A ladder of mass M and length L is leaned against a frictionless wall. It is rai

Question

A ladder of mass M and length L is leaned against a frictionless wall. It is raised an angle theta from the ground where there is friction. A plank of mass M/2 and length L/2 is hinged at the midpoint of the ladder and is always locked in the horizontal direction. At what angle theta will the plank have no effect of the normal force from the wall? With the angle in part (a), a person of mass 3M walks slowly on the plank from the hinge to the edge. How far from the hinge is the person who the normal force from the wall is zero? What maximum angle theta for the ladder will allow the person to walk all the way to the edge of the plank? The plank is kept horizontal for any angle. The trigonometry is a bit tricky. Look for right triangles.

Explanation / Answer

a)

The normal force from the wall is given by

N =mgcoshteta =Mgcostheta/4   to have no effect of normal force we can consider theta =90degrees

b)

The normal force from the wall is N =mgcostheta =3Mgcostheta

When the theta =90degrees then the persons stands on the hinge itself

c)

The maximum angle theta for the ladder will allow the person to walk all the way to the edge of the plank is theta =90degrees since the wall is frictionlesss, to avoid sliding.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.