Question

An effort of 200 N is required to just move a certain body up an inclined plane having angle of inclination
15°. If the angle of inclination of the plane changes to 20°, the effort required to just move the body
increases to 230 N. Force is applied parallel to the inclined plane in both the cases. Find the weight of the
body and the coefficient of friction.
​

Answer 1

Answer:

Weight of body is 394.3 N and its friction coefficient is 0.257

Explanation:

Let the weight of the body is W and it is pulled upward along the inclined plane

Now the two components of the weight of the body is

1) Along the inclined plane

2) Perpendicular to the inclined plane

Along the inclined plane the component of the weight is given as

$W_x = W sin15$

perpendicular to the inclined plane the component of the weight is given as

$W_y = W cos15$

now we have

$F_n = W cos15$

Friction force on the body along the inclined plane is given as

$F_f = \mu F_n$

$F_f = \mu(Wcos15)$

So we will have

$F = W sin15 + \mu W cos15$

$200 = W(sin15 + \mu cos15)$

again for next force 230 N we have

$230 = W(sin20 + \mu cos20)$

now from above two equations

$\frac{230}{200} = \frac{(sin20 + \mu cos20)}{(sin15 + \mu cos15)}$

$1.15 sin15 + 1.15 \mu cos15 = sin20 + \mu cos20$

$\mu(1.15 cos15 - cos20) = sin20 - 1.15 sin15$

$\mu = \frac{sin20 - 1.15 sin15}{1.15 cos15 - cos20}$

$\mu = \frac{0.044}{0.171}$

$\mu = 0.257$

now we have

$W = \frac{200}{sin15 + \mu cos15}$

$W = 394.3 N$

#Learn

Topic : Newton's laws of motion and friction

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