Why is the mass of the cart much greater than that of the weights?

[JuneLee]

The main reason why the mass of the cart is much greater than that of the weights is to reduce experimental errors. A detailed analysis is as follows: 1. In the experiment: The gravitational force of the weights is approximately considered as the pulling force on the cart. However, when exploring the relationship between acceleration, force, and mass, treating the pulling force on the cart as the gravitational force of the weights is incorrect because both the cart and the weights are in accelerated motion and not in a state of equilibrium. 2. In reality: Let the mass of the cart be M and the mass of the weights be m, with acceleration a. Since the weights provide the force, the experiment aims to verify F=Ma, i.e., a=F/M. However, in reality, F=mg=(M+m)*a, which means a=mg/(M+m). Because M>>m in the denominator, M+m can be approximately equal to M, allowing the gravitational force on the weights to be considered as the net external force on the cart. This approximation method is used here, so the mass of the cart must be much greater than that of the weights. The closer the tension in the rope on the cart is to the gravitational force of the weights, the more accurate the experiment will be.