Question 235: Work, Energy and Power & Circular Motion

Question

A block of mass $10 \mathrm{~kg}$ is moving along $\mathrm{x}$-axis under the action of force $F=5 x~ N$. The work done by the force in moving the block from $x=2 m$ to $4 m$ will be __________ J.

Accepted Answer

To calculate the work done by the force $F = 5x$ in moving the block from $x = 2m$ to $x = 4m$, we can use the formula for work done by a variable force:
$W = \int_{x_1}^{x_2} F(x) dx$
In this case, $F(x) = 5x$, $x_1 = 2m$, and $x_2 = 4m$. Now, we can substitute these values into the formula and evaluate the integral:
$W = \int_{2}^{4} 5x dx$
To evaluate the integral, we find the antiderivative of $5x$:
$\int 5x dx = \frac{5}{2}x^2 + C$
Now, we can find the work done by evaluating the antiderivative at the limits of integration:
$W = \left[\frac{5}{2}x^2\right]_{2}^{4} = \frac{5}{2}(4^2) - \frac{5}{2}(2^2)$
$W = \frac{5}{2}(16) - \frac{5}{2}(4) = 40 - 10 = 30 \mathrm{J}$
The work done by the force in moving the block from $x = 2m$ to $x = 4m$ is 30 J.

Work, Energy and Power & Circular Motion

A block of mass 10 \mathrm{~kg} is moving along \mathrm{x}-axis under the action of force F=5 x~ N. The work done by the force in moving the block from x=2 m to 4 m will be __________ J.

Integer / Numeric Answer Type