A 236 g cart moves on a horizontal, frictionless surface with a constant speed of 26.9 cm/s. A 66.1 g piece of modeling clay is dropped vertically onto the cart. If the clay sticks to the cart, find the final speed of the system. Answer in units of cm/s.

The final speed of the system is 21 cm/s.

Explanation:

Given:

Mass of the cart (M) = 236 g

Initial velocity of the cart (U) = 26.9 cm/s

Mass of the clay (m) = 66.1 g

Initial velocity of the clay (u) = 0 cm/s (At rest initially)

Let the final velocity of the system be 'v'.

Now, total initial momentum is given as:

Initial momentum = Initial momentum of cart + Initial momentum of clay

Final momentum of the system is given as:

Final momentum = Total mass × Final velocity

Now, from conservation of total momentum, final momentum is equal to initial momentum. So,

Therefore, the final speed of the system is 21 cm/s.

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