Estimating in Physics

Estimating in Physics

(How many 8 cm diameter balls will fit inside Suprenant Hall?)

Goals: Determine the number of a certain size balls that will fit in a particular building known as Suprenant Hall located on the Quinsigamond Community College Campus in Worcester, Massachusetts. In this lab I will use metric units, significant figures, order of magnitude, and scientific notation in my calculations and answers. I will have two final answers. One answer will be expressed with significant figures. The other answer will be displayed as an order of magnitude, which is a power of 10 only (example: 10²).

Data and Calculations: First we measure, using a metric tape measure, from the entrance of the Physics Lab to the end of the hallway and we get rough length of 42.0m. Then we measure the length of the lab itself to reveal a rough length of 16.0m.

Length of Suprenant Hall (Ls) = 5.0(42.0 + 16.0)

Ls = 290.0m

Second we will need to find the width. We use the same tape measure and measure from the inside of the exterior wall of one class room all the way across to the other inside of the exterior wall in the stairwell revealing an estimated measurement of 19.0m.

Width of Suprenant Hall (Ws) = 5.0(19.0)

Ws = 95.0m.

Third we gather the height of the second floor. The tape measure reveals 3.0m. I now want to add the space above the tile. This will be an estimated guess of 1.0m. Since we have five floors to the building we must multiply again by five.

The height of one of the floors at Suprenant Hall (Hs) = 5.0(3.0 + 1.0)

Hs = 20.0m

Now we figure out the Total volume (Vbuilding) = Ls x Ws x Hs

Vbuilding = 290.0m x 95.0m x 20.0m

Vbuilding = 551000.0m³

Next we will figure out the volume of one ball. We use a micrometer to estimate the diameter of the ball. We conclude the diameter of the ball is 8.0cm. We know the formula for the volume of a sphere is 4/3πr³, so I want to find the radius of the ball.

Radius = diameter/2.0

Radius = 8.0cm/2.0

Radius = 4.0cm

Radius = .04m (converted to meters)

Now we can apply the volume of a sphere formula to get the volume of the ball (Vball).