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MCAT Physics Question — Flotation Device

  • by John
  • Dec 02, 2014
  • MCAT Blog, MCAT Physics, MCAT Question of the Day

A child’s flotation device (ρ = 250 kg / m3) is held underwater at the beach (ρseawater = 1025 kg / m3). The toy is spherical and has a radius of one meter. When the toy is released, what is the magnitude and direction of the toy’s acceleration? (assume g = 9.8 m / s2)

 

A) 2.45 m / s2 downwards

B) 0 m / s2

C) 29.4 m / s2 upwards

D) 39.2 m / s2 upwards

 

 

Explanation

 

This problem asks us to solve for the net acceleration on a submerged object that is less dense than seawater. Before doing any calculations, we can see that the object’s density is approximately one fourth that of seawater. As a consequence, the object will float in seawater. Thus, when released, it will accelerate towards the water’s surface, where it will then float.

 

That lets us immediately eliminate choices (A) and (B). If you’re pressed for time, or are unsure how to proceed, then you can make an educated guess and move on.

 

To solve the problem, use Newton’s 2nd law:

 

Fnet = ma

 

The net force will be the buoyant force minus the force of gravity:

 

Fb – Fg = mtoya

 

We can then substitute for the forces:

 

ρseawaterVtoyg – mtoyg = mtoya

 

Because this is a buoyancy problem it’s often easier to work in terms of density than mass. We can substitute ρV for m in our equation:

 

ρtoy = mtoy / Vtoy

ρtoyVtoy = mtoy

 

ρseawaterVtoyg – ρtoyVtoyg = ρtoyVtoya

 

Factor out the left side of the equation:

 

seawater – ρtoy)Vtoyg = ρtoyVtoya

 

seawater – ρtoy)g = ρtoya

 

(1000 – 250)(10) = (250)a

(750)(10) = (250)a

(3)(10) = a

30 = a

 

The closest answer choice is (C).

 

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