Friction on the surface of a cotton reel

Classical Mechanics Level 4

Two forces of 100 N 100N and 20 N 20N act on a cotton reel of inner radius 5 m 5 m and outer radius 10 m 10 m as shown in the figure above. The reel is performing pure rolling motion. The surface produces sufficient necessary friction for pure rolling of the reel. Find the magnitude of the friction provided by the surface for reel to perform pure rolling.

Details and Assumptions

  • The mass of the cotton reel is 10 kg 10 \text{ kg} .

  • The moment of inertia of the reel about central axis is 1000 kg m 2 1000 \text{ kg m}^2 .

The problem is original.


The answer is 75.

Surya Prakash by Surya Prakash , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rohit Ner
Nov 18, 2015

The sense of rotation of the reel would be clockwise. Let f f be the frictional force, a a be the linear acceleration and α \alpha be the angular acceleration of the reel.
Equation of translational equilibrium :
20 + f − 100 = 10 a 20+f-100=10a .
Since the body is in pure rolling motion,
a = 10 α f − 80 = 100 α a=10\alpha\\f-80=100\alpha Equation of rotational equilibrium :
200 − 10 f + 500 = 1000 α 200-10f+500=1000\alpha .
On solving the equations obtained, we get
f = 75 N \huge\color{#3D99F6}{\boxed{f=75N}}


4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...