Calculating Force to Pull Copper Ball Upward

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To calculate the force required to pull a copper ball upward through a fluid at a constant speed, the drag force is proportional to speed, with a constant of 0.950 N-s/m. The resistive force is calculated using the equation R = -bv, resulting in a value of -0.0855 Newtons. The total force equation is set up as the sum of the weight of the ball and the resistive force equaling the pull force. The weight of the ball must be determined using its radius to find its mass, which is essential for the calculation. The correct units for the proportionality constant are confirmed as N-s/m, ensuring accurate force calculations.
anneseanandy
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I need to calculate the force required to pull a copper ball radius 2.00cm upward through a fluid at the constant speed 9.00cm/s. The drag forse is to be proportional to the speed, with proportionality constant .950kg/s. Ignore any boyant force.

What I did so far was figure out the resistive force using the equation: R=-bv, where b= .950kg/s and v= .09m/s
So that gives me -.0855Newtons.

My equation set up so far is:
SumYForces = mg+ Resitive force= Pull Force
and then from there I have no clue, the answer in the back of the book is 3.01 N, but I just can't seem to get it. Thanks -anne
 
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How about the weight of the ball?

PS: the unit of that proportionality constant is not kg/s. It must be N-s/m so that when you multiply it by m/s you end up with N.
 
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the weird thing is they give no mass, and that's what they give as the proportional constant.
 
You are given the radius of the ball. From that, with a little effort, you can find the mass (and then the weight).

As to the unit of the constant, you're right. Sorry, I guess I was too tired last night. (1kg/s)*(1m/s)=1(kg-m/s^2)=1N
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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