Question

problem 3: a 1 kg ball hangs from a string attached to the ceiling. a physics student attaches another string hanging below the ball, see diagram. if the student pull down from the bottom string (slowly) with a force of 1.2 n, find the tension on the top string. if the student pulled strongly enough, would the top string or bottom string break first?

Explanation:

Step1: Calculate gravitational force

The gravitational force on the ball $F_g = mg$, where $m = 1\ kg$ and $g= 9.8\ m/s^{2}$. So $F_g=1\times9.8 = 9.8\ N$.

Step2: Analyze tension in top - string when pulled slowly

When the student pulls down slowly with a force $F = 1.2\ N$, the tension in the top - string $T_{top}$ is the sum of the gravitational force on the ball and the pulling force. So $T_{top}=F_g + F=9.8+1.2 = 11\ N$.

Step3: Analyze which string breaks first

When pulled strongly, the bottom string has only the pulling force acting on it immediately. The top string has the pulling force and the weight of the ball acting on it. Since the top - string always has a greater force acting on it (weight of the ball plus pulling force) compared to the bottom string (just the pulling force), the top string will break first.

Answer:

The tension on the top string when pulled slowly is $11\ N$. The top string will break first when pulled strongly.