1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
givi [52]
3 years ago
15

A 4 m^3 metal block is suspended using a cable in salt water with density 1030 kg/m^3. Tension on the cable is 42600N. What is t

he weight of the block. What is the density of the block?
Physics
1 answer:
Misha Larkins [42]3 years ago
5 0

Answer:

The density of the block is 1113.216 kilograms per cubic meter.

The weight of the block is 43669.237 newtons.

Explanation:

According to the Archimedes' Principle, the drag force experimented by the metal block is equal to the weight of the volume of water displace by the block. Besides, the block has a weight that cannot be neglected and experiments a tension from the cable. Given that the metal block is suspended, then we could consider that block is at rest.

From Newton's Laws of Motion we obtain the following equation of equilibrium:

\Sigma F = T-\rho_{m}\cdot V_{m}\cdot g + \rho_{w}\cdot V_{m}\cdot g = 0 (1)

Where:

T - Tension on the cable, measured in newtons.

\rho_{w}, \rho_{m} - Densities of salt water and the metal block, measured in kilograms per cubic meter.

V_{m} - Volume of the metal block, measured in cubic meters.

g - Gravitational acceleration, measured in meters per square second.

If we know that T = 42600\,N, \rho_{w} = 1030\,\frac{kg}{m^{3}}, V_{m} = 4\,m^{3}, g = 9.807\,\frac{m}{s^{2}}, then the density of the block is:

T+\rho_{w}\cdot V_{m}\cdot g = \rho_{m}\cdot V_{m}\cdot g

\rho_{m} = \frac{T+\rho_{w}\cdot V_{m}\cdot g}{V_{m}\cdot g}

\rho_{m} = \frac{42600\,N+\left(1030\,\frac{kg}{m^{3}} \right)\cdot (4\,m^{3})\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{(4\,m^{3})\cdot \left(9.807\,\frac{m}{s^{2}} \right)}

\rho_{m} = 1113.216\,\frac{kg}{m^{3}}

The density of the block is 1113.216 kilograms per cubic meter.

Lastly, the weight of the block (W), measured in newtons:

W = \rho_{m}\cdot V_{m}\cdot g (2)

W = \left(1113.216\,\frac{kg}{m^{3}}\right)\cdot (4\,m^{3}) \cdot \left(9.807\,\frac{m}{s^{2}} \right)

W = 43669.237\,N

The weight of the block is 43669.237 newtons.

You might be interested in
A point charge is placed at each corner of square with side leanth a. The charges all have same magnitude q. My question, What i
nexus9112 [7]

Answer:

 E = k q / a²   (1.3535) (- i ^ + j ^)

  E = k q / a²  1.914  ,      θ’= 135

Explanation:

For this exercise we will use Newton's second law where we must add as vectors

        E_total = E₁₂ i ^ + E₁₄ j ^ + E₁₃

Let's look for the value of each term

On the x axis

       E₁₂ = k q / a²

On the y axis

       E₁₄ = k q / a²

For the charge in the opposite corner we look for the distance

        d = √ (a² + a²) = a √2

let's look for the field

      E₁₃ = k q / d²

      E₁₃ = k q / 2a²

let's use trigonometry to find the two components of this field

       cos 45 = E₁₃ₓ / E₁₃

       E₁₃ₓ = E₁₃ cos 45

       

       sin 45 = E_{13y} / E₁₃

       E_{13y} = E₁₃ sin 45

       E₁₃ₓ = k q / 2a²  cos 45

       E_{13y} = k q / 2a²  sin 45

let's find each component of the electric field

X axis

      Eₓ = -E₁₂ - E₁₃ₓ

      Eₓ = - k q / a² - k q / 2a² cos 45

      Eₓ = - k q / a² (1 + cos 45/2)

      cos 45 = sin 45 = 0.707

      Eₓ = - k q / a²   (1 + 0.707 / 2)

      Eₓ = - k q / a²    (1.3535)

Y axis  

      E_y = E₁₄ + E_{13y}

       E_y = k q / a² + k q / 2a²     sin 45

       E_y = k q / a² (1 + sin 45/2)

       E_y = k q / a²       (1.3535)

we can give the results in two ways

       E = k q / a²   (1.3535) (- i ^ + j ^)

In modulus and angle form, let's use Pythagoras' theorem for the angle

       E = √ (Eₓ² + E_y²)

        E = k q / a²    1.3535 √2

        E = k q / a²     1.914

we use trigonometry for the angle

        tan θ = E_y / Eₓ

         θ = tan⁻¹  (E_y / Eₓ)

         θ = tan⁻¹ (1 / -1)

         θ = 45

in the third quadrant, if we measure the angle of the positive side of the x-axis

           θ‘= 90 + 45

           θ’= 135

4 0
3 years ago
SI unit of specific heat is​
mote1985 [20]

Answer:

The S.I unit of heat is Joule .

Hope it helps you :--)

Explanation:

Please press thanks!! thank you!!

5 0
2 years ago
In a shipping yard, a crane operator attaches a cable to a 1,400 kg shipping container and then uses the crane to lift the conta
Molodets [167]

Answer:

Explanation:

Given

mass of crane m=1400\ kg

distance moved d=40\ m

Since it is moving with a constant velocity therefore net force on it is zero

Tension force=weight

T=mg

Work done by Tension T is

W_T=T\cdot d

W_T=1400\times 9.8\cdot 40

W_T=548.8\ KJ

Work done by Gravity will be equal in magnitude but opposite in sign and can be obtained by work energy theorem which states that change in kinetic energy of object is equal to work done by all the forces

W_T+W_g=0

W_g=-548.8\ KJ

                                 

4 0
3 years ago
What is measurement?​
Semmy [17]

Answer:

How long or wide something is

Explanation:

5 0
2 years ago
What is the momentum of an 18-kg object moving at 0.5 m/s?
Otrada [13]

sorry Idk the answer ..???

6 0
3 years ago
Other questions:
  • What type of evidence should be collected first ?
    13·1 answer
  • An aircraft acceleration from 100m/s to 300m/s in 100 s what is acceleration​
    15·1 answer
  • Technician A says that magnetism can cause electric current to flow in a conductor. Technician B says that magnetic lines of flu
    11·1 answer
  • V
    5·1 answer
  • Light travels fastest when moving through
    15·1 answer
  • The highest energy waves in the electromagnetic spectrum are
    5·1 answer
  • A machine has mechanical advantage 2.What does that mean​
    12·2 answers
  • What force will accelerate a 20 kg object at 4 m/s 2? *
    5·1 answer
  • 12. Which of the following is the property of a system?
    5·1 answer
  • URGENT PLEASE ANSWER
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!