Respuesta :
Answer:
[tex] m = \rho V[/tex]
Since we have an ball we can consider this like a sphere and the volume is given by [tex] V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.69cm)^3 = 20.218 cm^3 = 0.00002022 m^3[/tex]
The density for the copper is approximately [tex] \rho = 8940 kg/m^3[/tex]
So then the mass is :
[tex] m =8940 kg/m^3 * 0.00002022m^3 = 0.1808 Kg[/tex]
And now we have everything in order to replace into the formula for F, like this:[tex] F = 0.1808 Kg *9.8 m/s^2 + 0.884 kg/s * 0.093 m/s= 1.772 +0.975 N = 2.747 N[/tex]And that would be the final answer for this case.
Explanation:
For this case if we assume that we have a damping motion the force action on the vertical direction would be:
[tex] F = mg + bv[/tex]
Where F represent the upward force on the copper ball
m represent the mass
g = 9.8 m/s^2 represent the gravity
b = 0.884 kg/s represent the proportionality constant
v = 9.3 cm/s = 0.093 m/s represent the velocity
We can solve for the mass from the following expression:
[tex] m = \rho V[/tex]
Since we have an ball we can consider this like a sphere and the volume is given by [tex] V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.69cm)^3 = 20.218 cm^3 = 0.00002022 m^3[/tex]
The density for the copper is approximately [tex] \rho = 8940 kg/m^3[/tex]
So then the mass is :
[tex] m =8940 kg/m^3 * 0.00002022m^3 = 0.1808 Kg[/tex]
And now we have everything in order to replace into the formula for F, like this:[tex] F = 0.1808 Kg *9.8 m/s^2 + 0.884 kg/s * 0.093 m/s= 1.772 +0.975 N = 2.747 N[/tex]And that would be the final answer for this case.
