Question

you need to push a 180 pound ball up to a storage platform that is 15 feet above where you are now. you can use a 45 foot long ramp to push the ball up. how much effort is required to push the ball up the ramp to the storage platform?

30 lbs
45 lbs
60 lbs
90 lbs
135 lbs

Explanation:

Identify the given parameters

We are given:

• Weight of the ball (Resistance force, \(F_r\)): \(180\text{ lbs}\)
• Height of the platform (Resistance distance, \(d_r\)): \(15\text{ ft}\)
• Length of the ramp (Effort distance, \(d_e\)): \(45\text{ ft}\)

Calculate the mechanical advantage

Using the Mechanical Advantage knowledge point

$$ \text{MA} = \frac{\text{Length of Ramp}}{\text{Height of Platform}} = \frac{45\text{ ft}}{15\text{ ft}} = 3 $$

Determine the required effort force

Using the Mechanical Advantage knowledge point

$$ \text{Effort Force} = \frac{\text{Resistance Force}}{\text{MA}} = \frac{180\text{ lbs}}{3} = 60\text{ lbs} $$

Answer:

• 30 lbs
• 45 lbs
• 60 lbs (Correct answer)
• 90 lbs
• 135 lbs