A lab cart with a mass of 15 kg is moving with constant velocity, v, along a straight horizontal track. A student drops a 2 kg mass into it from directly above, and the cart continues moving. Which equation best represents the horizontal momentum in this situation?
Answer
A
15 v sub i plus 2 times 0 is equal to 15 v sub f plus 2 times 0
B
15 v sub i plus 2 v sub f is equal to 15 times 0 plus 2 v sub i
C
15 v sub i plus 2 times 0 is equal to open paren 15 plus 2 close paren times v sub f
D
15 times 0 plus 2 v sub i is equal to open paren 15 plus 2 close paren times v sub f
Explanation
The 15 kg cart initially has horizontal momentum 15vᵢ. The 2 kg mass is dropped from directly above, so its initial horizontal velocity—and horizontal momentum—is zero. After it lands, the cart and mass move together at v_f, giving final horizontal momentum (15 + 2)v_f. Thus, 15vᵢ + 2(0) = (15 + 2)v_f, which is choice C.
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