Question

if twice the force is exerted over twice the distance, how does the resulting increase in kinetic energy compare with the original increase in kinetic energy? express your answer as an integer. $\frac{delta k_{2}}{delta k_{1}}=$

Explanation:

Step1: Recall work - energy theorem

The work - energy theorem states that the change in kinetic energy $\Delta K$ is equal to the work done $W$, and $W = Fd$ (where $F$ is the force and $d$ is the distance). Let the original force be $F_1$ and the original distance be $d_1$, so the original change in kinetic energy $\Delta K_1=F_1d_1$.

Step2: Calculate the new change in kinetic energy

The new force $F_2 = 2F_1$ and the new distance $d_2=2d_1$. Then the new change in kinetic energy $\Delta K_2=F_2d_2=(2F_1)\times(2d_1) = 4F_1d_1$.

Step3: Find the ratio

We want to find $\frac{\Delta K_2}{\Delta K_1}$. Substitute $\Delta K_1 = F_1d_1$ and $\Delta K_2=4F_1d_1$ into the ratio: $\frac{\Delta K_2}{\Delta K_1}=\frac{4F_1d_1}{F_1d_1}=4$.

Answer:

4