Question

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
the truck will have the same 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 less momentum as long as the velocity is the same. it would take more brake power to slow the truck to a stop.

Explanation:

Step1: Recall the momentum formula

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

Step2: Calculate initial momentum

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

Step3: Calculate final momentum

After adding the trailer, the new mass \( m_2 = 1000 + 1000 = 2000 \, \text{kg} \), and velocity remains \( v = 5 \, \text{m/s} \). So final momentum \( p_2 = m_2v = 2000 \times 5 = 10000 \, \text{kg·m/s} \).

Step4: Analyze the change in momentum and braking power

Since momentum is directly proportional to mass (when velocity is constant), increasing the mass increases the momentum. A larger momentum means more force (braking power) is needed to stop the object, as force is related to the change in momentum over time (\( F=\frac{\Delta p}{\Delta t} \)).

Answer:

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