Question

in a closed system, an object with a mass of 1.5 kg collides with a second object. the two objects then move together at a velocity of 50 m/s. the total momentum of the system is 250 kg·m/s. what is the mass of the second object? (1 point)

○ 1.5 kg

○ 3.5 kg

○ 5.0 kg

○ 3.0 kg

Explanation:

Step1: Recall momentum formula

The formula for momentum is \( p = mv \), where \( p \) is momentum, \( m \) is mass, and \( v \) is velocity. For the combined system, \( p_{total}=m_{total}v \).

Step2: Find total mass

We know \( p_{total} = 250\space kg\cdot m/s \) and \( v = 50\space m/s \). Rearranging \( m_{total}=\frac{p_{total}}{v} \), so \( m_{total}=\frac{250}{50}=5\space kg \).

Step3: Calculate second mass

Let \( m_1 = 1.5\space kg \) (mass of first object) and \( m_2 \) be the mass of the second object. We know \( m_{total}=m_1 + m_2 \), so \( m_2=m_{total}-m_1 \). Substituting values, \( m_2 = 5 - 1.5 = 3.5\space kg \).

Answer:

3.5 kg (corresponding to the option "3.5 kg")