Question

There is a ladder 4m high which is placed against a wall with its foot at an angle of 30 degrees to the horizontal. calculate the force exerted by the wall on the ladder?There is a ladder 4m high which is placed against a wall with its foot at an angle of 30 degrees to the horizontal. calculate the force exerted by the wall on the ladder?

Answer 1

Task:

There is a ladder $4\mathrm{m}$ high which is placed against a wall with its foot at an angle of 30 degrees to the horizontal. Calculate the force exerted by the wall on the ladder?

Solution:

$$\mathbf {N} _ {2} + \mathbf {F} _ {\tau p} + \mathbf {F} + \mathbf {N} _ {1} = 0.$$ $$\mathrm {N} _ {2 \mathrm {x}} + \mathrm {F} _ {\tau \mathrm {p x}} + \mathrm {F} _ {\mathrm {x}} + \mathrm {N} _ {1 \mathrm {x}} = 0,$$ $$\mathrm {N} _ {2 \mathrm {y}} + \mathrm {F} _ {\tau \mathrm {p y}} + \mathrm {F} _ {\mathrm {y}} + \mathrm {N} _ {1 \mathrm {y}} = 0.$$ $$\mathrm {N} _ {2 \mathrm {x}} = 0, \mathrm {F} _ {\tau \mathrm {p x}} = \mathrm {F} _ {\tau \mathrm {p}}, \mathrm {F} _ {\mathrm {x}} = 0, \mathrm {N} _ {1 \mathrm {x}} = - \mathrm {N} _ {1},$$ $$\mathrm {N} _ {2 \mathrm {y}} = \mathrm {N} _ {2}, \mathrm {F} _ {\tau \mathrm {p y}} = 0, \mathrm {F} _ {\mathrm {v}} = - \mathrm {F}, \mathrm {N} _ {1 \mathrm {v}} = 0.$$ $$\mathrm {F} _ {\tau \mathrm {p}} - \mathrm {N} _ {1} = 0, \mathrm {F} _ {\tau \mathrm {p}} = \mathrm {k N} _ {2}$$ $$\mathrm {N} _ {2} - \mathrm {F} = 0.$$ $$\mathrm {k N} _ {2} - \mathrm {N} _ {1} = 0, \mathrm {N} _ {2} = \frac {\mathrm {N} _ {1}}{\mathrm {k}}$$ $$\frac {\mathrm {N} _ {1}}{\mathrm {k}} - \mathrm {F} = 0, \mathrm {N} _ {1} = \mathrm {k F}$$

$N_{1}, N_{2} - \text{reactive forces},$

$F_{\tau \mathrm{p}} - \text{force of friction}, F - \text{weight of the ladder},$

$k$ - coefficient of friction between the ladder and the floor

Answer:

$$N _ {1} = k F$$