A 22cm diameter bowling ball has a terminal speed of 77 m/s. What is the balls mass. I need to get the answer in kg. I can`t figure this one out for some reason. Thanks!!
Is it being dropped from an airplane or thrown down a bowling alley?
For the dropped-from-airplane situation, you need to know the density of the air and the value of the drag coefficient, which is usually called Cd.
For more about the drag coefficient, see
http://en.wikipedia.org/wiki/Drag_coefficient
The value of Cd for a sphere is approximately 0.47 (dimensionless) , but it is not a true constant. It varies with Mach and Reynolds' number. That's a long story.
So set the weight (M g) equal to
(1/2)*Cd*(air density)*(frontal area)*V^2
and solve for M.
The frontal "projected" area is
A = pi*(0.22)^2/4 = 0.038 m^2
The density of air depends upon the temperature and altitde. The bowling ball will decelerate as it falls into denser atmosphere. Assume
1 atm and 10 C temperature.
If the answer is not about 7 kg, something is wrong with the question's assumptions.
Thanks
To find the mass of the bowling ball, we can use the following steps:
Step 1: Calculate the radius of the bowling ball.
The diameter of the bowling ball is given as 22cm. The radius (r) can be calculated by dividing the diameter by 2:
r = 22cm / 2 = 11cm
Step 2: Convert the radius from centimeters to meters.
To express the radius in meters, divide it by 100 since there are 100 centimeters in a meter:
r = 11cm / 100 = 0.11m
Step 3: Calculate the cross-sectional area of the ball.
The cross-sectional area (A) can be found using the formula for the area of a circle:
A = π * r^2
Where π is a constant (approximately 3.14).
A = 3.14 * (0.11m)^2 = 0.038278m^2
Step 4: Calculate the drag coefficient (C).
Since the drag coefficient of a bowling ball is not given, it is assumed to be 0.5 for a smooth sphere.
C = 0.5
Step 5: Use the terminal speed formula to find the mass.
The terminal speed formula for an object falling through a fluid is:
m = (C * ρ * A * v) / g
Where m represents mass, C is the drag coefficient, ρ is the fluid density, A is the cross-sectional area, v is the terminal speed, and g is the acceleration due to gravity.
The fluid density, ρ, is typically around 1.2 kg/m^3 for air.
By rearranging the formula, we can solve for mass:
m = (C * ρ * A * v) / g
Plugging in the given values:
m = (0.5 * 1.2 kg/m^3 * 0.038278m^2 * 77 m/s) / 9.8 m/s^2
Calculating the equation:
m ≈ 5.486 kg
Therefore, the mass of the bowling ball is approximately 5.486 kg.
To find the mass of the bowling ball, we can use the following formula:
Terminal speed = (2 * (mass of the ball) * (acceleration due to gravity) / (density of the medium))^(1/2)
In this case, the terminal speed is given as 77 m/s, the diameter of the ball is 22 cm, and we are assuming the ball is falling through air (density: 1.2 kg/m^3). So, let's solve for the mass.
Step 1: Convert the diameter to meters.
Diameter = 22 cm = 0.22 m
Step 2: Calculate the radius of the ball.
Radius = Diameter / 2 = 0.22 m / 2 = 0.11 m
Step 3: Substitute all the known values into the formula.
77 = (2 * mass * 9.8) / (1.2)^(1/2)
Step 4: Rearrange the equation to solve for the mass.
mass = (77 * 1.2)^(1/2) / (2 * 9.8)
Step 5: Use a calculator to evaluate the expression.
mass ≈ 3.174 kg
Therefore, the mass of the bowling ball is approximately 3.174 kg.