Question

students are completing a lab in which they let a lab cart roll down a ramp. the students record the mass of the cart, the height of the ramp, and the velocity at the bottom of the ramp. the students then calculate the momentum of the cart at the bottom of the ramp.
trial mass of cart (kg) height of ramp (m) velocity at bottom (m/s)
1 200 2.0 6.5
2 220 2.1 5.0
3 240 1.5 6.4
4 260 1.2 4.8
which trials cart has the greatest momentum at the bottom of the ramp?
trial 1, because this trial has the greatest velocity
trial 2, because this trial has the greatest ramp height
trial 3, because this trial has a large mass and a large velocity
trial 4, because this trial has the greatest mass

Explanation:

Step1: Recall momentum formula

Momentum $p = mv$, where $m$ is mass and $v$ is velocity.

Step2: Calculate momentum for trial 1

$p_1=m_1v_1 = 200\times6.5=1300$ kg·m/s

Step3: Calculate momentum for trial 2

$p_2=m_2v_2=220\times5.0 = 1100$ kg·m/s

Step4: Calculate momentum for trial 3

$p_3=m_3v_3=240\times6.4 = 1536$ kg·m/s

Step5: Calculate momentum for trial 4

$p_4=m_4v_4=260\times4.8=1248$ kg·m/s

Step6: Compare momenta

Comparing $p_1 = 1300$, $p_2=1100$, $p_3 = 1536$, $p_4=1248$, we see that $p_3$ is the largest.

Answer:

trial 3, because this trial has a large mass and a large velocity