The scenario you've described involves the principle of conservation of momentum. When the lump of plasticine is dropped onto the trolley, the system (trolley plus plasticine) experiences an external force that changes its momentum.
Here's a breakdown of the process:
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Initial Momentum: Before the plasticine sticks to the trolley, the trolley is moving with a certain momentum given by the product of its mass and velocity (p_initial = m_trolley * v_trolley).
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Dropping the Plasticine: When the plasticine is dropped vertically onto the trolley, it initially has no horizontal momentum relative to the ground, as it is falling straight down.
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Sticking Together: When the plasticine sticks to the trolley, the two bodies (trolley and plasticine) become a single combined system. The total mass of this system now includes both the mass of the trolley and the mass of the plasticine (m_total = m_trolley + m_plasticine).
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Conservation of Momentum: The law of conservation of momentum states that in the absence of external horizontal forces, the total momentum of a system remains constant. In this case, we assume that the trolley is moving on a horizontal bench with minimal friction, so the external force affecting the horizontal motion can be considered negligible for this explanation.
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Final Momentum: After the plasticine sticks to the trolley, if we denote the new velocity of the combined system as \( v_{final} \), the momentum after the collision can be expressed as: \[ p_final = m_total * v_{final} \] According to conservation of momentum, \[ m_trolley * v_trolley = (m_trolley + m_plasticine) * v_{final} \]
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Change in Velocity: Since the mass of the system has increased (because of the added mass of the plasticine), in order to conserve momentum, the velocity of the system must decrease. This is why the trolley slows down.
In summary, the trolley slows down because the process of the plasticine sticking to it increases the total mass of the system while conserving momentum. To maintain the same momentum, the velocity of the combined system must decrease.
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