These questions should require little or no calculations. A heavy metal sphere i

ID: 1570093 • Letter: T

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These questions should require little or no calculations. A heavy metal sphere is held and then released below the surface of water in a lake. The sphere has a volume of 1.0 liter (0.0010 m^3). and a mass of 4.0 kg. The buoyancy force. F_B, acting on an object is equal to the weight of water displaced by the object. The water drag force will vary with velocity only. a. Sketch a free body diagram for the 4.0 kg sphere, indicating all forces: b. Write the momentum conservation equation for the 4.0 kg sphere. c. Is it possible for the sphere to reach a constant velocity? Use an equation to explain. d. When is the rate of acceleration of the sphere greatest? _ initially after being released __ after a long time __ remains constant __ acceleration is always zero

Explanation / Answer

FBD of the Sphere in water

mg, weight of the sphere

Fb - force of buoyancy

Fd - drag force.

b. The sphere is released from rest

Intial momentum is 0

Let the sphere is moving with a velocity vs

volume of the sphere = 1lt.

mass of water displaced by the sphere = 1kg

vw is the velocity of the water displaced then conserving the momentum

4vs + 1.vw = 0

c) The drag force is varying with velocity , Initially the sphere is subjected to a net force downward and moves down with an acceleration and the velocity increases and the drag force too increases.

The rgavitational force and the buoyancy force are constant, when the drag force is equal to the net downward force on the sphere , the acceleration becomes 0 and the spheremoves down with a constant velocity

Force of bouyancy = 1g

gravitational force = 4g

Net down ward force = 4g-1g = 3g

let vt be the velocity when the drag force is equal to the net force

drag force Fd = Cvt , C is the drag co-efficient , constant of proportionality for the drag force

3g = Cvt

vt = 3g/C

d) The acceleration is maximum initially after being released, as time progress and the sphere gains velcoity , the drag force increases and the acceleration decreases as the net force on the sphere decreases.

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These questions should require little or no calculations. A heavy metal sphere i

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