Question

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? 15vi 2vi = 15vf 2vf 15vi 2(0) = 15vf 2vf 15vi 2(0) = (15 2)vf 15vi 2vi = (15 2)vf.

Answer 1

The equation $15v_{i} + 2*0 = (15 + 2)v_{f}$ (option 3) represents the horizontal momentum of a 15 kg lab cart moving with a constant velocity, v, and that continues moving after a 2 kg object is dropped into it.  

The horizontal momentum is given by:

$p_{i} = p_{f}$

$m_{1}v_{1}_{i} + m_{2}v_{2}_{i} = m_{1}v_{1}_{f} + m_{2}v_{2}_{f}$

Where:

• m₁: is the mass of the lab cart = 15 kg

• m₂: is the mass of the object dropped = 2 kg

• $v_{1}_{i}$: is the initial velocity of the lab cart

• $v_{2}_{i}$: is the initial velocity of the object = 0 (it is dropped)

• $v_{1}_{f}$: is the final velocity of the lab cart

• $v_{2}_{f}$: is the final velocity of the object

Then, the horizontal momentum is:

$15v_{1}_{i} + 2*0 = 15v_{1}_{f} + 2v_{2}_{f}$

When the object is dropped into the lab cart, the final velocity of the lab cart and the object will be the same, so:

$15v_{1}_{i} + 2*0 = v_{f}(15 + 2)$

Therefore, the equation $15v_{i} + 2*0 = (15 + 2)v_{f}$ represents the horizontal momentum (option 3).

Learn more about linear momentum here:

• brainly.com/question/2141713?referrer=searchResults

• brainly.com/question/2400186?referrer=searchResults

I hope it helps you!