Velocity of falling anchor in water

[Ineedhopenow]

A sailor drops an anchor from a boat. As soon as the anchor is fully submerged in the water, how fast does the anchor fall to the bottom of a fresh water lake? Ignore drag forces.

a. increasing velocity
b. constant velocity
c. decreasing velocity
d. exponential velocity

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[Hanguk]

Constant velocity...Because force of the anchor going down will always equal the buoyant force pushing up. So if acceleration isnt changing, neither should velocity.

I'm not sure if I'm approaching this right? Is that the answer?

 

[ouroboros39]

I would say increasing velocity. It would be like dropping an object on land ignoring air resistance, except with a small added force against gravity - the buoyant force - which will be constant.

 

[BB8730]

Constant velocity...Because force of the anchor going down will always equal the buoyant force pushing up.

If the force of gravity was equal to the buoyant force, the anchor wouldn't sink.

Ignoring drag forces, the object would accelerate just as it would in air. The acceleration would be smaller due to the buoyant force, but the velocity would still be increasing.

 

[Hanguk]

If the force of gravity was equal to the buoyant force, the anchor wouldn't sink.

Ignoring drag forces, the object would accelerate just as it would in air. The acceleration would be smaller due to the buoyant force, but the velocity would still be increasing.

I'm confused. TBR said that Fb = mg always. The only reason why an object rises or sinks is because of its density only. I think I even got a question wrong in the passages because of it unless of course I misread (but I remember going over that piece of info more than once). Could you expand on your explanation?

 

[BB8730]

I'm confused. TBR said that Fb = mg always. The only reason why an object rises or sinks is because of its density only. I think I even got a question wrong in the passages because of it unless of course I misread (but I remember going over that piece of info more than once). Could you expand on your explanation?

Fb = mg for the displaced fluid. So the buoyant force equals the mass of water displaced times gravity - not the mass of the anchor.

 

[Hanguk]

Thanks.

 

[HopesandDreams]

Constant velocity...Because force of the anchor going down will always equal the buoyant force pushing up. So if acceleration isnt changing, neither should velocity.

I'm not sure if I'm approaching this right? Is that the answer?

Also you've made another huge conceptual error here. Constant acceleration does NOT equal constant velocity. If acceleration = 1m/s^2(or any number other than 0) the entire time for example, acceleration remains constant but velocity increases. This is definitely one of those important conceptual tidbits to know for the test.

 

[nabilesmail]

I thought of it as The boyant force remains constant, but as the anchor submerges further down, ther eis more water on top = more force ?

 

[smiley27]

Bouyant force is equal to mg when an object is floating at the surface. What is bouyant force? It's the force upward on the floating object to keep it bouyed.

What does the force diagram look like on an object that is floating? Well first we know that it's not accelerating in any direction so there isn't a net force. We have mg pointing down and the bouying force pointing up to keep it bouyed. No acceleration of a floating object therefore the two forces equal. Fg=Fb=mg=density of object times g times volume of fluid displaced.

But the question tells us that the anchor is dropped and it reaches the bottom. Therefore there must be a net force downwards for the anchor to reach the bottom. Fg>Fb. A net force causes an acceleration. Acceleration implies a change in the objects velocity.

 

[smiley27]

Notice than Fb does not equal Fg if an object is fully submerged under water. Which force is greater?
Well what follows if Fb > Fg? The bouying force would accelerate the object out of the water!!! Right?
Therefore Fg > Fb if an object is not floating but fully submerged which is why we can't use Fb=mg for a submerged object because mg>Fb to get the object fully under water and not float.

 

[smiley27]

I'm confused. TBR said that Fb = mg always. The only reason why an object rises or sinks is because of its density only. I think I even got a question wrong in the passages because of it unless of course I misread (but I remember going over that piece of info more than once). Could you expand on your explanation?

TBR says Fb always equals to mg? Are you sure cause I think this is incorrect. If you gently lay an anchor at the surface of the lake. How does it fall to the bottom if the two forces acting are mg and Fb and they are equal to each other? If it moves downward surely there must be a net force, right? Or else it will float.

 

[BB8730]

TBR says Fb always equals to mg? Are you sure cause I think this is incorrect. If you gently lay an anchor at the surface of the lake. How does it fall to the bottom if the two forces acting are mg and Fb and they are equal to each other? If it moves downward surely there must be a net force, right? Or else it will float.

As I said before, Fb=mg for the fluid displaced. m is the mass of the water displaced - not the anchor. Fb is significantly smaller than the downward force due to gravity.

 

[milski]

If drag is ignored and the anchors is not made from some very lightweight metal (same density or lower than water), it will continue to accelerate under water and the speed will be increasing.

For objects with density higher that water density Fb<Fg and the the net force will be Fg-Fb and will be larger than zero, pointed down and smaller than the net force above water. That means that the speed will continue to increase, although a bit slowly than before (smaller force Fg-Fb leads to lower acceleration).

If the object has the same density as water, when it enters the water Fb=Fg and it will stop accelerating. Presumably, it entered the water at some speed, which means that it will continue to sink at that constant speed.

Objects with density lower than water will have Fb>Fg and will have net force and acceleration pointed up. That will make them slow down and eventually reverse direction until they surface again, where they can establish equilibrium floating on top, partially submerged.