Question

a block is plased on an inclined plane of angle of inclination 37 degree to the horizontal. if the coefficient of friction between the block and the plane is 0.25.calculate the acceleration of block?

Answer 1

Question 32554

For motion over inclined plane, projection on axis, which is perpendicular to the surface of the plane gives: $N = mg\cos \varphi$ , $\varphi$ is the angle of inclination.

Projection over axis, parallel to the plane, together with $2^{\mathrm{nd}}$ Newton's law ( $\vec{F} = m\vec{a}$ ) gives:

$m a = m g \sin \varphi - F_{f}$ . $F_{f}$ is the friction force, which is calculated as $F_{f} = \mu N = \mu m g \cos \varphi$ ( $\mu$ is the friction coefficient, $\mu = 0.25$ ).

Hence, $a = g\sin \varphi -\frac{F_f}{m} = g\sin \varphi -\mu g\cos \varphi = 3.95\frac{m}{s^2}$