistance and thus more effort is needed. In this scenario, the coefficient of friction is mentioned as 0.8.
Comparing the work done on the two incline planes:
- If the work done on the 10 degrees inclined plane is less than the work done on the 40 degrees inclined plane (taking into account friction), a weak person would prefer the 10 degrees inclined plane.
- If the work done on the 40 degrees inclined plane is less than the work done on the 10 degrees inclined plane (taking into account friction), a weak person would prefer the 40 degrees inclined plane.
To summarize, the steps to find out the work done by effort on the 10 degrees and 40 degrees ramps are as follows:
1. Calculate the force required to lift the load.
2. Calculate the distances over which the force will be applied on each inclined plane using trigonometry.
3. Use the work formula to calculate the work done on each inclined plane.
4. Compare the work done, considering the coefficient of friction, to determine which inclined plane a weak person would prefer.