Answer to Question #252491 in Classical Mechanics for Tati

Question

I have a question regarding Newton's 2nd Law.

There's a hanging mass, and a cart attached to it via a string.

1) If the hanging mass is much heavier than the mass of the cart, what would be the acceleration of the system? Explain why.

2) If the hanging mass and the cart were the exact same mass, what would be the acceleration of the system? Explain why.

No values are required! Just a general explanation. Thanks.

Answer 1

Hi there! To answer your questions, apply Newton's second law for both hanging mass (call it M) and the cart (call it m). Assume there's no friction of any kind:

$$M: T-Mg=-Ma,\\ m: T=ma.\\\space\\ ma-Mg=-Ma,\\\space\\ a=g\frac{M}{m+M}.$$

1) If the hanging mass is much heavier, or M>>m we have

$$a=\lim_{M→\infty}\bigg[g\frac{M}{m+M}\bigg]=g.$$

2) If the masses are equal:

$$a=g\frac{m}{m+m}=0.5g.$$