Question

A cylinder of mass 0.6 kg and radius R is
falling under gravity without slipping as the
thread is unfolding. Find the tension in the
thread (in newton).​

Answer 1

: ) This might help

Answer 2

Answer:

The tension in the string T is 1.96 N

Step-by-step explanation:

Given: A cylinder of mass 0.6 kg and radius R is falling under gravity

To find: The tension in the thread

Solution:

A cylinder of mass 0.6 kg and radius R is falling under gravity

Therefore

The force of gravity acting on an object is its weight, which may be calculated by multiplying its mass by its gravitational acceleration.

w= mg

Considering translation, we get the equation as

mg - T = ma

Considering rotation, we get the equation as

T  × R = I ×d

T × R = $\frac{mR^{2} }{2}$ ×d

T = $\frac{mRd}{2}$

It is given that Radius R is falling under gravity without slipping.

Therefore for no slip condition the acceleration is

⇒ a = dR

⇒ d = $\frac{a}{R}$

Tension in the string is

⇒ T = $\frac{mRd}{2}$

⇒ T = $\frac{m R}{2} \frac{a}{R}$

⇒ T = $\frac{ma}{2}$

Tension in the rotation

⇒ mg - T= ma

⇒ mg - $\frac{ma}{2} = ma$

⇒ mg = $\frac{3ma}{2}$

⇒ g = $\frac{3a}{2}$

a = $\frac{2g}{3}$

Substitute acceleration in tension in the string

⇒ T = $\frac{ma}{2}$

⇒ T = $\frac{m}{2} \frac{2g}{3}$

T = $\frac{mg}{3}$

T = $\frac{0.6*9.8}{3}$

T = 1.96 N

T = 1.96 N

Final answer:

The tension in the thread is 1.96 N

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