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n200080 [17]
2 years ago
13

You apply the brakes of your car abruptly and your book starts sliding off the front seat. Three observers sitting in the car ex

plain this differently. Observer A says that the book continued moving and the car accelerated from underneath it. Observer B says that the car pushed forward on the book. Observer C says that she must be in a noninertial reference frame because the book started moving without any extra objects interacting with it. Which of the observers is correct? Assume that the car is a frame of reference of all observers.
Physics
1 answer:
krek1111 [17]2 years ago
7 0

Answer:

All the observers are correct.

Explanation:

This is simply a problem of reference frames from which the motion of the book is being viewed by the various observers.

From their various reference frames, they are all correct.

Observer A must be in the inertial reference frame.

<em>Observers who can explain the behavior of the book  and the car by using the relationship between the sum of  the forces and changing velocity are said to be observers in inertial reference frames.</em>

This is clearly shown by what observer A noticed. There was a relative motion between the book and the car as she pointed out, making her to be in an inertial reference frame.

<em>Similarly, observers in inertial reference frames can also explain the changes in velocity of objects  by considering the forces exerted on them by other objects.</em>

This is shown by observer B as he is able to notice how the force of the car affects the velocity of the book.

Observer C is actually in a non-inertial reference frame, as newtons law of force motion relationship are no longer observed. This occurs in the non inertial reference frame.

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A circular disc of mass 20kg and radius 15cm is mounted in an horizontal cylindrical axle of radius
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Using the concepts of energy, rotational Newton's second law and rotational kinematics we can find the kinematic energy of the system formed by the disk and the cylindrical axis

          KE = 0.23 J

given parameters

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  • Cylinder radius r = 1.5 cm = 0.0015 m
  • Disk mass M = 20 kg
  • Time t = 1.2 s
  • Force F = 12 N

to find

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This exercise must be solved in parts:

1st part. Endowment kinetic energy is the energy due to the circular motion of an object and is described by the equation

         KE = ½ I w²

Where KE is the kinetic energy, I the moment of inertia and w the angular velocity

The moment of inertia is a magnitude that measures the inertia for rotational movement, it is a scalar quantity, therefore it is additive. In this system it is composed of two bodies, the disk and the cylindrical axis, for which the total moment of inertia it is

         I_{ total} = I_{ disk} + I_{ cylinder}

the moments of inertia with respect to an axis passing through the center of mass are tabulated

disk          I_{disk} = ½ M R²

cylinder   I_{cylinder} = ½ m r²

where M and m are the masses of the disk and cylinder respectively, R and r their radii

         I_{total} = ½ (M R² + m r²) = ½ M R² ( 1 + \frac{m}{M} \ (\frac{r}{R})^2 )

         I_{total} = ½ M R² ( 1+ \frac{m}{20}  (\frac{0.015}{0.15} )^2 ) = \frac{1}{2} M R² (1 + 0.005 m)

As the shaft mass  is much lighter than the disk mass , the last term is very small, which is why we despise it.

         I_{total} = ½ M R²

2nd part. Let's use Newton's second law for endowment motion

        τ = I α

        α = \frac{\tau }{I_{total}}l

        τ = F R

        α = \frac{F \ R}{I_{total}}

With the rotational kinematics expressions, we assume that the system starts from rest (w₀ = 0)

        w = w₀ + α  t

where w is the angular velocity, alpha is the angular acceleration and t is the time

        w = 0 + \frac{\tau }{I_{total}} \ t

we substitute in the kinetic energy equation

        KE = ½ I_{total}  ( \frac{ \tau }{I_{total}} \ t )²

        KE = ½ \frac{ \tau^2 }{I_{total}} \ t^2

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        KE = \frac{F^2 \ R^4}{M \ R^2 } \ t^2

        KE = F² R² t² / M

let's calculate

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With the concepts of energy and rotational kinematics we can find the kinetic energy of the system is

       KE = 0.23 j

learn more about rotational kinetic energy here:

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