Multiple Choice Question If the kinetic energy of a particle \( T_{2} \) at point 2 is 13 J and the work done \( U_{1 \rightarrow 2} \) on the particle in moving it from point 1 to point 2 is 7 J , calculate the kinetic energy of the particle \( T_{1} \) at point 1 . Use the work-energy principle for a system of particles. O 0.538 J 091 J 0.875 J

To find the kinetic energy at point 1, we can use the work-energy principle, which states that the work done on a particle is equal to the change in its kinetic energy. The equation is given by: \[ T_{2} - T_{1} = U_{1 \rightarrow 2} \] Plugging in the values we know: \[ T_{2} = 13 \, \text{J}, \quad U_{1 \rightarrow 2} = 7 \, \text{J} \] We rearrange the equation to solve for \( T_{1} \): \[ T_{1} = T_{2} - U_{1 \rightarrow 2} = 13 \, \text{J} - 7 \, \text{J} = 6 \, \text{J} \] So, \( T_{1} = 6 \, \text{J} \). Since none of the given answers (0.538 J, 0.91 J, 0.875 J) match, it appears there might be a misunderstanding in the problem or answer choices! Here's a fun fact: the work-energy principle is like a magic trick! Your energy appears to vanish as you're moving from one point to another, but don’t be fooled—it’s simply transformed or transferred, coming from forces at play during your travel. To avoid common mistakes when applying the work-energy principle: always ensure that the signs of work done and changes in kinetic energy accurately reflect the directions of forces and movement. A positive work generally means energy is added to the system, while negative work means energy is taken away!