Answer to Question #253363 in Classical Mechanics for ANN

Question

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. Please try to explain in words (Ex. the acceleration would be zero because...) instead of just formulas, it helps me understand better! You may use formulas to represent what you are saying but I'd like a more wordy explanation. Thanks so much.

Answer 1

After the application of Newton's second law, we saw that the acceleration of the masses is

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

If the hanging mass is much heavier than the mass of the cart, the acceleration of the system would be equal to the acceleration due to gravity, or 9.8 m/s², because the lighter mass (since it is too light) does not have any inertia to slow down the heavier mass.

If the masses are equal, their acceleration will be equal to half of the acceleration due to gravity because both masses have equal inertia and the acceleration due to gravity (9.8 m/s²) is shared between two masses, one with 'zero' ability to accelerate vertically and one with 'full' such ability. Why? Because the acceleration due to gravity only accelerates bodies in the vertical direction. So, we have 2 bodies and acceleration due to gravity equally shared between their capacities to move vertically.