Calculate the force required to pull a copper ball of radius 2.00 cm upward through a fluid at the constant speed 9.00 cm/s. Take the drag force to be proportional to the speed, with proportionality constant 0.950 kg/s. Ignore the buoyant force

The force consists of two parts (with buoyancy neglected)

(1) The weight, (4/3)*pi*R^3*(density)
(2) The drag force, (0.95 kg/s)*V

Look up the density of copper and use SI units for R and V. Add the two components for the answer in Newtons.

To calculate the force required to pull the copper ball upward through a fluid at a constant speed, we need to consider the presence of drag force.

The drag force acting on the ball can be mathematically modeled as:

F_drag = k * v

Where:
F_drag is the drag force,
k is the proportionality constant (0.950 kg/s in this case),
v is the speed of the ball through the fluid.

In this scenario, the ball is moving upward at a constant speed of 9.00 cm/s, and the drag force opposes this motion. To find the force required to pull the ball upward at this speed, we need to determine the drag force first.

Let's substitute the given values into the equation:

F_drag = 0.950 kg/s * 9.00 cm/s

To perform this calculation, we need to ensure that our units are consistent. It is convenient to convert centimeters (cm) to meters (m) for the radius and speed. Let's convert the values:

Radius = 2.00 cm = 0.02 m
Speed = 9.00 cm/s = 0.09 m/s

Now, let's substitute the converted values into the equation:

F_drag = 0.950 kg/s * 0.09 m/s

Calculating this expression, we get:

F_drag = 0.0855 N

Therefore, the drag force acting on the copper ball is 0.0855 Newtons.

Since the drag force and the force applied to pull the ball upward are in opposite directions, the force required to move the ball at a constant speed upward through the fluid is 0.0855 Newtons in the downward direction.