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netineya [11]
3 years ago
6

A student in an undergraduate physics lab is studying Archimede's principle of bouyancy. The student is given a brass cylinder a

nd, using a triple beam balance, finds the mass to be 2.23 kg. 2.23 kg. The density of this particular alloy of brass is 8.44 g/cm 3 . 8.44 g/cm3. The student ties a massless string to one end of the cylinder and submerges it into a tank of water where there is an apparent reduction in the weight of the cylinder. With this information, calculate the volume, V , V, of the cylinder and the tension, T , T, in the string when it is submerged in the tank of water. The density of water is 1.00 g/cm 3 , 1.00 g/cm3, and the acceleration due to gravity is g
Physics
1 answer:
jonny [76]3 years ago
3 0

Answer:

V = 2.64 10⁻⁴ m³,    T = 21.85 N ,    T = 19.26 N

Explanation:

To calculate the cylinder volume we use the density equation

     ρ = m / V

    V = m / ρ

    ρ = 8.44 g / cm³ (1 kg / 1000g) (10² cm / 1m)³ = 8.44 10³ kg / m³

    V = 2.23 / 8.44 10³

    V = 2.64 10⁻⁴ m³

We calculate the tension with Newton's second law

In the air

    T-W = 0

    T = mg

    T = 2.23 9.8

    T = 21.85 N

In water

In this case we have the push up

   T + B -W = 0

   T = W -B

The push formula is

   B = \rho_{water}  g V

   T = m g - \rho_{water}  g V

   T = 2.23 9.8 - 1.00 103 9.8 2.64 10-4

   T = 21.85 - 2.5872

   T = 19.26 N

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Assume that block A which has a mass of 30 kg is being pushed to the left with a force of 75 N along a frictionless surface. Wha
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Answer:

The force of friction acting on block B is approximately 26.7N.  Note: this result does not match any value from your multiple choice list. Please see comment at the end of this answer.  

Explanation:

The acting force F=75N pushes block A into acceleration to the left. Through a kinetic friction force, block B also accelerates to the left, however, the maximum of the friction force (which is unknown) makes block B accelerate by 0.5 m/s^2 slower than the block A, hence appearing it to accelerate with 0.5 m/s^2 to the right relative to the block A.

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Now we can solve the system of 3 equations for a_A, a_B and finally for F_fr:

30kg\cdot a_A = 75N - F_{fr}\\24kg\cdot a_B = F_{fr}\\a_B= a_A-0.5 \frac{m}{s^2}\\\implies \\a_A=\frac{87}{54}\frac{m}{s^2},\,\,\,a_B=\frac{10}{9}\frac{m}{s^2}\\F_{fr} = 24kg \cdot \frac{10}{9}\frac{m}{s^2}=\frac{80}{3}kg\frac{m}{s^2}\approx 26.7N

The force of friction acting on block B is approximately 26.7N.

This answer has been verified by multiple people and is correct for the provided values in your question. I recommend double-checking the text of your question for any typos and letting us know in the comments section.

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