Question

a truck that weighs 1,000 kg is traveling 5 m/s. how would momentum be affected if the truck added a trailer with an additional mass of 1,000 kg but still traveled at the same velocity? answer options: select one of four it would take more brake power to slow the truck to a stop. the truck will have less momentum as long as the velocity is the same. it would take less brake power to slow the truck to a stop. the truck will have the same momentum as long as the velocity is the same.

Explanation:

Step1: Recall momentum formula

Momentum \( p = mv \), where \( m \) is mass and \( v \) is velocity.

Step2: Calculate initial momentum

Initial mass \( m_1 = 1000 \, \text{kg} \), velocity \( v = 5 \, \text{m/s} \). So \( p_1 = m_1v = 1000 \times 5 = 5000 \, \text{kg·m/s} \).

Step3: Calculate final momentum

Final mass \( m_2 = 1000 + 1000 = 2000 \, \text{kg} \), velocity \( v = 5 \, \text{m/s} \). So \( p_2 = m_2v = 2000 \times 5 = 10000 \, \text{kg·m/s} \).

Step4: Analyze momentum change and braking

Momentum increases. More momentum means more force (or brake power) is needed to stop it (by impulse - momentum theorem, \( F\Delta t=\Delta p \); to stop, \( \Delta p = p \), so larger \( p \) needs larger \( F \) if \( \Delta t \) is similar).

Answer:

It would take more brake power to slow the truck to a stop.