Acceleration and terminal speed problem

• jmwachtel
In summary: The correct answer is 2.5N.In summary, the copper ball is pulled upward through a fluid with a drag force of 2.5N.
jmwachtel

Homework Statement

A small piece of Styrofoam packing material is dropped from a height of 2.10 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g - bv. After falling 0.400 m, the styrofoam effectively reaches its terminal speed, and then takes 4.90 s more to reach the ground.

(a) What is the value of the constant b?
(c) What is the acceleration when the speed is 0.150 m/s?

Homework Equations

a = g-bv
- (a - g)/v = b
b = mg/vt (Don't know mass or terminal velocity.

The Attempt at a Solution

I know that after the Syrofoam reaches it's terminal speed acceleration goes to 0 and the velocity is constant. I don't know the acceleration or really the velocity to solve for b. I think c can be solved once a is figured out, but I'm not sure how to get there.

I actually just solved this one. My last problem is this:

Calculate the force required to pull a copper ball of radius 1.50 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.

So I would use R = -bv to calulate the force. B = .950 kg/s. V = .090 m/s.

I need to use F = mg in there right to sum the forces. so F = -bv - mg? How do I get the mass? Am I on the right track? Thank You.

They said ignore the buoyant force so you don't need to know the mass.
It's just a "pulling object against friction" question with the complication that the friction depends on speed.

So the radius has nothing to do with the problem? Is it just R = -bv?

Drag force is F = - b v for low velocities in a fluid.
The constant b is proprtional to radius,
b = 6 pi eta r where eta is the viscosity in kg / m / s, r is the radius, so the units of b should be kg/s as given.

Well F = -bv is equal to (.950k/s * .09 m/s) = .0855, which is not correct. What is missing? Where does gravity plan in? It's pulling down as we are lifiting it up.

I would have said that 'ignore bouyant force' also means ignore gravity, it could be being pulled through molten copper in which case the weigth and bouyant force cancel.
on the other hand it could mean you should include the weight but ignore any upthrust from the fluid ( assume it is in helium or some very light gass with a very large viscous drag!)
Try adding the weight and see if that's the right answer ( density of copper = 9g/cc)

Nope, I am looking for an answer that is around 3N. I am not where close.

Any other ideas?

No, I get the weight to be 1.25N and the viscous drag to be 0.09N like you do - sorry

1. What is acceleration and terminal speed?

Acceleration is the rate at which an object changes its velocity. It is a vector quantity, meaning it has both magnitude and direction. Terminal speed, also known as terminal velocity, is the maximum speed an object can reach when falling through a fluid or air. It occurs when the force of air resistance is equal to the force of gravity acting on the object.

2. How is acceleration and terminal speed calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. It is typically measured in meters per second squared (m/s^2). Terminal speed can be calculated by setting the force of air resistance equal to the force of gravity and solving for the velocity.

3. What factors affect acceleration and terminal speed?

The factors that affect acceleration include the mass and force acting on an object. Heavier objects require more force to accelerate at the same rate as lighter objects. The factors that affect terminal speed include the surface area and shape of an object, as well as the density and viscosity of the fluid or air it is falling through.

4. How does air resistance affect acceleration and terminal speed?

Air resistance, also known as drag, is a force that acts in the opposite direction of an object's motion through a fluid or air. It increases with the speed of the object, and at some point, it will become equal to the force of gravity acting on the object. At this point, the object will reach its terminal speed and will no longer accelerate.

5. Can an object have a constant acceleration and terminal speed?

Yes, an object can have a constant acceleration and terminal speed if the forces acting on it are balanced. This can occur when an object is in free fall and the force of gravity is balanced by the force of air resistance. In this case, the object will continue to fall at a constant speed, known as its terminal speed, until it reaches the ground.

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