Question

Astroturf is a durable artificial surface used to cover athletic fields. A soccer field 0.06214- mile-long by 253 ft wide is covered with a ½ inch layer of Astroturf. The density of the Astroturf is 187 oz/ft3. Calculate the weight of the Astroturf in Newtons (N)

Answer 1

Answer:

The weight of the Astroturf is 179,684.31 Newtons.

Explanation:

Length of a soccer field = 0.06214 mile = 328.0992 feet

(1 mile = 5280 feet)

Breadth of a soccer field  = 253 feet

Length of a Astroturf which soccer field is to be covered, l = 328.0992 feet

Breadth of a Astroturf which soccer field is to be covered ,b = 253 feet

Thickness of a Astroturf with which soccer field is to be covered = h

h = ½ inch = 0.5 inch = 0.041665 feet

(1 inches = 0.08333 feet)

Volume of the Astroturf ,V= l × b × h

$V=328.0992 ft\times 253 ft\times 0.041665 ft=3,458.574 ft^3$

Mass of the Astroturf = m

Density of the Astroturf = d = 187 $oz/ft^3$

$d=\frac{m}{V}$

$m=d\times V= 187 oz/ft^3\times 3,458.574 ft^3=646,753.35 oz$

1 oz = 0.0283495 kg

$m=646,743.35 oz=646,743.35\times 0.0283495 kg=18,335.13 kg$

Weight of the Astroturf = W

W = mg

$=W=18,335.13 kg\times 9.8 m/s^2=179,684.31 N$

The weight of the Astroturf is 179,684.31 Newtons.