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An object of mass 35 kg fell from a boat to the seabed - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1
Question 18
An object of mass 35 kg fell from a boat to the seabed. (a) The object reached terminal velocity as it fell. (i) Show that the drag force acting on the object at t... show full transcript
Worked Solution & Example Answer:An object of mass 35 kg fell from a boat to the seabed - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1
Step 1
Show that the drag force acting on the object at terminal velocity was about 200 N.
Answer
To find the drag force acting on the object at terminal velocity, we first calculate the upthrust (buoyancy) experienced by the object.
The upthrust is equal to the weight of the fluid displaced, given by:
ho imes g imes V$$ Where: - $ ho$ (density of seawater) = $1.03 imes 10^3 ext{ kg m}^{-3}$ - $g$ (acceleration due to gravity) = $9.81 ext{ m s}^{-2}$ - $V$ (volume of object) = $1.60 imes 10^{-2} ext{ m}^{3}$ Calculating the upthrust: $$ ext{Upthrust} = 1.03 imes 10^3 imes 9.81 imes 1.60 imes 10^{-2} = 162 ext{ N}$$ At terminal velocity, the forces are balanced, so: $$ ext{Weight of object} = ext{Upthrust} + ext{Drag force}$$ The weight of the object (mass = 35 kg) is: $$ ext{Weight} = 35 imes 9.81 = 343 ext{ N}$$ Therefore, $$343 ext{ N} = 162 ext{ N} + ext{Drag force} \\ ext{Drag force} = 343 ext{ N} - 162 ext{ N} = 181 ext{ N}$$ Hence, the drag force at terminal velocity is approximately 200 N.Step 2
Determine the terminal velocity of the object.
Answer
Using the formula for drag force:
At terminal velocity, the drag force equals the weight of the object. Thus,
Solving for :
v^2 = 82.27 \\ v ightarrow ext{taking square root}\\ ext{Terminal velocity} = ext{√}(82.27) \\ ext{Terminal velocity} ext{ is approximately } 9.1 ext{ m/s.}$$Step 3
Give two reasons why Stokes' law could not be used to calculate the terminal velocity of the object.
Answer
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The object might not be spherical, which is a prerequisite for applying Stokes' law effectively.
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The flow around the object might not be laminar, which again is required for Stokes' law to be applicable. Stokes' law holds for low Reynolds numbers where viscous forces dominate.
Step 4
Explain why the lift bag and object reached a maximum velocity.
Answer
The lift bag and object reached a maximum velocity due to the balance of forces acting on them. Initially, the drag force acting on the lift bag and the object is less than the buoyant force provided by the compressed air in the lift bag. As they ascend, the drag force increases with speed until it equals the net upward force acting on them. At this point, the forces are balanced, and the lift bag and object stop accelerating, achieving a constant maximum velocity. This is consistent with the principles of dynamics where the net force becomes zero at terminal velocity.