Physics

Problem

Two carts of masses

1.5\,\text{kg}

and

2.5\,\text{kg}

are connected by a light string. A constant horizontal force of

9.0\,\text{N}

pulls the rear cart to the right on a frictionless track. What is the magnitude of the acceleration of the two-cart system? a)

3.0\,\text{m}\!/\!\text{s}^2

2.25\,\text{m}\!/\!\text{s}^2

4.5\,\text{m}\!/\!\text{s}^2

1.8\,\text{m}\!/\!\text{s}^2

Intuitive explanation

The key insight is that when two objects are connected and move together, you can treat them as a single system with combined mass. Since the track is frictionless, the only horizontal force acting on the entire system is the $9.0\,\text{N}$ pull—the string between the carts is internal to the system and doesn't affect the overall acceleration. Use Newton's second law with the total mass to find how fast the system speeds up.

Intuitive explanation

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