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Math  /  Algebra

Question9. (II) Estimate the work you do to mow a lawn 10 m by 20 m with a 50−cm50-\mathrm{cm}-wide mower. Assume you push with a horizontal force of about 15 N .

Studdy Solution

STEP 1

1. The lawn is rectangular with dimensions 10 m by 20 m.
2. The mower has a width of 50 cm (or 0.5 m).
3. The force applied to push the mower is 15 N.
4. The work done is calculated as the force times the distance over which the force is applied.
5. The mower is pushed in straight lines across the lawn.

STEP 2

1. Calculate the total area of the lawn.
2. Determine the number of passes required to mow the entire lawn.
3. Calculate the total distance the mower travels.
4. Calculate the work done using the formula for work.

STEP 3

Calculate the total area of the lawn.
The area A A of the lawn is given by the product of its length and width:
A=10 m×20 m=200 m2 A = 10 \, \text{m} \times 20 \, \text{m} = 200 \, \text{m}^2

STEP 4

Determine the number of passes required to mow the entire lawn.
Each pass of the mower covers a strip of width 0.5 m. The number of passes n n required is the total width of the lawn divided by the width of the mower:
n=20 m0.5 m=40 n = \frac{20 \, \text{m}}{0.5 \, \text{m}} = 40

STEP 5

Calculate the total distance the mower travels.
Each pass is 10 m long, and there are 40 passes. Therefore, the total distance d d is:
d=40×10 m=400 m d = 40 \times 10 \, \text{m} = 400 \, \text{m}

STEP 6

Calculate the work done using the formula for work.
The work W W done is the product of the force F F and the distance d d :
W=F×d=15 N×400 m=6000 J W = F \times d = 15 \, \text{N} \times 400 \, \text{m} = 6000 \, \text{J}
The estimated work done to mow the lawn is:
6000 J \boxed{6000 \, \text{J}}

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