Joe pushes a lawn mower four times as far as Mary while exerting only half the force, who does more work? And by how much?
W1/W2=(F/2 *4d)/(F*d)=(2F*d)/(F*d)=2.
W1 = Joe's work.
W2 = Mary's work.
Joe does twice as much work as Mary.
To compare the work done by Joe and Mary, we can use the formula:
Work = Force × Distance
Let's denote the force exerted by Mary as F₁ and the force exerted by Joe as F₂. Similarly, let's denote the distance covered by Mary as D₁ and the distance covered by Joe as D₂.
From the problem, we know that:
F₂ = ½ F₁ (Joe exerts half the force of Mary)
D₂ = 4D₁ (Joe pushes the lawn mower four times as far as Mary)
Now let's calculate the work done by Mary and Joe:
Work by Mary (W₁) = F₁ × D₁
Work by Joe (W₂) = F₂ × D₂
Substituting the given relationships, we have:
W₁ = F₁ × D₁
W₂ = (½ F₁) × (4D₁) = 2 F₁ × D₁
Now we can compare the work done by Joe and Mary:
W₂ = 2 F₁ × D₁
W₁ = F₁ × D₁
Since W₂ > W₁, Joe does more work than Mary. The difference in work can be calculated as:
Difference = W₂ - W₁ = (2 F₁ × D₁) - (F₁ × D₁) = F₁ × D₁
Therefore, Joe does F₁ × D₁ more work than Mary.
To determine who does more work between Joe and Mary, we need to calculate the work done by each person. Work is defined as the product of force and displacement, so the equation to calculate work is:
Work = Force * Displacement
Let's assume Mary exerts a force of F1 and moves a distance of d1, while Joe exerts a force of F2 and moves a distance of d2.
According to the question, Joe pushes the lawn mower four times as far as Mary, which means d2 = 4 * d1.
It is also stated that Joe exerts only half the force compared to Mary, so F2 = 0.5 * F1.
Now let's calculate the work done by each individual:
Work done by Mary: W1 = F1 * d1
Work done by Joe: W2 = F2 * d2
Substituting the value of d2 and F2 from the given information, we have:
W2 = (0.5 * F1) * (4 * d1)
Simplifying further, we get:
W2 = 2 * F1 * d1
So, Joe does twice the work compared to Mary.
To summarize:
Joe does twice the work compared to Mary, or Joe's work is double Mary's work.