A girl pushes up an incline fives times longer than a man who lifts the same block the same height. How much more force does the man exert on the block?
To determine how much more force the man exerts on the block compared to the girl, we need to consider the work done on the block by both individuals.
Work (W) is calculated by the formula:
W = Force (F) * Distance (d) * Cosine (θ)
In this case, both the girl and the man are exerting a force to lift the block the same height. Let's assume the height is represented by 'h'.
For the girl:
W₁ = F₁ * d₁ * cos(θ₁)
For the man:
W₂ = F₂ * d₂ * cos(θ₂)
Since both the height and the angle are the same for both individuals, we can simplify the equation:
W₁ = F₁ * d₁
W₂ = F₂ * d₂
Given that the girl pushes up an incline five times longer than the man, we can say that d₁ = 5 * d₂.
Plugging this back into the equations:
W₁ = F₁ * 5 * d₂
W₂ = F₂ * d₂
Since the work done by both individuals is the same (as they are lifting the block to the same height), we can equate the two equations:
F₁ * 5 * d₂ = F₂ * d₂
Dividing both sides of the equation by d₂:
F₁ * 5 = F₂
Therefore, the man exerts a force that is five times greater than that of the girl.