Una palla di massa \( m_{1}=24 \mathrm{~g} \), che viaggia alla velocità \( v_{1} \), urta elasticamente una palla ferma di massa \( m_{2}=\frac{1}{2} m_{1} \). Dopo l'urto, la seconda palla va a colpire elasticamente una terza palla ferma, di massa \( m_{3} \). Tutti gli urti avven- gono lungo la stessa retta. Quale deve essere la massa \( m_{3} \) affinché la sua velocita dopo l'urto sia uguale a \( v_{1} \) ?

24. Let \( |\vec{A}|=150 N \) and the vector \( \vec{A} \) makes an angle of \( 60^{\circ} \) with the positive y axis. Let P be the scalar projection of \( \vec{A} \) on to the xz plane and it makes an angle of \( 30^{\circ} \) with the positive x axis. Express vector \( \vec{A} \) in terms of its rectangular \( (\mathrm{x}, \mathrm{y}, \mathrm{z}) \) components;

Example 10 Three coplanar forces of magnitudes \( F, 5,3 \) Newton act on a particle and the measure of the angle between the second the third force is \( 60^{\circ} \). Find the value of \( F \) if the forces are in equilibrium.

Describe the law of conservation of momentum as it pertains to a real-life scenario, and explain how it applies. Begin by identifying the real-life scenario. You may start your response with: - A real-life scenario pertaining to conservation of momentum is ... - In this scenario, the law of conservation of energy applies because . . .

must be the charge of a Figure \( 23-40 \) shows a section of a \( R=3.00 \mathrm{~cm} \), with a charge per unit length of \( \lambda=2.00 \times 10^{-8} \mathrm{C} / \mathrm{m} \). What is the magnitude \( E \) of the electric field at radial distance (a) \( r=R / 2.00 \) and (b) \( r=2.00 R \) ? (c) Graph \( E \) versus \( r \) forthe range \( r=0 \) to 2.00R.

27. Two trains, 1 and 2 , have an equal mass of \( m=5,000 \mathrm{~kg} \) each. Train 1 is traveling with a speed \( n=15 \mathrm{~m} / \mathrm{s} \) before striking train 2 , which was at rest. If the two trains lock together as the result of the collision. What is their common speed immediately after collision?