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Standard XII

Physics

Problem Solving

A plank with ...

Question

A plank with mass $M = 6 k g$ rests on top of two identical, solid, cylindrical rollers that have radius $R = 4 c m$ and mass $m = 2 k g$ . The plank is pulled by a constant horizontal force $\to F$ of magnitude 6 $N$ applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on the flat surface. Also, there is no slipping between the cylinders and the plank.

The total friction acting on the plank in newton is (answer upto two decimal places)

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Solution

Let $a_{p}$ be the acceleration of the plank.
For plank,
$6 - 2 f_{t} = 6 a_{P}$ ...(1)
For rollers,
$f_{t} - f_{b} = 2 \times \frac{a_{p}}{2}$ ...(2)
Also, $τ = I α$
$⟹ (f_{t} + f_{b}) R = \frac{m R^{2}}{2} \frac{a_{p}}{2}$ ...(3)
Solving equations (1), (2) and (3),
$f_{t} = 1 N, f_{b} = - 1 N, a_{p} = \frac{2}{3} m / s^{2}$
$∴$ total friction on the plank $= 2 f_{t} = 2 N$

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Similar questions

A plank with mass $M = 6 k g$ rests on top of two identical, solid, cylindrical rollers that have radius $R = 4 c m$ and mass $m = 2 k g$ . The plank is pulled by a constant horizontal force $\to F$ of magnitude 6 $N$ applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on the flat surface. Also, there is no slipping between the cylinders and the plank.

The total friction acting on the plank in newton is (answer upto two decimal places)

Q. A plank with a mass

M = 6.00 k g

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R = 5.00 c m

and

m = 2.00 k g

(figure). The plank is pulled by a constant horizontal force

\to F

of magnitude

6.00

N

applied to the end of the plank and perpendicular to the axes of the cylinders(which are parallel). The cylinders roll without slipping on a flat surface. There is also no slipping between the cylinders and the plank. All surfaces are rough.

The initial acceleration of the plank at the moment when the rollers are equidistant from the ends of the plank is

m / s^{2}

Q. A plank with a mass

M = 6.00 k g

rests on top of two identical solid cylindrical rollers that have

R = 5.00 c m

and

m = 2.00 k g

(figure). The plank is pulled by a constant horizontal force

\to F

of magnitude

6.00

N

The initial acceleration of the plank at the moment when the rollers are equidistant from the ends of the plank is

m / s^{2}

A solid cylinder of mass 'm' and radius 'R' rests on a plank of mass '2m' lying on a smooth horizontal surface. String connecting the cylinder to the plank is passing over a massless pulley mounted on a movable light block B, and the friction between the cylinder and the plank is sufficient to prevent slipping. If the block B is pulled with a constant force 'F', find the acceleration of the cylinder and that of the plank.

Q. A

2 k g

uniform cylinder is placed on a plank of mass

4 k g

which in turn rests on a smooth horizontal plane. A constant horizontal force of

20 N

is applied on the plank. If no slipping occurs between cylinder & plank, find the ratio of the magnitude of acceleration of the plank and the cylinder.

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Let ap be the acceleration of the plank. For plank, 6−2ft=6aP ...(1) For rollers, ft−fb=2×ap2 ...(2) Also, τ=Iα ⟹(ft+fb)R=mR22ap2 ...(3) Solving equations (1), (2) and (3), ft=1 N,fb=−1 N,ap=23 m/s2 ∴ total friction on the plank=2ft=2 N