Question

An engineer designing a ramp in a football stadium was told to keep the slope to a ratio of 1:10. The ramp height is 25 ft. What is the Ideal Mechanical Advantage of the ramp? (Its 10.05, but how do I solve it?)

Answer 1

we know that

To calculate the ideal mechanical advantage for an inclined plane, divide the length of the incline by the height of the incline

Step 1

Find the horizontal distance of the ramp

we know that

the ramp has a slope of
`1:10`

so

by proportion

`(1)/(10) (height)/(long) =(25)/(x) (height)/(long) \\ \\x=25*10 \\ \\ x=250\ ft`

Step 2

Find the length of the incline of the ramp

Applying the Pythagorean Theorem

`incline^(2)=height^(2)+horizontal^(2)`

substitute the values

`incline^(2)=25^(2)+250^(2)`

`incline^(2)=63,125`

`incline=251.25\ ft`

Step 3

Find the ideal mechanical advantage

`Ideal\ Mechanical\ Advantage=(incline)/(height)`

substitute the values

`Ideal\ Mechanical\ Advantage=(251.25)/(25)=10.05`

therefore

the answer is

the Ideal Mechanical Advantage of the ramp is
`10.05`