Question

You pull a solid nickel ball with a density of 8.91 g/cm3 and a radius of 1.40 cm upward through a fluid at a constant speed of 9.00 cm/s. The fluid exerts a drag force that is directly proportional to speed, and the proportionality constant is 0.950 kg/s. What is the magnitude of the force (in N) you exert on the ball? (You may ignore the buoyant force.)

Answer 1

`P = 1.090\,N`

Step-by-step explanation:

The constant speed means that ball is not experimenting acceleration. This elements is modelled by using the following equation of equilibrium:

`\Sigma F = P - W + F_(D)`

`\Sigma F = P - \rho \cdot V \cdot g + c\cdot v = 0`

Now, the exerted force is:

`P = \rho \cdot V \cdot g - c\cdot v`

The volume of a sphere is:

`V = (4\cdot \pi)/(3)\cdot R^(3)`

`V = (4\cdot \pi)/(3)\cdot (0.014\,m)^(3)`

`V = 1.149* 10^(-5)\,m^(3)`

Lastly, the force is calculated:

`P = (8910\,(kg)/(m^(3)) )\cdot (1.149\cdot 10^(-5)\,m^(3))\cdot (9.81\,(m)/(s^(2)) )+(0.950\,(kg)/(s))\cdot (0.09\,(m)/(s) )`

`P = 1.090\,N`