Two blocks with masses mA and mB are connected to each other by a string over a massless, frictionless pulley as shown below; both masses remain in contact with the surface which is frictionless. What is the magnitude of the acceleration of the two blocks?

Question

BlackTom AI · Accepted Answer

The provided data for this question is incomplete. The input shows a two-mass system with a string over a massless, frictionless pulley and both masses on a frictionless surface, but there are no answer options and no values given for mA and mB. Without the options (or at least the mass values), we cannot determine the intended correct choice.

What we would normally do if the masses and options were given:
- Identify the setup: two blocks on a frictionless horizontal surface connected by a string over a frictionless pulley. There is no external horizontal force mentioned besides the internal tension in the string, since gravity acts perpendicular to motion and friction is absent.
- Write Newton’s second law for the system along the direction of possible motion. Since there is no external horizontal force and the only forces are internal tensions, the net external force on the system is zero, implying the acceleration of the center of mass is zero. In a typical configuration like this, the blocks do not accelerate relative to the surface unless an external force or a difference in applied constraints exists.
- Consider special cases if masses or additional forces were specified: if one mass were connected to an external hanging weight (not described here), or if there were friction, or if one mass were on an inclined plane, the equations would change and could produce a nonzero acceleration.

Because the actual question text lacks both numerical values (mA, mB) and the list of answer choices, any assertion about the magnitude of acceleration would be speculative. To proceed, we would need either:
- The numerical values of mA and mB, and/or
- The explicit answer options to determine which matches the derived expression, if any nonzero acceleration is intended, or
- Additional description clarifying whether there is an external force acting on one of the masses or some constraint that would cause motion.

In short, with the information shown (two blocks on a frictionless surface, connected over a massless, frictionless pulley, and no other forces stated), the standard expectation is zero acceleration because there is no net external force along the direction of potential motion. However, since the question includes no options or masses, we cannot definitively map this to a specific choice from a provided list.

Section Merge: PHYS 211: Mechanics (UP; Spring 2025) phys211_MT2

Two blocks with masses mA and mB are connected to each other by a string over a massless, frictionless pulley as shown below; both masses remain in contact with the surface which is frictionless. What is the magnitude of the acceleration of the two blocks?

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