A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of 3.9 6.5 cm in contact with the floor. The total mass of the shelves plus the books stacked on them is 260. 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
First, we need to calculate the force exerted by the shelf footings on the surface. This force is equal to the weight of the shelves and books stacked on them.
Given that the total mass of the shelves plus the books is 260 kg, we can find the force using the formula:
Force = mass * gravity
where gravity is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Force = 260 kg * 9.8 m/s^2
Next, we need to calculate the area of contact between each leg and the floor. Given that the cross-sectional dimension of each leg is 3.9 cm x 6.5 cm, we convert these dimensions to meters:
Area = (3.9 cm / 100 m/cm) * (6.5 cm / 100 m/cm)
Now that we have the force and the area, we can calculate the pressure:
Pressure = Force / Area
Substituting the values we found:
Pressure = (260 kg * 9.8 m/s^2) / [(3.9 cm / 100 m/cm) * (6.5 cm / 100 m/cm)]
Calculating this expression will give us the pressure exerted by the shelf footings on the surface in pascals (Pa).