Question

a ball has a mass of 0.25 kg and is moving to the right at 1.0 m/s. it hits a ball of mass 0.15 kg that is initially at rest. after the collision, the 0.15 kg ball moves off to the right with a velocity of 0.75 m/s. what is the final velocity of the 0.25 kg ball? 0.42 m/s to the right 0.42 m/s to the left 0.55 m/s to the right 0.55 m/s to the left

Explanation:

Step1: Aplicar la ley de conservación de la cantidad de movimiento

La cantidad de movimiento inicial \(p_i = m_1v_{1i}+m_2v_{2i}\), donde \(m_1 = 0.25\ \text{kg}\), \(v_{1i}=1.0\ \text{m/s}\), \(m_2 = 0.15\ \text{kg}\), \(v_{2i} = 0\ \text{m/s}\). Entonces \(p_i=0.25\times1.0+0.15\times0=0.25\ \text{kg}\cdot\text{m/s}\)

La cantidad de movimiento final \(p_f=m_1v_{1f}+m_2v_{2f}\), donde \(v_{2f} = 0.75\ \text{m/s}\)

Por la ley de conservación de la cantidad de movimiento \(p_i = p_f\), es decir \(0.25=m_1v_{1f}+m_2v_{2f}\)

Step2: Despejar \(v_{1f}\)

Sustituir los valores: \(0.25 = 0.25v_{1f}+0.15\times0.75\)

\(0.25v_{1f}=0.25 - 0.1125\)

\(0.25v_{1f}=0.1375\)

\(v_{1f}=\frac{0.1375}{0.25}=0.55\ \text{m/s}\)

Como el signo es positivo, la dirección es a la derecha

Answer:

0.55 m/s to the right