Question

The $F-x$ graph is shown below. Find the change in potential energy from $x=0$ to $x=5\text{m}$

• A. $50\text{J}$
• B. $25\text{J}$
• C. $-35\text{J}$
• D. $10\text{J}$

Answer 1

The correct option is B $25\text{J}$

We know that, If the potential energy function $U\left(x\right)$ is known, then the force at any position can be obtained by taking the derivative of the potential energy

$\Rightarrow F=-\frac{dU}{dx}$

$\Rightarrow -{\int }_1^{2}dU={\int }_1^{2}Fdx$

$\Rightarrow U_1-U_2=$ Area under $F-x$ curve
$U_1-U_2=\frac{1}{2}\times 10\times 5=25\text{J}$

Hence option B is the correct answer