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Please help me with this SAT question from a released test.

A toy truck with a mass of $0.6$ kg initially coasts horizontally at a speed of $2$ meters per second. A child drops a beanbag with a mass of $0.2$ kg straight down onto the truck. What is the speed of the truck after it?

Attempt:

My teacher told me to use conservation of momentum in the horizontal direction. However, when the beanbag is dropped, isn’t the ground pushing the truck up so that an external force is acting on the system? If not what does an external force mean in momentum conservation as momentum is conserved if and only if no external forces act.

Also, I tried to use the fact that energy is conserved so that $(0.5) (0.6 )2^2 = 0.5 (0.6+0.2) v^2 $ but this doesn’t work. As the correct answer is $1.5$. Why is the kinetic energy not conserved during this collision?

Thank you in advance

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    $\begingroup$ Welcome to Physics! Please take a minute to read our guidelines for homework and exercise questions as well as check-my-work questions. We intend our questions to be potentially useful to a broader set of users than just the one asking, and we prefer conceptual questions over those just asking for a specific computation. $\endgroup$
    – Emilio Pisanty
    Commented Aug 12, 2019 at 21:40
  • $\begingroup$ Momentum is a vector quantity. As such, it is conserved in both the vertical and horizontal directions. Since the truck is initially moving horizontally, that is the direction that the question is directed at. $\endgroup$
    – David White
    Commented Aug 12, 2019 at 21:41

2 Answers 2

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isn’t the ground pushing the truck up so that an external force is acting on the system?

Yes, but it is exclusively acting in the vertical direction. (And, indeed, vertical momentum is not conserved, since the vertical momentum of the bag is lost during the collision.) However, there are no external forces with any horizontal components acting on the system, so the horizontal component of momentum is conserved.

Why is the kinetic energy not conserved during this collision?

The collision is quite clearly inelastic, so there is no requirement for kinetic energy conservation.

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  • $\begingroup$ Thank you! This helped me understand the general case better. $\endgroup$
    – Physicslearners9
    Commented Aug 12, 2019 at 21:59
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The answer to your first question is that if the bag and the truck are the system under consideration and there are no horizontal external forces then the horizontal momentum of the system is conserved.

The answer to your second question about the kinetic energy not being conserved is to do with the frictional forces which must be acting between the bag and the truck and the impossibility of having an infinite acceleration.
Just before the bag hits the truck it has zero horizontal velocity whilst the truck does have a horizontal velocity.
When the bag hits the truck there must be a frictional force on the bag due to the truck to accelerate the bag and a frictional force on the truck due to the bag to produce a negative acceleration of the truck.
There also must be relative movement between the bag and the truck as the accelerations cannot be infinite.
So you have frictional forces acting and relative movement which will generate heat until the bag and the truck have the same velocity. So some of the initial kinetic energy of the truck is converted into heat.

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