A Ping-Pong ball has a mass of 2.3 g and a terminal speed of 8.2 m/s. The drag force is of the form bv2 What is the value of b?
To determine the value of b, we can use the equation for the drag force:
Fd = bv^2
Where:
Fd = Drag force
b = Constant
v = Velocity
Given that the terminal speed is 8.2 m/s and the mass of the Ping-Pong ball is 2.3 g (or 0.0023 kg), we can calculate the drag force at terminal speed using the formula:
Fd = m * g
Where:
m = Mass (0.0023 kg)
g = Acceleration due to gravity (9.8 m/s^2)
Fd = 0.0023 kg * 9.8 m/s^2
Fd = 0.02254 N
Now, we can substitute the values into the drag force equation to find b:
0.02254 N = b * (8.2 m/s)^2
Simplifying:
b * (8.2 m/s)^2 = 0.02254 N
(8.2 m/s)^2 is equal to 67.24 m^2/s^2, so we can write:
b * 67.24 m^2/s^2 = 0.02254 N
To isolate b, divide both sides of the equation by 67.24 m^2/s^2:
b = 0.02254 N / 67.24 m^2/s^2
Calculating:
b ≈ 0.000335 N/(m^2/s^2)
Therefore, the value of b is approximately 0.000335 N/(m^2/s^2).
To find the value of b, we need to use the equation for drag force:
Drag force (F_drag) = b * v^2
Given information:
Mass of the Ping-Pong ball (m) = 2.3 g = 0.0023 kg
Terminal speed (v) = 8.2 m/s
Drag force (F_drag) at the terminal speed = Weight of the ball (F_weight)
Since the ball is at its terminal speed, the drag force (F_drag) is equal to the weight of the ball, which can be calculated using the equation:
F_weight = m * g
where g is the acceleration due to gravity.
Considering these calculations, we can set up the following equation:
F_drag = F_weight
b * v^2 = m * g
Now, rearranging the equation to solve for b:
b = (m * g) / v^2
To calculate the value of b, substitute the given values:
m = 0.0023 kg
g = 9.8 m/s^2
b = (0.0023 kg * 9.8 m/s^2) / (8.2 m/s)^2
b = 2.2672 kg⋅m^2/s^2 / 67.24 m^2/s^2
b ≈ 0.0337 kg/m
Therefore, the value of b is approximately 0.0337 kg/m.