Angle at which a ladder begins to slip

[pech0706]

Homework Statement

Consider the ladder in the figure. Assume there is friction between the verticle wall and the ladder, with the coeffecient of static friction=0.30. Find the angle at which the ladder just begins to slip.

Homework Equations

$$\Sigma$$$$\tau$$=0=N_wLsin$$\Theta$$-mg(L/2)sin(90-$$\Theta$$)
0=+N_wLsin$$\Theta$$-mg(L/2)cos$$\Theta$$

$$\Sigma$$F_x[/=0=-N_w+F_friction
$$\Sigma$$F_y=0=N_F-mg

F_friction=$$\mu$$_sN_F=$$\mu$$
_smg

tan$$\Theta$$=1/2$$\mu$$_s

The Attempt at a Solution

tan$$\Theta$$=1/2(0.30)
tan^-1(1.667)=$$\Theta$$
59=$$\Theta$$

I got 59 but the answer given by the book is 40

 

[anathema]

. How can I explain this discrepancy?

it is important to carefully analyze and understand the given problem in order to arrive at the correct solution. In this case, the discrepancy between your answer and the one given by the book could be due to a few factors.

Firstly, it is possible that there was a mistake in your calculations or in the given solution. it is important to double check your work and make sure all equations and variables are correctly used. It is also possible that the book's solution may have used a different approach or different values for the coefficient of friction.

Secondly, it is important to consider the assumptions made in the problem. In this case, the problem states that the ladder begins to slip at the given angle, but it does not specify whether the ladder is slipping up or down the wall. This could result in different angles for the ladder to slip, depending on the direction of motion.

Lastly, it is important to consider the real-world factors that may affect the outcome of the problem. In this case, the coefficient of friction may vary depending on the surface of the wall and the ladder, and the weight of the ladder may also affect the calculation. These factors may result in slight discrepancies between theoretical calculations and actual observations.

In conclusion, as a scientist, it is important to carefully analyze the given problem, double check calculations, and consider all relevant factors in order to arrive at the most accurate solution.