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A person pushes a large block on a horizontal ice surface in a straight line to the right with constant speed, as shown above. The mass of the block is 10kg and frictional forces between the block and the ice are negligible. However, the block has a wide cross-sectional area such that air resistance acting on the block cannot be neglected. The opposite is true for the person: air resistance on the person is negligible, but the person’s shoes do not slip on the ice. The table shows the force exerted by the person on the block for several values of constant speed. Force of person’s push (N) Constant speed of block (m/s) ±0.05 20 1.25 40 2.51 60 3.73 80 5.00 (a) A student claims that the data show that the magnitude of the force of air resistance is proportional to the speed of the object, within experimental uncertainty. Use physics principles to explain whether the claim is correct. 0 / 10000 Word Limit Question 2 (b) As the person pushes the block, the person moves with the same constant speed as the block. Consider the scenario in which the person’s speed is 5.00 m/s. i. On the dot below, which represents the person, draw and label the forces (not components) exerted on the person. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. The figure presents a large dot. 0 / 10000 Word Limit Question 3 ii. The person now stops and releases the block. Determine the magnitude and direction of the block’s acceleration at the instant the block is released.

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Answer:

b

Explanation:

Newton's second law and graphical analysis allow to find the results for the questions about the air resistance force are:

   A) The air resistance is proportional to the velocity because the graph of force vs velocity is linear.

   B) In the adjoint we see the free body diagram on the man, where all the forces are in equilibrium.

   C) The block acceleration is: a = - 0.03 m/s²

Part A

Newton's second law establishes a relationship between the net force and the product of the mass and the acceleration of the body

      ∑ F = m a

   

Where the bold letters indicate vectors, F is the forces, m the mass and the acceleration of the body.

Indicates that the only significant force is air resistance.

      ∑ F = [tex]f_{air\ resistence}[/tex]

They give a table of force versus speed.

  F (N)    v (m / s)

 0.05       20

 1.25        40  

 2.51        60

 3.73        80

In the attachment we make a graph of the force versus velocity and we see that it is a linear relationship, therefore the air resistance must be proportional to the value of the body, an expression can be:

     f_{air\ resistence} = - b v

The results of the equation of the linear regression is:

     f = 0.0615 v -1.19

For this case the term b found from the linear regression is

     b = 0.0615 N s / m

Part 2

in the second attachment see a free body diagram of the force on the person

The normal force and weight are in balance.

The force applied by the person on the box (F) and there is a force applied by the box on the person (F '), are in equilibrium since the speed is constant, therefore the acceleration is zero.

Part 3

Indicate that the person stops, ask the acceleration of the block of mass 10 kg for the speed of 5 m / s.

Let's write Newton's second law for the x-axis.

           f_{air\ resistence} = m a

           - b v = m a

           a = [tex]- \frac{b v}{m}[/tex]

Let's calculate

             a = [tex]- \frac{0.0615 \ 5}{10}[/tex]  

             a = -0.03 m / a²

The negative sign indicates that the block is stopping.

In conclusion, using Newton's second law and graphical analysis we can find the results for the questions about the air resistance force are:

   A) The air resistance is proportional to the velocity because the graph of force vs velocity is linear.

   B) In the adjoint we see the free body diagram on the man, where all the forces are in equilibrium.

   C) The block acceleration is: a = - 0.03 m / s²

Learn more here: brainly.com/question/19226427

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