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Buoyant force

A small piece of Styrofoam packing material is dropped from a

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Hard

Solving time: 4 mins

A small piece of Styrofoam packing material is dropped from a height of $2.00 m$ above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by $a = g - B v$ . After falling $0.500 m$ , the Styrofoam effectively reaches terminal speed and then takes $5.00 s$ more to reach the ground.
(a) What is the value of the constant $B$ ?
(b) What is the acceleration at $t = 0$ ?
(c) What is the acceleration when the speed is $0.150 m / s$ ?

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A small piece of Styrofoam packing material is dropped from a height of

2.00 m

above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by

a = g - B v

. After falling

0.500 m

, the Styrofoam effectively reaches terminal speed and then takes

5.00 s

more to reach the ground.
(a) What is the value of the constant

B

?
(b) What is the acceleration at

t = 0

?
(c) What is the acceleration when the speed is

0.150 m / s

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

(a) The acceleration of the Styrofoam is given by

a = g - B v

When

v = v_{T}, a = 0

and

g = B v_{T} \to B = \frac{g}{v _{T}}

The Styrofoam falls

1.50 m

at constant speed

v_{T}

5.00 s

. Thus,

v_{T} = \frac{h}{Δ t} = \frac{1.50 m}{5.00 s} = 0.300 m / s

Then

B = \frac{g}{v _{T}} = \frac{9.80 m / s ^{2}}{0.300 m / s} = 32.7 s^{- 1}

(b) At

t = 0, v = 0

, and

a = g = 9.80 m / s^{2}

down (c) When

v = 0.150 m / s

a = g - B v

= 9.80 m / s^{2} - (32.7 s^{- 1}) (0.150 m / s)

= 4.90 m / s^{2}

down.

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Question Text	A small piece of Styrofoam packing material is dropped from a height of $2.00 m$ above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by $a = g - B v$ . After falling $0.500 m$ , the Styrofoam effectively reaches terminal speed and then takes $5.00 s$ more to reach the ground. (a) What is the value of the constant $B$ ? (b) What is the acceleration at $t = 0$ ? (c) What is the acceleration when the speed is $0.150 m / s$ ?
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	58

Text solutionVerified

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