- #1
Your answers to a and b are correct, but I'm not sure if you're just blindly pulling equations out of somewhere without understanding their derivations. The differential equation is difficult to solve, but it's not that hard to write it down, because it is just Newton's 2nd law for constant mass: [tex]F_{net} = ma[/tex], or in its calculus based differential form, [tex]F_{net} = m(dv/dt)[/tex]. So what is [tex]F_{net}[/tex] on the ball?tachu101 said:I would think that at the begging only gravity would act on it so it would be 9.8
Then for part two all I can get is that F=kv and it is given that F=-bmv so I think that k=-bm then I have an equation here that says that terminal velocity will equal Vt=mg/k, pluging k into the equation will get -g/b (is that right)
For the final part i really don't know where to start (i am in calculus this year).
tachu101 said:Can you have F=-bmv which means that acceleration equals -bv? then I'm not sure about the calculus on how to get time factored into the equation.
you are not applying Newton 2 correctly. You've got to look at all the forces acting on the ball, not just the resistive force. The resistive fluid drag force on the ball is given as 'bmv' acting up. There's another force on the ball acting down...please identify it. Then determine the net force which will be the algebraic sum of thise 2 forces, and set it equal to 'ma'. Your correct answers to parts a and b will come directly from that equation, using the known conditions that v=0 when the ball is first dropped into the water, and a = 0 at terminal velocity.tachu101 said:Can you have F=-bmv which means that acceleration equals -bv?
The "ball falling through a liquid" experiment is a classic physics experiment that demonstrates the effects of drag and buoyancy on a falling object. It involves dropping a ball, such as a marble or a ping pong ball, into a container of liquid and observing its motion as it falls through the liquid.
The speed of the ball falling through a liquid is affected by several factors, including the density and viscosity of the liquid, the size and shape of the ball, and the surface area of the ball. These factors affect the amount of drag and buoyancy acting on the ball, which can either increase or decrease the speed of the ball's descent.
The density of the liquid has a significant impact on the ball's motion. A denser liquid will provide more resistance to the ball's motion, resulting in a slower descent. On the other hand, a less dense liquid will offer less resistance, allowing the ball to fall faster.
Drag is the force that acts on an object as it moves through a fluid, such as air or liquid. It is caused by the resistance of the fluid to the object's motion. Buoyancy, on the other hand, is the upward force exerted on an object by a fluid, which opposes the object's weight. In the "ball falling through a liquid" experiment, both drag and buoyancy affect the ball's motion.
The shape of the ball can greatly impact the results of the "ball falling through a liquid" experiment. A ball with a streamlined shape, such as a cylinder or a sphere, will experience less drag and therefore fall faster through the liquid. On the other hand, a ball with a larger surface area, such as a cube or a flat disc, will experience more drag and fall slower through the liquid.