A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 2.7 5.2 cm in contact with the floor. The total mass of the shelves plus the books stacked on them is 246 kg. Calculate the pressure in pascals exerted by the shelf footings on the surface.
To calculate the pressure exerted by the shelf footings on the surface, we can use the formula:
Pressure = Force/Area
In this case, the force is the weight exerted by the shelves and the books stacked on them. We need to calculate the weight first.
Weight = mass x acceleration due to gravity
Since the total mass is given as 246 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight as:
Weight = 246 kg x 9.8 m/s^2
Next, we need to calculate the area of one footing. Since the cross-sectional dimension of each leg is given as 2.7 cm x 5.2 cm, we can convert it to meters:
Width = 2.7 cm = 0.027 m
Length = 5.2 cm = 0.052 m
Now, we can calculate the area as:
Area = Width x Length
Now that we have the weight and the area, we can calculate the pressure:
Pressure = Weight/Area
Plug in the values:
Pressure = (246 kg x 9.8 m/s^2) / (0.027 m x 0.052 m)
Calculate the numerator:
Pressure = (2410.8 N) / (0.001404 m^2)
Finally, divide the numerator by the denominator to get the pressure in pascals:
Pressure = 1,719,434.4 Pa