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.

Forcedrag=k v
= .950kg/s * .09m/s= ? joules

I got this answer too.
but the book says the answer is 3.01 N up?

Total force required = Weight + drag = (4/3) pi R^3 * density * g
+ (0.950) kg/s * 9*10^-2 m/s

Use g = 9.8 m/s^2,
R = 2*10^-2 m,
and density = 8.92*10^3 kg/m^3

AHHH!
thank you SO much.
can i ask you how you got the
"weight" part of the equation?

Weight = Mass * g = Volume*density* g

The answer will be in Newtons, by the way

fdv

To calculate the weight of the copper ball, you need to multiply the mass of the ball by the acceleration due to gravity. The mass of the ball can be calculated using its volume and density. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the ball. The density of copper is given as 8.92 * 10^3 kg/m^3.

So, the mass of the ball can be calculated as follows:
mass = density * volume
mass = (8.92 * 10^3 kg/m^3) * [(4/3) * π * (0.02 m)^3]
mass = (8.92 * 10^3 kg/m^3) * [(4/3) * 3.142 * (0.008 m^3)]
mass = (8.92 * 10^3 kg/m^3) * (0.0335 m^3)
mass = 297.52 kg

Now, calculate the weight of the ball:
weight = mass * g
weight = 297.52 kg * 9.8 m/s^2
weight = 2918.10 N

Therefore, the weight of the copper ball is approximately 2918.10 N.

Sure! To calculate the weight, we first need to find the mass of the copper ball. The mass can be calculated using the equation:

Mass = Volume * Density

The volume of a sphere is given by the formula:

Volume = (4/3) * pi * (radius)^3

In this case, the radius of the copper ball is given as 2.00 cm, which is equal to 2 * 10^-2 m.

Next, we need to find the density of copper. The problem statement doesn't explicitly provide the density, but it mentions that we can neglect the buoyant force. This implies that the copper ball is submerged in a fluid, whose density can be taken as the density of water (approximately 1000 kg/m^3). However, the book provides a different density value of 8.92 * 10^3 kg/m^3 for copper, so we'll use that instead.

Once we have the mass, we can calculate the weight as:

Weight = Mass * g

where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

So, the weight part of the equation becomes:

Weight = Volume * Density * g

= (4/3) * pi * (radius)^3 * density * g

Substituting the values given in the problem statement, we can calculate the weight.