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

The weight of the Astroturf is 179,684.31 Newtons.

Step-by-step 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* 253 ft* 0.041665 ft=3,458.574 ft^3`

Mass of the Astroturf = m

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

`d=(m)/(V)`

`m=d* V= 187 oz/ft^3* 3,458.574 ft^3=646,753.35 oz`

1 oz = 0.0283495 kg

`m=646,743.35 oz=646,743.35* 0.0283495 kg=18,335.13 kg`

Weight of the Astroturf = W

W = mg

`=W=18,335.13 kg* 9.8 m/s^2=179,684.31 N`

The weight of the Astroturf is 179,684.31 Newtons.