You visited us 1 times! Enjoying our articles? Unlock Full Access!

Tension in a String

If μ s and μ ...

Question

If $μ_{s} and μ_{k}$ represent the coefficients of static and kinetic friction with appropriate suffixes for the two bodies shown, find the acceleration of the system. Take $g = 10 m / s^{2}$ .

Zero

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4.2 m / s^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5.2 m / s^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

10 m / s^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $5.2 m / s^{2}$
The given system can be shown in the FBDs as

So, we have from the above condition
$f_{1 m a x} = μ_{s 1} (5 g) = 0.6 \times 50 = 30 N$
$f_{2 m a x} = μ_{s 2} (2 g) = 0.5 \times 20 = 10 N$
and, applied force $= 13 g = 130 N$

$∵$ the applied force > Total friction force of the system, the system will acclerate
$∴$ we have
$f_{k 1} = μ_{k 1} (5 g) = (0.4) (5 g) = 20 N$
$f_{k 2} = μ_{k 2} (2 g) = (0.3) (2 g) = 6 N$

So, from force equations: Taking the $5 k g$ and $2 k g$ masses as a system, we get
$13 g - T_{2} = 13 a$
$\frac{T_{2} - f_{k_{1}} - f_{k 2} = (5 + 2) a}{13 g - 20 - 6 = 20 a}$
$\Rightarrow a = \frac{130 - 26}{20} = 5.2 m / s^{2}$

Suggest Corrections

Similar questions

μ_{s}

μ_{k}

[

g = 10 {m/s}^{2}]

μ_{s} and μ_{k}

g = 10 m / s^{2}

2 kg

μ_{s} = 0.5

μ_{k} = 0.4

[

g = 10 {m/s}^{2}]

5 kg

30^{\circ}

{m/s}^{2}

μ_{k} = \frac{1}{2 \sqrt{3}}

g = 10 {m/s}^{2}

A

B

g = 10 m / s^{2}

Join BYJU'S Learning Program