PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

Q. 255. A spool with a thread wound on it is placed on an incl

Problems in General Physics

Class 11

IE Irodov

Chapter 1: PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

277 questions

Q. 254. Thin threads are tightly wound on the ends of a uniform solid cylinder of mass

m

. The free ends of the threads are attached to the ceiling of an elevator car. The car starts going up with an acceleration w₀. Find the acceleration w' of the cylinder relative to the car and the force F exerted by the cylinder on the ceiling (through the threads).

Q. 255. A spool with a thread wound on it is placed on an inclined smooth plane set at an angle

α = 3 0^{\circ}

to the horizontal. The free end of the thread is attached to the wall as shown in Fig. 1.61. The mass of the spool is

m = 200 g

, its moment of inertia relative to its own axis

I = 0.45 g \cdot m^{2}

, the radius of the wound thread layer

r = 3.0 cm

. Find the acceleration of the spool axis.

Q. 256. A uniform solid cylinder of mass

m

rests on two horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force

F

(Fig. 1.62). Find the maximum magnitude of the force

F

which still does not bring about any sliding of the cylinder, if the coefficient of friction between the cylinder and the planks is equal to

k

. What is the acceleration

w_{m a x}

of the axis of the cylinder rolling down the inclined plane?

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Question

Hard

Solving time: 5 mins

Q. 255. A spool with a thread wound on it is placed on an inclined smooth plane set at an angle $α = 3 0^{\circ}$ to the horizontal. The free end of the thread is attached to the wall as shown in Fig. 1.61. The mass of the spool is $m = 200 g$ , its moment of inertia relative to its own axis $I = 0.45 g \cdot m^{2}$ , the radius of the wound thread layer $r = 3.0 cm$ . Find the acceleration of the spool axis.

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Book:

Problems in General Physics (IE Irodov)

Text solutionVerified

Let us depict the forces and their points of application for the spool. Choosing the positive direction for

x

and

φ

as shown in the fig.,

we apply

F_{x} = m w_{c x}

and

N_{cz} = I_{c} β_{z}

and get

m g sin α - T = m w; T r = I β

"Notice that if a point of a solid in plane motion is connected with a thread, the projection of velocity vector of the solid's point of contact along the length of the thread equals the velocity of the other end of the thread (if it is not slacked)"
Thus in our problem,

v_{p} = v_{0}

but

v_{0} = 0

hence point

P

is the instantaneous centre of rotation of zero velocity for the spool. Therefore

v_{c} = ω r

and subsequently

w_{c} = β r

Solving the equations simultaneously, we get

w = \frac{g s i n α}{1 + \frac{I}{m r ^{2}}} = 1.6 m / s^{2}

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Q. 255. A spool with a thread wound on it is placed on an inclined smooth plane set at an angle

α = 3 0^{\circ}

to the horizontal. The free end of the thread is attached to the wall as shown in Fig. 1.61. The mass of the spool is

m = 200 g

, its moment of inertia relative to its own axis

I = 0.45 g \cdot m^{2}

, the radius of the wound thread layer

r = 3.0 cm

. Find the acceleration of the spool axis.

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Question Text	Q. 255. A spool with a thread wound on it is placed on an inclined smooth plane set at an angle $α = 3 0^{\circ}$ to the horizontal. The free end of the thread is attached to the wall as shown in Fig. 1.61. The mass of the spool is $m = 200 g$ , its moment of inertia relative to its own axis $I = 0.45 g \cdot m^{2}$ , the radius of the wound thread layer $r = 3.0 cm$ . Find the acceleration of the spool axis.
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	26

Text solutionVerified

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