Question

12. A body of mass 10 kg is placed on rough
surface, pulled by a force F making an angle
of 30° above the horizontal. If the angle of
friction is also 30°, then the minimum
magnitude of force F required to move the
body is equal to (take, g = 10 ms?)​

Answer 1

The minimum  magnitude of force F required to move the  body is 100 N.

Explanation:

Given that,

Mass of body = 10 kg

Angle = 30°

Frictional angle = 30°

We need to calculate the frictional coefficient

$\mu=\tan\theta$

$\mu=\tan30$

$\mu=\dfrac{1}{\sqrt{3}}$

We need to calculate the minimum  magnitude of force F required to move the  body

Using balance equation

$F=mg\sin\theta+\mu mg\cos\theta$

Put the value into the formula

$F=10\times10\sin30+\dfrac{1}{\sqrt{3}}\times10\times10\cos30$

$F=10\times10\dfrac{1}{2}+\dfrac{1}{\sqrt{3}}\times10\times10\times\dfrac{\sqrt{3}}{2}$

$F=100\ N$

Hence, The minimum  magnitude of force F required to move the  body is 100 N.

Learn more :

Topic : frictional force

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