Chapter 5.3, Problem 35PP

To determine

The normal force between F and the banister.

Answer to Problem 35PP

  $336.54\text{N}$

Explanation of Solution

Given:

The mass of F is $43.\text{0 kg}$ , and it slides down the banister making an angle of the $35.0°$ with the horizontal.

Formula used:

The rectangular components of a vector A making an angle of $\theta$ with the horizontal axis or x -axis, is given by,

  $A_x=A\cos \theta$

  $A_y=A\sin \theta$

Calculation:

When any object slides down an incline making an angle $\theta$ with the horizontal, the component of its weight acting in perpendicularly downwards direction to the surface of the incline is given by,

  $W_{per}=W\cos \theta$

Now, since there is no motion of F in the perpendicular direction of the surface of the banister, the normal force between F and banister will be balanced by the perpendicular component of the weight of the F, that is

  $\begin{array}{c}N=W_{per}\\ =m_{\text{Fernando}}g\cos \theta \end{array}$

Using given and known values in above, we get

  $\begin{array}{c}N=\left(43\right)\left(9.8\right)\cos 37°\\ =336.54\text{N}\end{array}$

Conclusion:

Thus, the normal force between F and banister is 336.54N.