# Mass, Pressure and Area

A force of 1.05x 10^3 N is required to lift an object that is under the influence of an acceleration due to gravity of 7.76ft/sec^2. What is the object's mass in kilograms?

A waterbed mattress has the following dimensions: 210 cm X 160 cm X 23 cm. The density of water is 62.4 lb/ft^3. What is the weight of the bed in pounds? If the mattress is placed on the floor (no bed frame), how much pressure does it exert on the floor in pounds per square inch?

A stack of bricks weighs 174 KN (Kilo-newtons). The stack exerts 200 KPa (Kilo-pascals) of pressure on the ground. What is the area upon which this pressure is exerted (in square ft)?

The Hubert H. Humphrey Metrodome in Minneapolis opened in 1982 at a cost of $55 million. To prepare for the footings, et cetera, 3.00 x 10^5 cubic yards of dirt were removed. The Metrodome's inflatable roof covers 10.0 acres and its interior volume is 60.0 x 10^3 cubic feet. During construction, 40.0 x 10^3 cubic yards of concrete, 11.9 x 10^3 tons of reinforcing steel, and 5.00 x 10^2 tons of structural steel were utilized. The roof material includes an outer layer of Teflon-coated glass and an inner layer of woven fiberglass. Given this information, answer the following: If removed evenly over the 10.0 acres, how deep a hole would be formed as a result of the excavation? In yards ? If the two-layer fiberglass roofing material has a mass of 0.667 lb_m/ft^2, what is the total mass of the roof? In lb m ?If 10.0 inches of wet snow collected on the roof (this happened in 1982), what is the added mass on the roof? (Assume 1 inch of water equals 10 inches of snow).

Please answer and explain?

#### Solution Preview

1. To lift an object a minimum force equal to its weight is required to be applied on the object in the upward direction.

Minimum force required to lift the object = F = Weight of the object =Mass of the object x Acceleration due to gravity = mg

Given: F = 1.05 x 10^3 N, g = 7.76 ft/sec^2 =7.76 x 0.3048 = 2.37 m/s^2 (as 1 ft = 0.3048 m)

Mass of the object m = F/g =1.05 x 10^3/2.37 = 443 kg

2. Dimensions of the mattress are given in cms; first these need to be converted into ft.

1 centimeter = 0.3937 inches and 1 inch = 1/12 ft. Hence, 1 cm = 0.3937/12 = 0.0328 ft

Hence, dimensions of the mattress in ft are: (210 x 0.0328)ft x (160 x 0.0328)ft x (23 ...

#### Solution Summary

Mass, pressure and areas are examined. The areas of pressures exerted are provided.