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storchak [24]
3 years ago
7

A ball rolling along a floor doesn't continue rolling indefinitely. is it because it is seeking a place of rest or because some

force is acting upon it?
Physics
1 answer:
Ivan3 years ago
7 0
It is because gravity is pushing down on the ball
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A reasonable estimate of the moment of inertia of an ice skater spinning with her arms at her sides can be made by modeling most
Oxana [17]

Answer:

A)  I_{total} = 1.44 kg m², B) moment of inertia must increase

Explanation:

The moment of inertia is defined by

     I = ∫ r² dm

For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is

      I = ½ m R²

A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is

    I = I_{cm} + m D²

Let's apply these equations to our case

The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms

      I_{total}=I_{body} + 2 I_{arm}

       I_{body} = ½ M R²

The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body

       M = 7/8 m total

       M = 7/8 64

       M = 56 kg

The mass of the arms is

      m’= 1/8 m total

      m’= 1/8 64

      m’= 8 kg

As it has two arms the mass of each arm is half

     m = ½ m ’

     m = 4 kg

The arms are very thin, we will approximate them as a particle

    I_{arm} = M D²

Let's write the equation

     I_{total} = ½ M R² + 2 (m D²)

Let's calculate

    I_{total} = ½ 56 0.20² + 2 4 0.20²

    I_{total} = 1.12 + 0.32

    I_{total} = 1.44 kg m²

b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase

6 0
3 years ago
A 200 g load attached to a horizontal spring moves in simple harmonic motion with a period of 0.410 s. The total mechanical ener
defon

Complete question:

A 200 g load attached to a horizontal spring moves in simple harmonic motion with a period of 0.410 s. The total mechanical energy of the spring–load system is 2.00 J. Find

(a) the force constant of the spring and (b) the amplitude of the motion.

Answer:

(a) the force constant of the spring = 47 N/m

(b) the amplitude of the motion = 0.292 m

Explanation:

Given;

mass of the spring, m = 200g = 0.2 kg

period of oscillation, T = 0.410 s

total mechanical energy of the spring, E = 2 J

The angular speed is calculated as follows;

\omega = \frac{2\pi}{T} \\\\\omega = \frac{2\pi}{0.41} \\\\\omega = 15.33 \ rad/s

(a) the force constant of the spring

\omega = \sqrt{\frac{k}{m} } \\\\\omega^2 = \frac{k}{m} \\\\k = m \omega^2\\\\k = (0.2)(15.33)^2\\\\k = 47 \ N/m

(b) the amplitude of the motion

E = ¹/₂kA²

2E = kA²

A² = 2E/k

A = \sqrt{\frac{2E}{k} } \\\\A = \sqrt{\frac{2\times 2}{47} }\\\\A = 0.292 \ m

7 0
3 years ago
What is the magnitude of the applied electric field inside an aluminum wire of radius 1.2 mm that carries a 3.0-a current? [ σal
galben [10]
Hello

1) First of all, since we know the radius of the wire (r=1.2~mm=0.0012~m), we can calculate its cross-sectional area
A=\pi r^2 = 3.14 \cdot (0.0012~m)^2=4.5\cdot10^{-6}~m^2

2)  Then, we can calculate the current density J inside the wire. Since we know the current, I=3~A, and the area calculated at the previous step, we have
J= \frac{I}{A}= \frac{3~A}{4.5\cdot10^{-6}~m^2} = 6.63\cdot10^5 ~A/m^2

3) Finally, we can calculate the electric field E applied to the wire. Given the conductivity \sigma=3.6\cdot10^7~ \frac{A}{Vm} of the aluminium, the electric field is given by
E= \frac{J}{\sigma}= \frac{ 6.63\cdot10^5 ~A/m^2}{3.6\cdot10^7~ \frac{A}{Vm} } = 0.018~V/m

4 0
3 years ago
Estimated speed of the vehicle
SSSSS [86.1K]

Really, Gundy ? ! ?

The formula for the car's speed is given and discussed in the box.  The formula is

v = √(2·g·μ·d)

Then they <em>tell</em> you that μ is 0.750 , and then they <em>tell</em> you that d = 52.9 m .  Also, everybody knows that 'g' is gravity = 9.8 m/s² .

They also tell us that the mass of the car is 1,000 kg, and they tell us that it took 3.8 seconds to skid to a stop.  But we already <em>have</em> all the numbers in the formula <em>without</em> knowing the car's mass or how long it took to stop.  The police don't need to weigh the car, and nobody was there to measure how long the car took to stop.  All they need is the length of the skid mark, which they can measure, and they'll know how fast the guy was going when he hit the brakes !

Now, can you take the numbers and plug them into the formula ? ! ?

v = √(2·g·μ·d)

v = √( 2 · 9.8 m/s² · 0.75 · 52.9 m)

v = √( 777.63 m²/s²)

v = 27.886 m/s

Rounded to 3 digits, that's  <em>27.9 m/s </em>.

That's about 62.4 mile/hour .



3 0
3 years ago
A bowling lane is 18 meters long. How long would it take a 1.5 m/s bowling ball to
lara31 [8.8K]

Divide distance by speed:

18 meters / 1.5 meters/ second = 12 seconds

Answer: 12 seconds

5 0
2 years ago
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