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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.

Respuesta :

Answer:

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

[tex]P_i=MU+mu\\\\P_i=236\times 26.9+0=6348.4\ g\cdot cm/s[/tex]

Final momentum of the system is given as:

Final momentum = Total mass × Final velocity

[tex]P_f=(M+m)v\\\\P_f=(236+66.1)v\\\\P_f=302.1v[/tex]

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

[tex]P_f=P_i\\\\302.1v=6348.4\\\\v=\frac{6348.4}{302.1}=21\ cm/s[/tex]

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

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