A \( 20-\mathrm{m} \) long steel wire (cross-section \( 1 \mathrm{~cm}^{2} \), Young's modulus \( 2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \) ), is subjecte to a load of \( 25,000 \mathrm{~N} \). How much will the wire stretch under the load? \( \begin{array}{lllll}\text { A) } 0.25 & \text { B) } 2.5 \mathrm{~cm} & \text { C) } 12.5 \mathrm{~cm} & \text { D) } 25 \mathrm{~cm} & \text { E) } 1.25\end{array} \)

Exercice 12 Placé dans un champ électrostatique uniforme horizontal, un pendule électrostatique porte une boule chargée positivement, de dimensions négligeables et de masse \( \mathrm{m}=5 \mathrm{~g} \). Le fil s'écarte d'un angle \( \alpha=20^{\circ} \) de la verticale. La charge de la boule vaut \( q=1 \mu C \). On donne \( \mathrm{g}=10 \mathrm{~N} / \mathrm{Kg} \). 1) Fais le bilan des forces qui s'exercent sur la boule. 2) Calcule l'intensité de la force électrique. 3) Détermine les caractéristiques du champ électrostatique 4) Fais un schéma et dessine de façon approximative

Deux charges ponctuelles \( \mathrm{q}_{1}=10 \mu \mathrm{C} \) et \( \mathrm{q}_{2}=30 \mu \mathrm{C} \) sont placées respectivement en A et B distantes de 40 cm . 1) Calcule le module du champ électrique \( \overrightarrow{\mathrm{E}} \) au point M milieu de AB . 2) Détermine le point P de \( [\mathrm{AB}] \) où le champ est nul. 3) Détermine le module du champ électrique \( \overrightarrow{\mathrm{E}} \) a) En un point N situé entre A et B à 10 cm de A . Représente ce champ sur un schéma clair. b) En un point Q situé sur lá médiatrice de AB à 20 cm du milieu M de AB .

Ejemplo 2 Encontremos la velocidad de una bala de 0.02 kg que adquiere una energia cinética de 400 J. \( \begin{array}{lll}\text { Datos: } \\ m=0.02 \mathrm{~kg} & E_{k}=\frac{1}{2} m v^{2} \\ E_{k}=4001 & \frac{2 E_{k}}{m}=v^{2} & \begin{array}{l}\text { Despejamos la velocidad dejándola e } \\ \text { uno de los lados de la ecuación. }\end{array}\end{array} \)

11. A particle is projected into the air at a speed of \( 25 \mathrm{~m} / \mathrm{s} \) at an angle \( 40^{\circ} \) above the horizontal. (a) How long does it take the particle to reach its maximum height? (b) What is its horizontal distance covered? 12. A stone is projected with a speed of \( 17.32 \mathrm{~m} / \mathrm{s} \) at an angle of \( 60^{\circ} \) to the horizontal. Calculate the maximum height and the range covered by the stone. 13. A ball is projected horizontally from the edge of a platform at \( 12.0 \mathrm{~m} / \mathrm{s} \). If the platform is 8.0 m above the floor, what are the magnitude and direction of the ball's velocity as it hits the floor? 14. A particle is launched such that its maximum range is 26.4 m . What is the speed at which it is launched? 15. A rifle fires a bullet at \( 360 \mathrm{~m} / \mathrm{s} \). (a) At what angle must the rifle be positioned for the bullet to hit a target 242.4 m away at the same height as the rifle?(b) If gravitational force does not act on the bullet, how far above the target will the bullet pass maintaining the same angle? 16. A particle projected at an angle of \( \theta \) above the horizontal has a velocity of \( v=(16 i+5 j) \mathrm{m} / \mathrm{s} \) at time \( t=0.8 \mathrm{~s} \) after launching. (a) What is the maximum height of the particle? (b) What is the range of the particle? 17. A ball is kicked into the air. When it reaches the vertical height of 7.5 m , the velocity is measured to have a horizontal component of \( 10.4 \mathrm{~m} / \mathrm{s} \) and a vertical component of \( 3.7 \mathrm{~m} / \mathrm{s} \). Calculate the maximum height and horizontal distance, which the ball travels.

II. Workout the following problems 8. A vertical, solid steel post 25 cm in diameter and 2.50 m long is required to support a load of 8000 kg . You can ignore the weight of the post. What are (a) the stress in the post; (b) the strain in the post; a (c) the change in the post's length when the load is applied?