Question

A body of mass m resting on a wedge of angle а.Given acceleration f.What is the value of f to set free the mass from inclind plane?

Answer 1

A body of mass m resting on a wedge of angle a. Given acceleration f. What is the value of f to set free the mass from inclined plane?

Solution:

Condition of the problem does not say the direction of acceleration $\vec{f}$ , so let it be directed perpendicular to the inclined plane.

At the time of separation from the inclined plane reaction force $\overrightarrow{N_r}$ is equal to zero (the object does not touch the wedge):

Newton's second law: $\vec{F} +\overrightarrow{mg} +\overrightarrow{N_r} +\overrightarrow{F_{friction}} = \vec{0}$

$$y: (m g) _ {y} - F = 0$$ $$(m g) _ {y} = m g \cdot \cos a \rightarrow$$ $$y: m g \cdot \cos a - F = 0 (1)$$ $$F = m f (2) \text{ (Newton's second law)}$$ $$m g \cdot \cos a - m f = 0$$ $$f = g \cdot \cos a = 9.8 \frac{m}{s^{2}} \cos a$$

Answer: $f = 9.8 \frac{m}{s^2} \cos a$