A 10 kg crate is placed on a rough horizontal surface \( \mu_{\mathrm{k}}=0.4 \) and connected with 12 kg hanging mass via a string that passes over a massless and frictionless pully as shown in the figure beside. Thé mass ( kg ) that must be added to the crate so that the crate moves with constant velocity is:

प्रश्न 20. एक कण सरल आवर्त गति से एक सरल रेखा पर गतिमान है। जब कण की केन्द्र से दूरी \( x_{1} \) तथा \( x_{2} \) है तथा इसक वेग कमशः \( \nu_{1} \) तथा \( v_{2} \) है। सिद्ध कीजिये कि आवर्त काल होगा

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

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?

2. Aball is thrown upward with a speed of \( 19.6 \mathrm{~m} / \mathrm{s} \). a. How high doesit go until its upward speed decreases to zero. b. How long does the ball take in this upward trip? \( c \). How long does the ball take to return to the initial position? \( d \). What will be its velocity then

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