Answer:
The tension in the string will increase by a factor of two, while the acceleration will not change.
Explanation:
To approach this problem, we begin by sketching the situation and creating free body diagrams for both masses involved. (Refer to the attached image)
Let’s first examine the free body diagram for the cart. Assuming there’s no friction between the cart and the horizontal surface, and focusing solely on horizontal forces, we can write the force balance as follows:
Given that tension is the only horizontal force on the cart, we state:
Next, consider the hanging mass, taking downward as the positive direction. Summing forces yields:
The two forces acting here are gravity and tension, so:
Combining the two equations results in:
Solving for acceleration gives:
This represents the acceleration for the original setup. What happens if both masses are doubled? Let’s analyze:
Factoring 2 out of the denominator produces:
Which simplifies to:
You can observe this matches the original acceleration, confirming it remains unchanged.
Regarding tension, by substituting the doubled masses into the initial force expression:
The initial tension was:
Therefore, doubling the masses causes the tension to double as well.
