A 8.4 kg cart moving horizontally on a frictionless surface initially at 7.6 ms-1, has a 1.4 kg load dropped vertically in it, increasing the cart's total mass.The duration of the drop took 0.7 s.Based on the conservation of momentum, calculate the final velocity of the now combined cart and load.

Question

BlackTom AI · Accepted Answer

Begin by identifying the physical principle at play: horizontal momentum is conserved in the absence of external horizontal forces. Here, the cart moves on a frictionless surface, and the load drops vertically inside the cart, so there is no external impulse in the horizontal direction that would change the total horizontal momentum.

Step 1: Compute the initial horizontal momentum before the load is dropped. The cart has mass 8.4 kg and initial velocity 7.6 m/s, so p_initial = m_cart * v_initial = 8.4 kg * 7.6 m/s = 63.84 kg·m/s.

Step 2: Determine the final mass after the load is dropped. The load adds 1.4 kg, so the combined mass becomes m_final = 8.4 kg + 1.4 kg = 9.8 kg.

Step 3: Apply conservation of momentum to find the final velocity vf of the combined cart and load. Since momentum is conserved, p_initial = p_final, and p_final = m_final * vf. Therefore vf = p_initial / m_final = 63.84 kg·m/s / 9.8 kg ≈ 6.514 m/s.

Step 4: Consider rounding. The exact value is about 6.514 m/s, so reporting to two decimal places gives roughly 6.51 m/s. Some sources might round differently (e.g., 6.54) depending on the precision used in intermediate steps, but 6.51–6.52 m/s is the precise result for the given data.

Notes: The 0.7 s duration of the drop is not needed for momentum calculation in this horizontal-impulse-free scenario; it would matter if there were horizontal impulses or if we were analyzing forces during the drop, but not for the final velocity under momentum conservation.

MUF0121 Physics Unit 1 - Semester 2, 2025

A 8.4 kg cart moving horizontally on a frictionless surface initially at 7.6 ms-1, has a 1.4 kg load dropped vertically in it, increasing the cart's total mass.The duration of the drop took 0.7 s.Based on the conservation of momentum, calculate the final velocity of the now combined cart and load.

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