Question

The force exerted by a weird, stretch cord at given displacements is shown in the above table. Experimentally the force is found to vary proportionally to the square of the displacement, i.e. $F\left(x\right)=-h{x}^2$ where $h$ is some constant.
If the potential energy at $x=0m$ is $U_0=0J$ as shown above, determine the potential energy at $x=1.5m$.

• A. $1.13J$
• B. $2.25J$
• C. $4.50J$
• D. $6.75J$
• E. $7.50J$

Answer 1

The correct option is B $2.25J$

The force exerted by weird $F=-h{x}^2$

Given : $F=-2$ N at $x=1$ m

$\therefore$ $-2=-h\times 1^2$ $⟹h=2$

Thus the force is $F=-2x^2$ N

Potential energy $U=\int -Fdx=\int 2x^{2}dx=\frac{2}{3}{x}^3$ J

$⟹$ $U{|}_{x=1.5}=\frac{2}{3}\times (1.5{)}^3=2.25$ J