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A yo-yo with a mass of 0.075 kg and a rolling radius of 2.50 cm (the distance from the axis of the pulley to where the string comes off the spool) rolls down a string with a linear acceleration of 6.50 m/s2. Approximate the rotational inertia of the yo-yo with that of disk with mass, m, and radius, r, rotating about its center (mr2/2). Calculate the tension in the string.

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boffeemadrid

Answer:

0.24825 N

0.0000238701923077 kgm²

Explanation:

m = Mass of yo yo = 0.075 kg

a = Acceleration = 6.5 m/s²

g = Acceleration due to gravity = 9.81 m/s²

The net force is given by

[tex]F_n=mg-T[/tex]

[tex]\Rightarrow T=mg-ma[/tex]

[tex]\Rightarrow T=m(g-a)[/tex]

[tex]\Rightarrow T=0.075(9.81-6.5)[/tex]

[tex]\Rightarrow T=0.24825\ N[/tex]

The tension in the string is 0.24825 N

Angular acceleration is given by

[tex]\alpha=\dfrac{a}{r}\\\Rightarrow \alpha=\dfrac{6.5}{2.5\times 10^{-2}}\\\Rightarrow \alpha=260\ rad/s^2[/tex]

Torque is given by

[tex]\tau=I\alpha\\\Rightarrow Tr=I\alpha\\\Rightarrow I=\dfrac{Tr}{\alpha}\\\Rightarrow I=\dfrac{0.24825\times 2.5\times 10^{-2}}{260}\\\Rightarrow I=0.0000238701923077\ kgm^2[/tex]

The moment of inertia is 0.0000238701923077 kgm²

Lanuel

The tension in the string is equal to 0.2475 Newton.

Given the following data:

  • Mass of yo-yo = 0.075 kg
  • Radius = 2.50 cm to m = [tex]\frac{2.5}{100} = 0.0025 \;m[/tex]
  • Linear acceleration = 6.50 [tex]m/s^2[/tex]

To determine the tension in the string:

First of all, we would determine the downward force applied by the yo-yo's weight:

[tex]F_y = mg[/tex]

Where:

  • [tex]F_y[/tex] is the yo-yo's weight.
  • m is the mass of the yo-yo.
  • g is acceleration due to gravity.

Substituting the given parameters into the formula, we have;

[tex]F_y = 0.075 \times 9.8\\\\F_y = 0.735 \; Newton[/tex]

Next, we would determine the force acting on the string:

[tex]F_s = 0.075 \times 6.5\\\\F_s = 0.4875\;Newton[/tex]

Now, we can find the tension in the spring:

[tex]Tension = F_y - F_s\\\\Tension = 0.735 - 0.4875[/tex]

Tension = 0.2475 Newton.

Read more: https://brainly.com/question/18792908

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